022132-4-T MICROWAVE DIELECTRIC BEHAVIOR OF VEGETATION MATERIAL Mohamed A. El-Rayes Fawwaz T. Ulaby Radiation Laboratory Department of Electrical Engineering and Computer Science The University of Michigan Ann Arbor, MI 48109-2122 January, 1987 Supported by: NASA/Goddard Space Flight Center Earth Survey Applications Division Earth Resources Branch Greenbelt, MD 20771 Contract NAG 5-480

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ABSTRACT The microwave dielectric behavior of vegetation was examined through the development of theoretical models involving dielectric dispersion by both "bound" and "free" water and supported by extensive dielectric measurements conducted over a wide range of conditions. The experimental data were acquired using an open-ended coaxial probe that was developed for sensing the dielectric constant of thin layers of materials, such as leaves, from measurements of the complex reflection coefficient using a network analyzer. The probe system was successfully used to record the spectral variation of the dielectric constant over a wide frequency range extending from 0.5 GHz to 20.4 GHz at numerous temperatures between -400C and +400C. The vegetation samples - which included corn leaves and stalks, tree trunks, branches and needles, and other plant material - were measured over a wide range of moisture conditions (where possible). To model the dielectric spectrum of the bound water component of the water included in vegetation, dielectric measurements were made for several sucrose-water solutions as analogs for the situation in vegetation. The results were used in conjunction with the experimental data for leaves to determine some of the constant coefficients in the theoretical models. Two models, both of which provide good fit to the data, are proposed. The first model treats the water in vegetation as two independent components, a bound water component with a relaxation frequency of 0.178 GHz and a free water component with a relaxation frequency of 18 GHz at 220C. The second model treats all the water as a single mixture with a relaxation frequency that increases with moisture content from about 0 for dry vegetation to 18 GHz for vegetation with very high moisture contents.

ACKNOWLEDGEMENTS This report documents the results of research conducted from 1982-1986. The first phase covered the period 1982-1984 and was conducted at the University of Kansas, and the latter phase was conducted at the University of Michigan.

Table of Contents ABSTRACT............................................................. i ACKNOWLEDGEMENTS.................................................ii TABLE OF CONTENTS.................................................. iii LIST OF FIGURES.................................... vii LIST OF TABLES....................................................... xxii 1. INTRODUCTION.................................................... 2. BACKGROUND...................................6................... 6 2.1 Dielectric Properties Of Liquid Water..............................7 2.1.1 What Is A Relaxation Process................................... 7.......... Polar Molecules.................................................8.........Debye's Equation...........................9........9..... 2.1.2 Pure Water.........................15.....2.1.3 Saline Water........................ 16.....2.1.4 Bound Water........................................ 19..... 2.1.5 Temperature Dependence.................................... 23 2.2 Dielectric Mixing Models.........................................25..... 2.2.1 DeLoor's Mixing Model......................................26..... 2.2.2 Semi-Empirical Models...................................... 28.....2.2.3 Empirical Models............................................30 2.3 Water In Plant Materials.........................................31..... 2.3.1 Ecological And Physiological Importance Of Water...........31..... 2.3.2 Uses Of Water In Plants.....................................31 2.4 Previous Studies.................................................32.....2.4.1 Carlson(1967).............................................33..... 2.4.2 Broadhurst(1970)............................................33.....2.4.3 Tan(1981)..............................................34..... 2.4.4 Ulaby And Jedlicka(1984)....................... 35 ~. 1 1

..... 2.4.5 Summary....................................... 35 3. DIELECTRIC MEASUREMENT SYSTEMS - GENERAL..........38 3.1 Transmission Techniques.........................................38..... 3.1.1 Waveguide System........................................... 39..... 3.1.2 Free-Space System................................42 3.2 Reflection Technique............................................. 42..... 3.2.1 Slotted Line System................................... 42..... 3.2.2 Probe System...............................................48 3.3 Resonance Techniques............................................ 52..... 3.3.1 The Filled-Cavity Approach.................................52..... 3.3.2 The Partially-Filled Cavity Approach......................... 54 3.4 Comparison......................................................56..... 3.4.1 Usable Frequency Band...................................... 56..... 3.4.2 Measurement Accuracy And Precision.......................58.....3.4.3 Dielectric Values Limit...................................... 60.....3.4.4 Practical Aspects................................. 61 4. OPEN-ENDED COAXIAL PROBE SYSTEM.63 4.1 System Description...............................................63 4.2 Analysis........................................................64.....4.2.1 Error Correction................64.....4.2.2 Equivalent Circuit Modeling.................................. 68..... 4.2.3 Calibration And The Inverse Problem......................70 4.3 Probe Selection..................................................71..... 4.3.1 Optimum Capacitance.......................................71..... 4.3.2 Sensitivity................................................... 77.....4.3.3 Higher Order Modes........................87..... 4.3.4 Contact And Pressure Problem..................90 4.4 Probe Calibration............................................... 91.....4.4.1 Choice Of Calibration Materials 91..... 4.4.2 Error Analysis..........................................92..... 4.4.3 Thin Sample Measurements................................ 103..... 4.4.4 Comparison To The Waveguide Transmission System 123..... 4.4.5 Probe Usage And Limitations-Other Probe Configurations.. 123 5. MEASUREMENT RESULTS............................. 126 5.1 Plant Type, Part, And Location..............................127 iv

5.2 Frequency Dependence...................................... 132 5.3 Water Content Dependence...................................... 138 5.4 Salinity Effects..................................................142 5.5 Bound Water Effects............................................156 5.6 Temperature Effects.............................................178 5.7 Density Effects................................................ 209 6. MODELING EFFORTS........................................ 212 6.1 Liquid Water Dielectric Properties...............................213..... 6.1.1 Distilled Water...........21...............................213.... 6.1.2 Saline Water......................................213..... 6.1.3 Temperature Effects........................................ 214.....6.1.4 Bound Water....................................... 216..... 6.1.5 Temperature Effects (Bound Water)................... 217 6.2 Volume Fraction Calculations....................................220..... 6.2.1 Assumptions And Definitions...............................220..... 6.2.2 Volume Fractions For A Sample That Shrinks...............222.....6.2.3 Volume Fractions For A Sample That Does Not Shrink.....224..... 6.2.4 Volume Fractions For Sucrose Solutions.....................228 6.3 Models.......................................................... 232.....6.3.1 DeLoor's Model (Upper Limit).............................232..... 6.3.2 Debye's Model (With Two Relaxation Spectra).............235.....6.3.3 Birchak Model (Semi-Empirical)............................255..... 6.3.4 Polynomial Fit (Empirical Model)..........................256.....6.3.5 Single-Phase Single-Relaxation Spectrum Debye Model......264 7. CONCLUSIONS AND RECOMMENDATIONS..................... 301 7.1 Conclusions.....................................................301..... 7.1.1 Measurement System.................... 301..... 7.1.2 Measurements................................303.... 7.1.3 Modeling................................................... 304 7.2 Recommendations............................................... 305.....7.2.1 Measurement System....................................... 305..... 7.2.2 Measurements And Modeling...............................306 REFERENCES.......................................................... 310 APPENDIX A. Dielectric Measurements at Room Temperature........... A.0 APPENDIX B. Dielectric Measurements as a Function of Temperature.... B.0 V

APPEND C. Probe Modeling Program Listing....................... C.O vi

LIST OF FIGURES Figure 2.1. Dielectric constant spectra for liquid water with salinity (in ppt) as parameter at room temperature (200C). Calculated from [ Stogryn, 1971]..................................................... 17 Figure 3.1. Waveguide transmission measurement system.................41 Figure 3.2. 3-18 GHz free-space transmission measurement system........44 Figure 3.3. A schematic diagram of the coaxial wave guide used for the leaf measurements and the corresponding standing wave patterns assumed in the derivation of the working equations [Broadhurst, 1971]........... 45 Figure 3.4. Block diagram of the probe dielectric system. Frequency coverage is 0.1-20 GHz............................................... 50 Figure 3.5. Schematic diagram of the measurement set-up for microwave cavity measurements......5.....4...........................54 Figure 4.1. Error models used for test set connection errors...............67 Figure 4.2. Coaxial probe (a), and its equivalent circuit (b)...............70 Figure 4.3. Calibration algorithm for the full equivalent circuit parameters, C, Co, B,andA.......73.............................73 vfi

Figure 4.4(a). Calculated optimum capacitance for methanol(0.1-1 GHz). 74 Figure 4.4(b). Calculated optimum capacitance for methanol(1-20 GHz)..75 Figure 4.4(c). Calculated optimum capacitance for distilled water(0.1-1 GHz). 76 Figure 4.4(d). Calculated optimum capacitance for distilled water(1-20 GHz). 77 Figure 4.5. Calculated probe sensitivity for distilled water (0.1-1 GHz)... 80 Figure 4.6. Calculated probe sensitivity for distilled water (1-20 GHz)... 81 Figure 4.7. Calculated probe sensitivity for methanol (0.1-1 GHz).........82 Figure 4.8. Calculated probe sensitivity for methanol (1-20 GHz)........ 83 Figure 4.9. Calculated probe sensitivity for 1-butanol (0.1-1 GHz)....... 84 Figure 4.10. Calculated probe sensitivity for 1-butanol (1-20 GHz)........ 85 Figure 4.11. Calculated probe sensitivity for 1-octanol (0.1-1 GHz)....... 86 Figure 4.12. Calculated probe sensitivity for 1-octanol (1-20 GHz)........ 87 Figure 4.13. Estimated relative errors % for measurements on yellow cheese both accuracy and precision...........................................96 Figure 4.14. Estimated relative errors %o for measurements on white cheese both accuracy and precision..........................................97 viii

Figure 4.15. Estimated relative errors %o for measurements on 1-octanol both accuracy and precision using the 0.250" probe........................ 98 Figure 4.16. Estimated relative errors % for measurements on 1-octanol both accuracy and precision using the 0.141" probe........................ 99 Figure 4.17. Estimated relative errors %o for measurements on 1-butanol both accuracy and precision using the 0.250" probe....................... 100 Figure 4.18. Estimated relative errors %o for measurements on 1-butanol both accuracy and precision using the 0.141" probe.......................101 Figure 4.19. Comparison of calculated [ref. 2 is Bottreau et al, 1977] and measured data using the 0.141" probe for 1-butanol (real part).......... 102 Figure 4.20. Comparison of calculated [ref. 2 is Bottreau et al, 1977] and measured data using the 0.141" probe for 1-butanol (imaginary part).... 103 Figure 4.21. Probe technique for measuring dielectric of (a) thick layers and (b) thin layers...................................................... 105 Figure 4.22(a). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=1 GHz............................................................ 106 Figure 4.22(b). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=5 GHz.................................................... 107 Figure 4.22(c). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=8 GHz.................................. 108 ix

Figure 4.23. Thin sample configuration against a background material (known). 110 Figure 4.24(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 1 GHz(real part)................................113 Figure 4.24(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 1 GHz(imaginary part)..........................114 Figure 4.25(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 8 GHz(real part)................................115 Figure 4.25(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 8 GHz(imaginary part)..........................116 Figure 4.26(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 1 GHz(real part)................................117 Figure 4.26(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 1 GHz(imaginary part)..........................118 Figure 4.27(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 8 GHz(real part).................................119 Figure 4.27(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 8 GHz(imaginary part)..........................120 Figure 4.28(a). Spectra of measured one leaf/metal, one leaf/plexiglass, and thick stack/plexiglass along with the calculated values from the thin-thick formula (real parts). Above 11 GHz high-order modes propagation (upper curve) causes large errors........................................... 121

Figure 4.28(b). Spectra of measured one leaf/metal, one leaf/plexiglass, and thick stack/plexiglass along with the calculated values from the thin-thick formula (imaginary parts). Above 11 GHz high-order modes propagation (upper curve) causes large errors..................................... 122 Figure 4.29. Comparison between the probe and the waveguide systems. 125 Figure 5.1. Comparison between corn leaves and soybeans leaves. Curves were fitted to measured data using a second order polynomial fit.......... 129 Figure 5.2. Comparison between corn stalks(measured on the inside part) and tree trunk (Black-Spruce). Curves were fitted to measured data using a second order polynomial fit.......................................... 130 Figure 5.3. Comparison between corn leaves and corn stalks. Curves were fitted to measured data using a second order polynomial fit............ 131 Figure 5.4. Measured dielectric constant and calculated volumetric moisture for fresh corn stalks as a function of height above the ground (cm)... 133 Figure 5.5. Measured spectra of the dielectric constant of corn leaves with volumetric moisture MV as parameter (real parts)....................... 134 Figure 5.6. Measured spectra of the dielectric constant of corn leaves with volumetric moisture M. as parameter (imaginary parts)................135 Figure 5.7. Measured spectra of the dielectric constant (real and imaginary parts) at the low frequency band (.1-2 GHz) for Crassulaceae Echeveria leaves.................................................. 137 Figure 5.8(a). Measured dielectric constant of corn leaves at 1, 4, and 17 GHz, respectively, with frequency as parameter............................139

Figure 5.8(b). Measured spectra of the dielectric constant of soybeans leaves with volumetric moisture MV as parameter (real parts).......... 140 Figure 5.8(c). Measured spectra of the dielectric constant of soybeans leaves with volumetric moisture M. as parameter (imaginary parts)........141 Figure 5.9. Measured salinity in (ppt) for extracted fluids from corn leaves at different volumetric moisture levels, plants were excised and naturally dried................................................... 147 Figure 5.10 Spectra of the extracted fluids from corn leaves. The data points are measured and the solid lines are calculated from [Stogryn, 1971] for saline water solution with 8 ppt salinity.............................. 150 Figure 5.11 Spectra of the extracted fluids from corn stalks. The data points are measured and the solid lines are calculated from [Stogryn, 1971] for saline water solution with 8 ppt salinity................................. 151 Figure 5.12 Spectra of the extracted fluids from corn stalks. The data points are measured and the solid lines are calculated from [Stogryn, 1971] for saline water solution with 8 ppt salinity (the pressure guage showed 10 tons during the extraction, 3 tons for Figure 5.11)................... 152 Figure 5.13. Measured spectra of the dielectric properties of potatoes and apples. The measured salinity of the extracted fluids were 7 and 0.8 ppt, respectively......................................................... 157 Figure 5.14. Measured spectra of the sucrose solution (A) with x=0.5. Two probes were used to measure the lower (.25") and upper (.141") bands. V, Vb, andVf are sucrose, bound, and free water volume fractions, respectively..........................................................161 Figure 5.15. Measured spectra of the sucrose solution (D) with x=2. Two probes were used to measure the lower (.25") and upper (.141") bands. xii

V, Vb, andVf are sucrose, bound, and free water volume fractions, respectively............................................... 162 Figure 5.16. Measured spectra of the sucrose solution (G) with x=3.17. Two probes were used to measure the lower (.25") and upper (.141") bands. V,, Vb, andVf are sucrose, bound, and free water volume fractions, respectively............................................................... 163 Figure 5.17. Measured spectrum of the imaginary part for sucrose solution (D) with x=2. The peak is at around 1 GHz. The agreement between the two sets of data produced by two different probes is fairly good.......... 164 Figure 5.18. Spectra for the sucrose solution (G) with x=3.17. The data points are measured and the solid lines are calculated using Equation 2.18 in the text..................................................................166 Figure 5.19. Measured spectra for dextrose solution with x=2. Two probes were used to measure the lower(.25") and upper(.141") bands........ 167 Figure 5.20. Measured spectra for Silica gel (X3) with x=0.5............168 Figure 5.21. Measured spectra for Gelatin (X1) with x=1. Two probes were used to measure the lower(.25") and upper(.141") bands............. 169 Figure 5.22. Measured spectra for starch solution with x=-1..............171 Figure 5.23. Measured spectra for Accacia (Arabic Gum) solution with x=0.8. 172 Figure 5.24. Measured spectra for natural honey. Two probes were used to measure the lower(.25") and upper(.141") bands..................... 173 xiii

Figure 5.25. Measured spectra for egg white. Two probes were used to measure the lower(.25") and upper(.141") bands.........................174 Figure 5.26. Measured spectra for egg yolks............................175 Figure 5.27. Measured spectra for human skin (finger tips). Two probes were used to measure the lower(.25") and upper(.141") bands............. 176 Figure 5.28. Dielectric constant behavior versus temperature with frequency as parameter for distilled water (s=0 ppt). Calculated from [Stogryn, 1971]. 179 Figure 5.29. Dielectric constant behavior versus temperature with frequency as parameter for saline water solution (s=4 ppt). Calculated from [Stogryn, 19711............1*8...0e........................................ 180 Figure 5.30. Dielectric constant behavior versus temperature with frequency as parameter for saline water solution (s=8 ppt). Calculated from [Stogryn, 1971].................................. 181 Figure 5.31. Measured dielectric constant versus temperature from -400C to +300C at 1 GHz for Fatshedera leaves. Mg(before) = 0.745 and Mg(after) = 0.711. @185 Figure 5.32. Measured dielectric constant versus temperature from -400C to +300C at 4 GHz for Fatshedera leaves. Mg(before) = 0.745 and M2(after) = 0.711.......e.. eo............................................... 186 Figure 5.33. Measured dielectric constant versus temperature from -400C to +30~C at 8 GHz for Fatshedera leaves. Mg(before) = 0.745 and Mg(after) = 0.711............. *........... o............. e.......... 187 Figure 5.34. Measured dielectric constant versus temperature from -40QC to +30~C at 20 GHz for Fatshedera leaves. Mg(before) = 0.745 and Mg(after) xiV

0.711....................................................... 188 Figure 5.35. [Levitt, 1956]............................................... 189 Figure 5.36. Measured spectra for Fatshedera leaves with temperature as parameter (real parts) Mg(before) = 0.745 and M,(after) = 0.711'. 191 Figure 5.37. Measured spectra for Fatshedera leaves with temperature above freezing as parameter (imaginary parts) Mg(before) = 0.745 and Mg(after) = 0.711................................................. 192 Figure 5.38. Measured spectra for Fatshedera leaves with temperature below freezing as parameter (imaginary parts) Mg(before) = 0.745 and Mg(after) = 0.711................................................. 193 Figure 5.39. Measured dielectric constant versus temperature from -450C to +500C at 1 GHz for a tropical tree leaves. Mg (before) = 0.839 and M (after) =0.818.....................4.............................. 194 Figure 5.40. Measured spectra for a tropical tree leaves at -15C........ 195 Figure 5.41. Measured dielectric constant versus temperature from -400C to +300C with frequency as parameter for Fatshedera leaves (real parts). M9(before) = 0.736 and M,(after) = 0.718........................... 197 Figure 5.42. Measured dielectric constant versus temperature from -400C to +300C with frequency as parameter for Fatshedera leaves (imaginary parts). M,(before) = 0.736 and Mg(after) = 0.718........................... 198 Figure 5.43. Measured dielectric constant versus temperature from -40QC to +300C at 1 GHz for Fatshedera leaves. A freezing-thawing cycle is shown for the real part.................................................. 199 xv

Figure 5.44. Measured dielectric constant versus temperature from -40 C to +300C at 1 GHz for Fatshedera leaves. A freezing-thawing cycle is shown for the imaginary part....................................... 200 Figure 5.45. Measured dielectric constant versus temperature from -350C to +300C with frequency as parameter for corn leaves (real parts). Mg(before) = 0.835 and Mg(after) = 0.781...................................... 202 Figure 5.46. Measured dielectric constant versus temperature from -350C to +300C with frequency as parameter for corn leaves (imaginary parts). M,(before) = 0.835 and Mg(after) = 0.781.......................... 203 Figure 5.47. Measured dielectric constant versus temperature from -350C to +300C at 1 GHz for corn leaves. A freezing-thawing-freezing cycle is shown for the real part.................................................... 204 Figure 5.48. Measured dielectric constant versus temperature from -350C to +300C at 1 GHz for corn leaves. A freezing-thawing-freezing cycle is shown for the imaginary part................................. 205 Figure 5.49. Measured dielectric constant versus temperature from -200C to +500C with frequency as parameter for sucrose solution (#9 or G) for the real partrs.......................................................... 207 Figure 5.50. Measured dielectric constant versus temperature from -20~C to +500C with frequency as parameter for sucrose solution (#9 or G) for the imaginary partrs.................................................... 208 Figure 5.51. Measured dielectric constant versus temperature from -800C to +300C at 1 GHz for sucrose solution (#9 or G). The measured solution in this case is not exactly (#9 or G) because of solid sucrose precipitation at low temperatures................................................... 210 Figure 86.1. Calculated volume fractions for a vegetation sample that shrinks. Va, Vf, Vb, and V, are the volume fractions of air, free, bound water, and xvi

bulk vegetation material that binds water, respectively...............225 Figure 6.2. Calculated volume fractions for a vegetation sample that shrinks. M, Vf, Vb, and Vv are the volume fractions of water, free water, bound water, and bulk vegetation material that binds water, respectively... 226 Figure 6.3. Calculated volume fractions for a vegetation sample that shrinks. M,, V,, V,,, and V,,m are the volume fractions of water, bulk vegetation material that binds water, remaining bulk material that does not bind water, and the total or maximum bulk material, respectively............ 227 Figure 6.4. Calculated volume fractions for a vegetation sample that does not shrink. Va, Vf, Vb, and V, are the volume fractions of air, free, bound water, and bulk vegetation material that binds water, respectively.......... 229 Figure 6.5. Calculated volume fractions for a vegetation sample that does not shrink. M,, Vf, Vb, and V, are the volume fractions of water, free water, bound water, and bulk vegetation material that binds water, respectively. 230 Figure 6.6. Calculated volume fractions for a vegetation sample that does not shrink. M,,, V,, V,,, and Vv,, are the volume fractions of water, bulk vegetation material that binds water, remaining bulk material that does not bind water, and the total or maximum bulk material, respectively.... 231 Figure 6.7. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=220C for Mg=0.681............................. 236 Figure 6.8. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=220C for MD=0.333............................ 237 xvii

Figure 6.9. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=220C for Mg=0.168............................ 238 Figure 6.10. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T=220C for Mg=0.681......................................... 241 Figure 6.11. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T=220C for Mg=0.333.................................. 242 Figure 6.12. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T-220C for MgO0.168.................... 243 Figure 6.13. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=1 GHz)................... - *...............*...........244 Figure 6.14. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=4 GHz)........................... o. e..e............245 Figure 6.15. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=12 GHz).............. 246 Figure 6.16. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=20 GHz)........................*.........*...........247 Figure 6.17. Calculated real parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.681). 249 xviii

Figure 6.18. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.681). 250 Figure 6.19. Calculated real parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.333). 251 Figure 6.20. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.333). 252 Figure 6.21. Calculated real parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.168). 253 Figure 6.22. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (M = 0.168). 254 Figure 6.23. Comparison of calculated and measured dielectric spectra for corn leaves using Birchak's model ( Mg = 0.681)..........................257 Figure 6.24. Comparison of calculated and measured dielectric spectra for corn leaves using Birchak's model ( Mg = 0.333)...........................258 Figure 6.25. Comparison of calculated and measured dielectric spectra for corn leaves using Birchak's model ( Mg = 0.168).......................259 Figure 6.26. Comparison of calculated and measured dielectric spectra for corn leaves using a polynomial fit ( Mg = 0.681)......................261 Figure 6.27. Comparison of calculated and measured dielectric spectra for corn leaves using a polynomial fit ( Mg = 0.333)...........................262 xix

Figure 6.28. Comparison of calculated and measured dielectric spectra for corn leaves using a polynomial fit ( Mg = 0.168).......................... 263 Figure 6.29. Comparison of calculated and measured dielectric spectra for sucrose solution (A) using a Debye-like model with a single variable relaxation spectrum (V, = 0.239 and My = 0.761).............................. 268 Figure 6.30. Comparison of calculated and measured dielectric spectra for sucrose solution (B) using a Debye-like model with a single variable relaxation spectrum (V, = 0.385 and My = 0.615).............................. 269 Figure 6.31. Comparison of calculated and measured dielectric spectra for sucrose solution (C) using a Debye-like model with a single variable relaxation spectrum (V, = 0.485 and M. = 0.515).............................. 270 Figure 6.32. Comparison of calculated and measured dielectric spectra for sucrose solution (D) using a Debye-like model with a single variable relaxation spectrum (V, = 0.559 and Mu = 0.441).......................... 271 Figure 6.33. Comparison of calculated and measured dielectric spectra for sucrose solution (E) using a Debye-like model with a single variable relaxation spectrum (V. = 0.613 and M, = 0.387).................... 272 Figure 6.34. Comparison of calculated and measured dielectric spectra for sucrose solution (F) using a Debye-like model with a single variable relaxation spectrum (V, = 0.655 and M. = 0.345).............................. 273 Figure 6.35. Comparison of calculated and measured dielectric spectra for sucrose solution (G) using a Debye-like model with a single variable relaxation spectrum (V, = 0.667 and M. = 0.333)............................. 274 Figure 6.36. For the single phase model, y(Vvm/M,) is plotted against gravimetric moisture M,................................................275

Figure 6.37. The effective resonant frequency fo(GHz) of the single water phase versus gravimetric moisture M..................................... 279 Figure 6.38. Volume fractions of corn leaves as calculated from the single phase model. M, Vm,,, Va, and V,, + V, are the volume fractions of water, bulk vegetation material, air, and dry vegetation material, respectively.... 280 Figure 6.39. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.681......................................... 281 Figure 6.40. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.605........................................ 282 Figure 6.41. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.601......................................... 283 Figure 6.42. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.551.................................... 284 Figure 6.43. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.472......................................... 285 Figure 6.44. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.333.....................................................286 Figure 6.45. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.258........................287..... 287 XX1

Figure 6.46. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.252.......................288 Figure 6.47. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.168...................................................... 289 Figure 6.48. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.074......................................... 290 Figure 6.49. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for Mg = 0.041.............................................. 291 Figure 6.50. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 0.7 GHz.................................. 292 Figure 6.51. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 1 GHz.................................... 293 Figure 6.52. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 2 GHz................................ 294 Figure 6.53. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 4 GHz......... 295 Figure 6.54. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable rexxii

laxation spectrum for f = 8 GHz.................................... 296 Figure 6.55. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 17 GHz........................... 297 Figure 6.56. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 20.4 GHz................................. 298 xxiii

LIST OF TABLES Table 1.1. Examples of space missions..................................... 2 Table 1.2. Available and desired ranges of parameters...................... 4 Table 2.1. Comparison between previous microwave dielectric measurements on vegetation materials..................................................37 Table 3.1. Comparison between different microwave dielectric measurement techniques............................................................... 63 Table 4.1. Dimensions and cut-off wavelengths for the TMol mode for the probes used in this study............................................. 89 Table 4.2. (A,), for distilled water........................................90 Table 4.3. Evaluation of the thin-thick formula for the 0.141" probe......123 Table 5.1. Measured salinity of liquids extracted from corn plants at different pressures (in tons per unit area) and at different plant heights.......144 Table 5.2. Salinity and gravimetric moisture for corn leaves and stalks... 145 Table 5.3. Comparison between measured corn leaves grown in Kansas and Michigan.......................................................... 148 xxiv

Table 5.4. Comparison between salinity measurements using conductivity meter and using dielectric measurements............................... 149 Table 5.5. Fresh corn leaves and stalks at 1.0 GHz (Michigan, Dec. 1985, samples grown in Botanical Gardens)................................... 153 Table 5.6. Freshly cut desert plants (at 1 GHz)...........................155 Table 5.7. Dielectric of potatos, tomatos, and apples (Mg > 0.8 and f=1 GHz). 155 Table 5.8. Volume fractions and dielectric constants of sucrose solutions at 1 GHz).........................................159 Table 5.9. Measured E' and E' of various materials (some with known waterbinding capacity, X = solid weight / water weight) at 1 GHz.........177 Table 5.10. Liquid water temperature coefficients......................... 182 Table 5.11. Measured data for poplar tree trunk at 1 and 5 GHz.........211 Table 6.1. Statistics associated with the regression fits given by 6.29 to 6.33. 219 Table 6.2. Model accuracy for corn leaves, DeLoor's model with Aj=(0,0,1) and E* = E, at T = 22~C................................................ 235 Table 6.3. Model accuracy for corn leaves data, Debye-like model at T = 220C. 240 Table 6.4. Model accuracy for corn leaves, Birchak model (c = 0.873) at T = 220C..............................................256 XXV

Table 6.5. Model accuracy for corn leaves data, polynomial fit at T = 220C. 260 Table 6.6. Model accuracy of single-phase Debye model as applied to the sucrose solutions data at T = 220C....................................267 Table 6.7. Model accuracy for corn leaves data, single-phase Debye model, T = 220C............................................................278 Table 6.8. Comparison between different models for corn leaves data at 220C (real parts)........................................................ 299 Table 6.9. Comparison between different models for corn leaves data at 220C (imaginary parts)................................................... 300 xxvi

Chapter 1 Introduction Over the past two decades, spaceborne microwave sensors have been playing an increasingly important role in the study of the earth's surface and atmosphere. They can provide near-global coverage of the earth's surface unhampered by cloud cover and with independence of sun angle. Furthermore, the ability of microwave energy to penetrate through dry media has proved useful for studying subsurface terrain features (Carver et al, 1985). In recent years, the field of microwave remote sensing has made significant advances along several fronts. A prime example of a major technological development is the recent realization of digital techniques that can provide real-time processing of SAR images. Also, improved scattering and emission models are now available to relate the backscattering coefficient ao and emissivity e of a distributed target to its dielectric and geometric properties. Since 1962, numerous microwave radiometers have been flown on earth-orbiting satellites; some examples of these space missions are given in Table 1.1(Ulaby et

al, 1982): Year 1962 1972 1973 1978 Spacecaft Mariner 2 Nimbus 5 Skylab Nimbus 7 Instrument acronym S193 SMMR Frequency(GHz) 15.8,22.2 19.3 13.9 6.6,10.7,18,21,37 Type Of Scanning Mechanical Electrical Mechanical Mechanical Swath-Width (Km) Planetary 3000 180 800 Resolution (Km) 1300 25 16 18x27 Table 1.1 Examples of space missions. Also, several SAR systems have been flown in space including Seasat(1978), SIR-A (1981), and SIR-B (1984).Many experiments have been conducted to relate &o and e to target characteristics at various frequencies and polarizations. Some of these experiments have utilized truck-mounted radar systems to observe the backscattering and emission from natural targets as a function of frequency, look angle, and polarization (Ulaby et al, 1982). The dielectric properties of natural targets play a key role in remote sensing. Its importance stems from the fact that it determines, besides the sensor parameters and the target geometrical features, the backscattering and natural emission from a distributed target. Also, the dielectric properties of a target relate its physical properties (e.g. its water content or temperature) to its a~ and e. This feature is very important in remote sensing science because it is a

critical ingredient of the inverse scattering process. Yet, understanding of the dielectric behavior of natural materials remains superficial at the present time and this is particularly true in the case of vegetation. Only a few experiments have been conducted to date to examine the dielectric properties of vegetation material. Reviewing the literature requires a minor effort because only a few measurements and modelling attempts (Carlson, 1967; Broadhurst, 1971; Tan, 1981; Ulaby and Jedlicka, 1984) have been conducted so far. Moreover, these attempts were limited to narrow ranges of the major parameters of interest, namely plant type and parts, frequency band, moisture content, effective salinity, and temperature. The following table provides a comparison between the range of parameters already tested and those desired from the standpoint of natural variability -as far as the physical parameters are concerned- and in terms of the frequency range of interest to the remote sensing community: Measured Parameter Available Data Desired Range Frequency (GHz) 1-2,3.5-6.5,7.5-8.5.1-20 Moisture Content (percent gravimetric) 0-60 0-90 Temperature (~C) 20 to 25 -40 to +40 Effective NaCl (Parts Per Thousands) 11 4 to 40.~~~~~~~~~~~

Table 1.2 Available and desired ranges of parameters. Another shortcoming of the studies already conducted on this subject is the lack of a comprehensive model that relates different plant physical parameters to the dielectric properties using as a few free parameters as possible. This lack of knowledge motivated the current research to study these missing pieces and to try to develop a universal model for vegetation materials. The parameters of interest are frequency (.1 to 20 GHz), temperature (-40 to +40 ~ C), water content (0 to 90 %o gravimetric), vegetation density (by testing different plants and parts), and salinity (4 to 40 parts per thousand). An additional major goal is to establish the role of bound water in the dielectric process. The goals of this study can be summed up as follows: 1. To develop a dielectric measurement system suitable for dielectric measurements of plant parts. The system should be fast, reliable, accurate, operate over a broad frequency range, and suitable for temperature measurements. 2. To generate a dielectric constant database for a variety of plant types and parts as a function of: (a) moisture level, (b) electromagnetic frequency,

(c) vegetation bulk density, (d) effective NaCI salinity of included liquids, (e) temperature, and (f) part location relative to root system. 3. To develop an understanding of the different mechanisms that contribute to the overall dielectric behavior of vegetation materials, and to establish, if possible, the roles of salinity and bound water. 4. To develop a general physical mixing model for plant materials that incorporates all of the previously mentioned parameters. Empirical and semiempirical models will be developed as well.

Chapter 2 Background A vegetation material, such as a leaf, can be considered a heterogeneous vegetation-water mixture consisting of four components: (1) free water, (2) bound water, (3) bulk vegetation matter, and (4)air. Since plants are, in general, found in nature with a very high water content, their dielectric properties are mainly determined by the properties of included water. It was found (Ulaby and Jedlicka, 1984) however, that these fluids have a finite salinity equivalent to an NaCl salinity of about 10 ppt 1. Therefore, the first section of this chapter will provide the background material for the dielectric properties of liquid water as a function of various physical parameters. It is of great importance to note the similarity between the general dielectric behavior of liquid water and that of wet plants. Any deviation however, should be studied and properly attributed to other causes. Some of these causes may include the effects of bound water which differs substantially from free water. Another important cause may be the various structural differences within a plant part which may affect the de1Parts Per Thousand

polarization shape factors (DeLoor, 1968;DeLoor, 1982), which, in turn, may have a significant influence upon the dielectric constant of the vegetation-water mixture. This topic is examined in section 2.2. Next, in section 2.3, a short review is presented of the general principles of plant physiology as they relate to the study of the dielectric properties of vegetation material. Finally, in section 2.4, a brief discussion of previous studies is presented. 2.1 Dielectric Properties Of Liquid Water The dielectric properties of water have been extensively studied, and are quite well understood with regard to the dependence on salinity, frequency, and temperature. A complete analysis is presented in Hasted (Hasted, 1973). Also, a comprehensive summary of the dielectric properties of natural targets, including water, is provided by Ulaby et al (Ulaby et al, 1986). Since the dielectric properties of liquid water are based on the well known Debye equation (Debye, 1912), it will prove useful to provide a brief background of the Debye equation and the associated relaxation process. 2.1.1 What Is A Relaxation Process This section is intended to present a brief description of the mechanism by which water molecules exhibit a spectral absorption line at microwave frequencies. For a complete analysis the reader is referred to the classical book of Debye (Debye, 1912), or those by Hasted (Hasted, 1973) and Pethig (Pethig, 1979).

Polar Molecules The permittivity of a material may be regarded as the proportionality factor between electric charge and electric field intensity. Also, it reflects the extent to which a localized charge distribution can be distorted through polarization by an external electric field. The polarizability, a, is defined as the dipole moment induced by a unit electric field and is given by at = ae + aa + ao (2.1) where at is the total polarizability, ca is the electric polarizability (due to displacement of the electron cloud relative to the nuclei), aa is the atomic polarizability (due to displacement of the atomic nuclei relative to one another), and ae is the orientational polarizability (due to a permanent electric dipole moment). Thus, ao only exists in polar materials, e.g. water, and the higher the polarizability of a material, the higher its static dielectric constant. For non-polar materials, the polarizability arises from two effects, namely electronic and atomic polarization. Since the dispersion due to the fall-off of the atomic polarization, aa, occurs at frequencies comparable with the natural frequencies of vibrations of the atoms in a molecule (i.e. in the infrared spectrum around 1014 Hz), and that for electronic polarization, a., occurs at still higher frequencies corresponding to electronic transitions between different energy levels in the atom (visible, UV, and X-ray frequencies), the dielectric properties of non-polar materials are constant in the microwave band and do not show any temperature dependence either.

Polar molecules, although electrically neutral, have a charge distribution such that the centers of positive and negative charge are not coincidental. These molecules are termed polar, and were found to have a high static dielectric constant (e.g., E8 of water is about 80.). The slowest polarization mechanism is often that of dipolar reorientation. The dipole moments are just not able to orient fast enough to keep in alignment with the applied electric field and the total polarizability falls from at to (at - co). This fall in polarizability, with its related reduction in dielectric constant (e.g., e, drops roughly from 80 to 4.5 for water), and the occurence of energy absorption is referred to as dielectric relaxation or dispersion. It is worth noting here that the dispertion due to ao is completely different from that due to a. or ae. The former is a relaxation dispersion while the later is a resonance dispersion 2. Debye's Equation The total dipole moment of molecules in a polar material represents the degree of polarization aquired after the application of an external electric field = atE (2.2) where mn is the dipole momont and E1 is the local electric field. This equation may be written in the form m = + aE/l (2.3) 2e.g. relaxation dispersion has the broadest spectrum known in physics which is approximately 1.4 decades wide.

where A is the permanent dipole moment and a = ac + ae. Since ft is a permanent moment, the application of an electric field will generate a torque At x E tending to align the molecules with the field. Obviously, this orienting tendency is opposed by thermal agitation. The potential energy of a dipole moment F in a field E1 is given by U = -TF1 = — E1 cos 0 (2.4) where 0 is the angle between pi and E1. According to the Boltzmann distribution law, the relative probability of finding a dipole oriented in an element of solid angle dO is proportional to exp(-U/KT) and the thermal average of cos 0 can be shown to be (Pethig, 1979) 1 < cos O >= cothx - - (2.5) where x = KT. It was shown, for E1 < 105v/m, that < cos 0 > — zKT (2.6) and that the average moment per dipole in the direction of the applied field, Pd, is given by d = < cos >= 3KT (2.7) Hence, the total polarizability is at = 3KT a + a,. (2.8) We must keep in mind, however, that equation ( 2.8) is only valid for small values of electric field (E1 < 105v/m); if the fields are higher than that, a more complicated expression is required (Hasted, 1973).

One of the most difficult problems in dielectric theory is to relate the local field (acting on a molecular dipole), to the externally applied field (macroscopic field). Many researchers have tried to relate E1 to E and their results were not generally satisfactory (e.g. the Mossotti-Clausius-Lorentz formulation). To derive a mathematical model for the orientational relaxation process, we shall assume that the polarization, P is given by P = Pi + P2= X1E + P2 (2.9) where P1 is the polarization due to atomic and molecular displacements (it responds instantly to E, at least at microwave frequencies), P2 is the polarization due to dipolar reorientation (it lags behind E at microwave frequencies), and X1 is the dielectric susceptibility. It can be shown that (Pethig, 1979) dP2 = (X2E - P2) (2.10) dt r where X2E is the final value of P2, and r is the relaxation time constant. Solving equation ( 2.10) for E as a step function at t = 0 when P2 = 0 yields -t P = P1 + P2 = (X1 + X2(1- exp-))E, (2.11) which shows that the polarization reaches its final value exponentially with a time constant r. A solution for ( 2.11) of an alternating field, E = o exp(jwt), can be shown to be (Pethig, 1979) x2 P = P1 + P = (Xl + )E (2.12) 1 + jW

which corresponds to a complex dielectric constant of the form f = E00 + (2.13) 1 + jwr where e is the macroscopic complex dielectric constant, Eo, is its high frequency (or optical) limit, e, is its low frequency (or static) limit, and r is the relaxation characteristic time. The complex dielectric constant can be expressed in real numbers as E =' — E" (2.14) and the real and imaginary parts can be expressed as, = + e, - eoo (2.15) 1 + W272 and (.= - EOO)WT E=('' 1+")W 7 (2.16) 1 + co2r2 (26) Equations ( 2.13) to ( 2.16) are commonly known as the Debye dispersion formulas. Some of the interesting features of the Debye relaxation process are: 1. Its transition extends roughly over four decades in frequency. 2. The width of the c" peak at the half-height value is roughly 1.4 decades in frequency (very broad!). 3. It is possible to represent a relaxation graphically in two different ways:

(a) Two straight lines: If we plot the following relations E"w = (e, - E')/r and E"/w = (E'- E,)r, we will have two straight lines whereby r can be estimated from their slopes (Pethig, 1979). This is a useful technique if the measurement data are not enough to describe the relaxation behavior (e.g. measurement frequency band is either lower or higher than resonance frequency). (b) Cole-Cole plot: In order to check for single or multiple relaxation times, this plot can prove very useful. Using equations ( 2.15) and (2.16), and by eliminating wr, we can show that (E'- e - Eoo)2 + (E")2 = (E_ - E,)2 (2.17) 2 4 Equation ( 2.17) is an equation of a circle. A Cole-Cole plot can be easily constructed by plotting E" versus E' with frequency as a variable parameter. 4. Since relaxation time r represents a molecular process that usually follows an Arrhenius temperature law, we can write r= A exp(RT) (2.18) where AH is the Arrhenius activation enthalpy per mole, and A is a constant. From equation ( 2.18) a(ln r) AH (2.19) a() = R

so that a plot of In r against ~ gives a straight line of slope -R. A more complete expression for (2.18) can be given as (Pethig, 1979). h -AS AH r= K exp( R )exp(RT) (2.20) where h is Planck's constant and AS is the molar entropy of activation. A plot of ln(rT) or ln(',,) against j should be a straight line of negative slope, from which AH can be calculated. It is generally the practice to plot simply ln(w.) against T and compare with other activation energy graphs (because of the approximate nature of this treatment). 5. Deviation from an ideal Debye-type single relaxation could occur for many molecular systems. This effect tends to smear the relaxation pattern (e" curve becomes broader). Examples of this phenomena and their respective representation can be given as follows: (a) Cole-Cole equation = E0 + (wr) (2.21) 1 + (jwr) where a represents the width of the symmetrical distribution of relaxation times. A graphical technique (using chords) was designed (Hasted, 1973) to analyze data that has a symmetrical distribution of relaxation times. (b) Modified Cole-Cole equation =E -2oo e -= %, + I +1-a (wr) 1-(2.22) 14

where p is a constant less than unity. (c) Cole-Davidson equation e = 1oo + (1E. - o (2.23) (1 + j(1.). This equation corresponds to an asymmetrical distribution of relaxation times and gives rise to a skewed arc in E'(E") diagram. (d) In general, we can write =a:) ( - ~~o) i 1+ jwr (2.24) where G(r) represents a general distribution of relaxation times. 2.1.2 Pure Water For pure water, it is assumed that the ionic conductivity is zero, which means that there are no free ions to contribute to the total loss (especially at low frequencies). The frequency dependence is given by the Debye equations ( 2.13)( 2.16): e+ Ew- +uoo (2.25) 1 + jwr, It was found experimentally that wOO, Ew, and fw (=1/27rrw) are functions of temperature, especially ew, and f,. Complete analysis and polynomial expressions can be found in (Hasted, 1973; Stogryn, 1971; Klein & Swift, 1977; and Ulaby et al, 1986).

The importance of liquid water at microwave frequencies stems from the fact that its relaxation frequency lies within this band. For example, f/(0OC) = 9GHz (2.26) and fw(200C) = 17GHz (2.27) It was found that e,, - 4.9 by Lane and Saxton (1952). Figure 2.1 illustrates the frequency behavior of El and E, for water at 200C Curves for sea water (s ~ 30 ppt)are shown also for comparison purposes. 2.1.3 Saline Water A saline solution is defined as a solution that contains free ions whether these ions are of organic or non-organic nature. The salinity, s, of a solution is defined as the total mass of dissolved solid salts in grams in one kilogram of solution. An equivalent Debye-like equation could be used to represent saline solutions in the following modified form El' - "WO + EMS- Cl+ (2.28) and E (t (COWS - f)woo) 1i (2.29) W 1 + ( - )2 27rEof Siemens/m, and eo is the free space dielectric constant (Eo = 8.854 x 10-12f/m). 16

120 E' El" 120... S'60/oo -- - S 3001oo 100 I - S - -o No 40_ 0 -20 I s 0 20 0 _ tIIII I tI I I I I I I 1 111 1 2 5 10 20 Frequency (GHz) Figure 2.1. Dielectric constant spectra for liquid water with salinity (in ppt) as parameter at room temperature (200C). Calculated from [ Stogryn, 19711. 17

Again, ar, E.wo, and fawo were found to be functions of salinity (in addition to their temperature dependence). Complete expressions are given in (Stogryn, 1971 )and (Klein and Swift, 1977) in the form of polynomial fits. The equations are repeated here because they will be used in future chapters: Eswoo - 4.9, (2.30) E,,W(T, 0) = 87.74 - 4.0008T + 9.398 x 10-4T2 + 1.410 x 10-6T3, (2.31) 2irr(T, 0) = 1.1109 x 10-1~ - 3.824 x 10-12T + 6.938 x 10-14T2 - 5.096 x 10-16T3, (2.32),c.a watcr(T, S) = rcea water (25, S)exp(-A a), (2.33) where A = 25 - T and a is a function of T and S, a = 2.033x 10-2+1.266x 10-4A+2.464x 10-6A2-S[1.849x 10-5-2.551x 10-7A+2.551x 10-8x (2.34) and aeawate,(25, S) = S[0.182521- 1.46192x10 3S+2.09324x10-5S2 -1.28205x 10(7S3], (2.35)

in the range 0 < S < 40. 2.1.4 Bound Water The term bound water is always encountered in the literature of plant physiology, especially that dealing with cold and drought resistance (Kramer, 1955). The concept of bound water is founded on the observation that a part of the water in both living and nonliving materials behaves in a different manner from free water. While free water freezes at 00C, acts as a solvent, and is usually available for physiological processes, bound water does not. It remains unfrozen at some low temperature, usually -200C or -250C, it is also known not to function as a solvent, and in general it seems to be unavailable for physiological processes. It should be understood here that there is no sharp distinction between unbound and bound water; rather, there exists a gradual transition between free water and completely bound water. Bound water was found to resist oven drying even at 1000C for a long period of time. Obviously, water bound that firmly plays an important role as a cell constituent in the tolerance of drying of some seeds, spores, microorganisms, and a few higher plants (Kramer, 1983). Much of the bound water is held on the surfaces of hydrophilic colloids 3, but some is associated with hydrated ions and molecules. Kramer (Kramer, 1955) wrote a thorough review on bound water and described 14 different methods for measuring it: 3A colloid is a phase dispersed to such a degree that the surface forces become an important factor in determining its properties

1. The Cryoscopic Method, based on the assumption that bound water does not act as a solvent. 2. The Dilatometric Method, using the fact that ice occupies more volume than water and that bound water does not freeze at normal freezing temperatures. 3. The Calorimetric Method, since one gram of free water ice absorbs about 79.75 calories when it thaws, it is possible to estimate the amount of total free water in plant tissues using a calorimeter. 4. The Direct Pressure Method, differences in the amount of water expressed from various materials under a given pressure can indicate differences in bound water contents. 5. Refractometric Method, using a refractometer (Dumanskii, 1933; and Siminova, 1939). 6. Polarimetric Method, (Koets, 1931) 7. The X-ray Method, the presence of shells of oriented water molecules should give X-ray patterns similar to those produced by ice, this method is useful qualitatively and not quantitatively. 8. Infrared Absorption, Infrared transmission curve for bound water was found to be different from that of free water.

9. Heat Of Welting, it is known that when colloids imbibe water, heat is released because water molecules loose part of their kinetic energy when they are adsorbed on the interfaces. 10. Specific Heat Method, it was observed that bound water has an abnormally low specific heat. 11. Drying Method, since bound water is so tightly held by colloids, it remains in samples dried at temperatures as high as 2000C. 12. Osmotic Pressure Method (Levitt and Scarth, 1936). 13. Dielectric Constant Method, since, in general, the dielectric constant of free water is much higher than that of bound water (Marinsco 1931), it is possible to estimate bound water content using dielectric measurements (as will be discussed in Chapter 5). 14. Vapor-pressure Method, adding a nonelectrolyte to free water lowers its vapor pressure. If adding sucrose, e.g., results in an abnormally large decrease in vapor pressure, this indicates that a certain amount of the water is bound. Although there are many methods to measure the amount of bound water in plant tissues, only a few of them proved to be accurate enough to produce meaningfull results. The calorimetric, dilatometric, and cryoscopic methods are used most frequently. According to Kramer (Kramer, 1955), the amount of bound

water found in plant tissues varies with the species tested, the environment in which the plants are grown, and the method used to measure it. There is more bound water in woody plants than there is in herbacious plants. Also some research (Levitt, 1980) indicates that plants have more bound water in the winter than in the summer and more in plants from dry habitats than in those from moist habitats. As a final remark, bound water exists in general in cell walls where it can scarcely affect the protoplasm, and it is held so firmly that it can not act as a solvent or take part in physiological processes. Hence, bound water may have some importance in seeds, spores, and other air-dry plant structure, but it probably is of little significance in growing plants. The last remark underscores the bound water importance in physiological processes; however, its importance in determining the dielectric properties of vegetation materials is significant, especially at microwave frequencies. Many researchers claimed to observe a relaxation frequency for bound water similar to that of free water, except it takes place at frequencies well below that of free water (e.g. Hoekstra and Doyle, 1971). A possible peak of power absorption takes place around 500 - 1500 MHz and was attributed to bound-water relaxation. There are two factors, however, that hold back a proper characterization of this relaxation: 1. Ionic Conductivity dominates losses at and below 1 GHz and tends to mask the effect of bound water. It would be useful to test a plant tissue that has very low values of salinity, if such a plant really exists.

2. Small Volume Fractions of bound water pose another serious problem, especially for fresh plants, where the free water volume is the largest component. If we attempt to examine a dried plant part that has a low moisture level, the increase in salinity would tend to counteract the relative increase in the volume ratio of bound water to free water and hence ionic conductivity would still be dominant. In Chapter 5, an attempt was made to isolate an appreciable amount of bound water that has no free ions and hence, no conductivity losses. This water was bound on the surfaces of sugar molecules (e.g., sucrose and dextrose) and was tested over the frequency range from.2-20 GHz. The observed relaxation frequency was found to be in agreement with previous reports which place it at around 1 GHz. A complete description and analysis of the experiment will be given in Chapter 5. In Chapter 6, however, a conclusion was reached that the nature of bound water is subjective and it depends entirely on how we look at it. Two approachs were used: (i) the dual relaxation spectrum (refer to Sec. 6.3.1 to 6.3.4) and (ii) the single relaxation spectrum (refer to Sec. 6.3.5). 2.1.5 Temperature Dependence As mentioned in Section 2.1.1 and 2.1.2, the dielectric behavior of liquid water has a strong dependence on temperature above freezing. The dependence is even more drastic below freezing, which is called the freezing point discontinuity,

where the magnitudes of the real and imaginary parts drop rather sharply4. One way to detect a relaxation behavior is to measure the dielectric constant of a material as a function of temperature and observe the gradient of the imaginary part. Three cases would arise: 1. If ~y is negative, the dominant loss mechanism is relaxation and the measurement frequency is below the relaxation frequency (f < fo). 2. If aaT is positive, then either: (a) losses are completely or partially caused by a relaxation process and in this case f > fo, (b) losses are completely or partially caused by conductivity, or (c) both relaxation (f > fo) and conductivity losses exist. 3. If aa is 0 O then either: (a) the material is lossless (e.g. dry), (b) there are two different mechanisms affecting the losses, relaxation (with f < fo) and conductivity, and they are comparable in magnitude, or (c) a relaxation peak (f = fo) exists at that particular temperature. As mentioned above, at the freezing point discontinuity the dielectric properties of a sample drastically change because liquid water (with, e.g., E -_ 80- j4 4free water freezes at O~C while bound water freezes around (or even below) -25~C

at 1 GHZ) changes into ice (whose E - 3.15 - jO at 1 GHz) which represents big steps in both the real and imaginary parts. Bound water, however, freezes at temperatures well below free water; it was reported in several papers (e.g., Hoekstra and Doyle, 1971) to have a freezing point between -200C and -300C. This last observation could prove useful in studying the bound water in plant tissues by extending the temperature measurements down to -500C. A complete report of these measurements will be given in Chapter 5. 2.2 Dielectric Mixing Models A vegetation part, such as a leaf, is considered to be a heterogeneous mixture of free water, bound water, bulk vegetation material, and air. An average dielectric constant can be measured for a particular heterogeneous mixture consisting of two or more substances. This average quantity depends on the volume fractions, the dielectric constants, the shape factors, and the orientation (relative to the applied electric field) of each and every constituent in the mixture. The continuous medium (or the host material) is usually taken to be the substance with the largest volume fraction in the mixture. For a more complete review, the reader is referred to (Ulaby et al, 1986). For the purpose of this study, only randomly oriented and randomly distributed inclusions will be considered. In the general development of most dielectric mixing models, it is assumed that the inclusions are much smaller in size than the applied wavelength in order for the equations to hold. These conditions are suitable assumptions for vegetation

materials in most cases. However, a study of the effect of inclusions' orientations could be useful in future research, especially for parts that have an obvious orientation pattern (e.g., a tree trunck). In the following three sections, a brief discussion of the mixing models used in the course of this study is given. They include theoretical models (DeLoor, 1968), semi-emperical models (Birchak et al, 1974), and emperical models (Dobson et al, 1985). 2.2.1 DeLoor's Mixing Model The mixing formula as proposed by Polder and Van Santan (Polder and Van Santan, 1946) and DeLoor (DeLoor, 1956) for a host medium with dispersed randomly-oriented and randomly-distributed inclusions is given by: mEn V= (i- h) 1 ( Cm —i +31 + (E - 1)Ai (2.36) where cm is the macroscopic dielectric constant of the mixture, Ch is the host or continuum dielectric constant, vi and (, are the volume filling factor and the dielectric constant of the ith dispersed inclusion, respectively, c* is the effective relative dielectric constant near an inclusion-host boundary, A, are the depolarization factors along the main axes of the ellipsoidal inclusions, and n is the number of different inclusions in the mixture. The sum of the depolarization factors is equal to EAj = 1 (2.37) j=1 These factors, known also as shape factors, are determined by the inclusion shapes. Three special cases are considered as follows: 26

1. Circular discs; Aj = (0,0, 1) Equation (2.36) will reduce to the following form nvi em = eh + (Ei - Eh)(2 + ) (2.38) 1= 1f 2. Spheres; Aj =(3, 3 n 3E* E, = Eh + vi(i - Eh) 2E* + Ei (2.39) i=1 3. Needles; Aj = ( O) n Vi 5e* - Ei e E = eh + Z (ei - Eh) (2.40) e* + Ei Equation 2.36 can not be used in its present form, since no information is available on E*. However, after a thorough investigation of the available data, it was found (DeLoor, 1956; DeLoor, 1968) that E*, in general, lies between Em and Eh. An upper and a lower limit for Em can be established by setting E* = Em and E* = ek in (2.36), respectively. Moreover, when the depolarization factors are not known, which is generally the case, it is still possible to estimate the limits of Em. The limits in this latter case lie further apart than when the shape factors are known. These limits are given by (DeLoor, 1968): 1. Upper Limit (circular discs; e* = em) EC + S i=l Vi(l- fh) (2.41) 1-~I~~v~(1 -, 2. Lower Limit (spheres; E* = h) Em Eh + 3 E (e, - Eh) (2.42) ZiV (2Eh + E.) 27

where the variables used in ( 2.38)-( 2.42) are as defined in connection with ( 2.36). These limits are of great help in studying the unknown shape factors for any system by plotting the measured data along with the expected limits. 2.2.2 Semi-empirical Models There are two semi-empirical models that have proved to be useful for modeling vegetation material, namely, Birchak and the Debye-like models. 1. Birchack Model n E = (I Evi)1/a (2.43) i=l where a is the only free parameter. When ca is equal to.5, the Birchak model is called the refractive model. 2. Debye-like Model Since the dielectric properties of biological materials are dominated by the dielectric properties of liquid water, a Debye-like model would, in general, be the obvious choice for semi-empirical modeling. Of course, a slight modification is necessary to this formulation in order to include conductivity losses and a spread of relaxation times. The proposed form of Debye's equation is as follows EMs - Cmoo. m Em = Emoo + (2.44) where the variables are as defined earlier and the subscript m indicates the vegetation mixture. moo and Em,, could be evaluated for a particular 28

mixture provided that we know the following: (a) the volume fractions, vi, of all the constituents, (b) Eoi and,, of all the constituents, and (c) the proper mixing formulas relating Em, to E,i of the constituents, and similarly for Eoo. Since volume fractions can be determined from vegetation physical parameters, 5, and Eoo~ and Ei are known, the only unknown is the proper mixing formulas. It is possible, for convenience, to use Birchack model, which gives N Ea= ZVE,i, (2.45) i=l and N =es - Visi'. (2.46) i=l The problem now is to determine a suitable value (or values) for a to best fit the measured data. Similarly, fm can be selected by optimizing the model to fit the data points, and the relaxation frequency of liquid water can be used as an initial condition. The form of a,, is not known, since the effective NaCI salinity changes as a function of moisture content. Hence, in general, oa = f(MU) (2.47) where M, is the volumetric moisture of the material. Two possible representations for ra, may be proposed 6As will be discussed in chapter 6 29

1. a,,, = A - BM, and 2. A Obviously, the first form is more suitable since a,, remains finite even at M, = 0. For a vegetation mixture, the number of constituents can be two, three, or four depending on the model used. Since the bulk vegetation material and air are non-polar materials, they do not have any temperature sensitivity. The only temperature-dependent constituents are the free and bound water. 2.2.3 Empirical Models The most suitable and most commonly used empirical model for the dielectric constant of vegetation materials is simply a polynomial function. Linear regression can be used to determine the unknown coefficients and an evaluation of the fit is performed in terms of correlation and mean-squared errors. Individual polynomials are generated for E' and E" as a function of M, (volumetric moisture) for a particular plant type, part, and at a given frequency and temperature. The disadvantages of this approach are 1. there is no physical significance for the coefficients, and 2. the model is not easily extendable to other moisture, temperature, and/or frequency conditions. On the other hand, the major advantages are * Simplicity, and 30

* The ability to achieve almost a perfect fit to the data by properly choosing the order of the polynomial. 2.3 Water in Plant Materials Water is one of the most common and most important substances on the earth's surface. It is the most significant single environmental factor that determines the kinds and amounts of vegetation cover on various parts of the globe. 2.3.1 Ecological and Physiological Importance of Water It is almost a general rule that wherever water is abundant, vegetation cover is lushy, and deserts are where water is scarce. The ecological importance of water stems from its physiological importance. Every plant process is affected directly or indirectly by the water supply. If the water supply is decreased, plants will suffer loss of turgor and wilting, cessation of cell enlargement, closure of stomata, reduction in photosynthesis, interference with many basic metabolic processes, and continued dehydration will, eventually, cause death of most organisms (Kramer, 1983). 2.3.2 Uses of Water in Plants According to Kramer, the function of water in plant materials may be listed as follows: 1. Constituent: Fresh weight of most herbaceous plant parts is 80-90% water, and water constitutes over 50% of the fresh weight of woody plants. Some

plant parts, e.g. seeds, can be dehydrated to the air-dry condition, or even to the oven-dry condition without loss of viability, but a marked decrease in physiological activity accompanies the loss of water. 2. Solvent: Gases, minerals, and other solutes can enter plant cells and move from cell to cell and organ to organ through the continuous liquid phase throughout the plant. 3. Reactant: Water is essential to many processes such as photosynthesis and hydrolytic processes. 4. Maintenance of Turgidity: This is important for cell enlargement and growth and for maintaining the form of herbaceous plants. It is also important for various plant structures (Kramer, 1983). 2.4 Previous Studies Very few studies have been conducted to date with the goal of measuring and modeling the microwave dielectric properties of green vegetation. Extensive dielectric measurements have been conducted and reported for grains (Nelson, 1978) however. This short section reviews some of the reported data for green vegetation, and provides brief discussions of the measurement systems used and their reliability.

2.4.1 Carlson (1967) A cavity perturbation technique was employed to measure the relative dielectric constant of green vegetation samples (grass, corn, spruce, and taxus) at room temperature and at a single frequency of 8.5 GHz. The measurements were made as a function of water content from freshly-cut samples to perfectly dry ones. The relative dielectric constant was found to be roughly proportional to the moisture content and can be modeled as I II (E'l - jE) = 1.5 + ( 2i _ j- )f (2.48) 2 3 for the samples of corn, grass, and taxus, where E' - jE" is the relative dielectric constant of vegetation samples, El -j E is the relative dielectric constant of water, and f is the fractional amount of water in the sample. The major source of errors in this experiment was due to the measurement uncertainty of the sample size. 2.4.2 Broadhurst (1970) Broadhurst (1970) used a TEM coaxial waveguide with a specimen of the material under test occupying some of the space between the coaxial conductors. His measurements were conducted at room temperature (230C) on living foliage, plant materials, and clay soil over a wide frequency band extending from 100 KHz to 4.2 GHz. In order to calibrate the system for accuracy, distilled water was measured and compared to reported data. The results were within 10% accuracy for the real part, while sizeable errors were observed for the imaginary part. Also, a check on the precision of the leaf measurements was made

by taking six separate samples from a leaf type and by measuring each sample three different times (after each measurement the sample was removed from the chamber and then repacked and measured). An analysis of variance was then conducted on the data to ascertain the components of variance for instrumental error and for variability between leaves. The scatter in the data due to the leaf was, generally, greater than that due to instrumental errors. The scatter due to the leaf was primarily due to measurement errors of leaf thickness, and secondarily due to variations in leaf biological structure. The uncertainty in the thickness measurements amounts to 5 - 10% and the overall uncertainty was below 20%. Excessive scatter in the data above 1 GHz was caused by higher-order mode propagation in the line. 2.4.3 Tan (1981) Similar to Carlson's set-up, Tan used a cavity waveguide resonator at 9.5 GHz to measure tropical vegetation samples (grass, casuarina, rubber leaf, rubber wood) at room temperature. Measurements were made as a function of sample water content. The overall accuracy of the system is estimated to be 10-15% for both the real and imaginary parts of E. Extending Carlson's modeling approach, Tan used six different mixing formulas to model his data. He concluded that the best model that fits his data was the Polder and Van Santen model (1946) with parameters E* = Em and Ai = (0,0, 1). In other words the water inclusions have a circular disc shape within the vegetation host. Again, the main source of error is due to thickness measurements of the plant samples.

2.4.4 Ulaby and Jedlicka (1984) These measurements (Ulaby and Jedlicka, 1984) were conducted using a waveguide transmission technique in three different bands, namely, L-band (1.11.9 GHz), C-band (3.5 - 6.5 GHz), and X-band (7.6 - 8.4 GHz). Vegetation types investigated included wheat, corn, and soybeans. Leaves, stalks, and corn heads were measured as a function of their water content. Also, extracted fluids from these parts were measured and compared to saline solutions. An accurate systematic procedure (McKinley, 1983) was developed to measure vegetation densities as they change with volumetric moisture. Uncertainties in the data were due to sample preparation and data-reduction techniques rather than to variations in measurement system stability. In the modeling efforts conducted, the vegetation medium was considered to be a fourcomponent mixture with the vegetation bulk material as the host and free water, bound water, and air as the inclusions. Also, a three-phase mixture model was attempted with dry vegetation as the host (bulk vegetation material and air) and free water, and bound water as inclusions. The volume of bound water and its dielectric properties were chosen arbitrarily to be 5% and (3.15 - jO), respectively. The reason behind the latter assumption is the view of bound water as a state where water molecules are so strongly bound to colloidal surfaces that they assume the dielectric properties of ice. Another modeling approach was adopted using a two-phase mixture model, in which the host was taken to be the dry vegetation part (bulk vegetation and air) and the inclusions were taken to

be liquid water with effective (or depressed ) dielectric properties. 2.4.5 summary Table 2.1 shows a summary of the previous studies: 36

Carlson,1967 Broadhurst,1970 Tan,1981 Ulaby and Parameter t Jedlicka,1984 System Partially-filled TEM Coaxial Partially-filled Waveguides, cavity Cell Cavity Transmission Frequency 8.5 GHz 100 KHz- 9.5 GHz 1.1-1.9 GHz 4.2 GHz 3.5-6.5 GHz 7.6-8.4 GHz Moisture % 65 80 60 80 Temperature 230C 230C 210C 230C Accuracy E'% 10-20 10 10-20 5 Accuracy E"% 10-20 10-100 10-20 5-37 Plants grass bampoo grass corn corn Tulip tree casuarina wheat taxus rubber soybeans blue spruce Parts leaves leaves leaves leaves branchs wood stalks fluids Table 2.1: Comparison between previous microwave dielectric measurements on vegetation material. 37

From the brief discussion in the previous subsections, we can conclude the following: 1. Only a few attempts have been made to date to study the microwave dielectric properties of plants. 2. The available measurements were made in limited microwave frequency bands. 3. None of these measurements covered temperature ranges beyond room temperatures (20 - 250C). 4. Attempts to model the dielectric behavior of vegetation-water mixtures have been only marginally successful, at best. These shortcomings motivated the development and use of a measurement technique that would operate over a wide frequency range, that is suitable for dielectric measurements as a function of temperature, and that can measure the dielectric constant accurately, rapidly, and non-destructively. This technique is the subject of Chapter 4. 138

Chapter 3 Dielectric Measurement Systems-General Many studies have been conducted in the past (Von Hippel,1954) to examine the dielectric properties of natural and artificial materials. However, very few of these were concerned with vegetation materials. In the past three decades, great improvements have been realized in terms of microwave measurement techniques. The development of automatic network analyzers and sweep frequency measurements has led to the development of better and faster dielectric measurement techniques. This chapter will provide a review of microwave dielectric measurement techniques and systems, with particular emphasis placed on those that may be suitable for vegetation materials. 3.1 Transmission Techniques The measured quantity in this case is the transmission coefficient (both amplitude and phase, Tm and km). The problem is to measure it accurately and then use it to infer the dielectric constant of the unknown material. The most com

monly used trsnsmission systems are the waveguide and the free space systems and these will be the subject of the next two sections. 3.1.1 Waveguide System The block diagram shown in Fig. 3.1 represents a standard system used for measuring the amplitude and phase of the TE10o mode transmission coefficient. The main part of the system is a network analyzer capable of comparing the phase and amplitude of both arms, when the sample holder is empty, and again when the sample holder is filled with the unknown material. If we assume that the sample holder is of length L, we can write (Hallikainen et al, 1985). Tm = (1 Tm R2)e-2L (3.1) where _ propagation constant of the dielectric-filled waveguide and cy = ac+ j. R _ the field reflection coefficient - ZZ where Zo -the characteristic impedance of the waveguides connected to the sample holder. Z and Zo are given by jwlo 2'rr/o =(1 + j/p) (3 Z 2+ 2 (3.2) and jwLO 27rr/o Z= -- == (3o3) 7o Ao/o where w = 27rf, 40

Sweep Coax Oscillator Reference Arm Isolator aNetwork Analyzer >~. Isolator Section Isolator Reference Magic T Coax-Waveguide -Transition 1ert solatorIsolator Attenuator Frequency I S lefArConverter Sample Arm Figure 3.1. Waveguide transmission measurement system.

/.o -permeability of free space, Ao _ free space wavelength, o = (,ho/Eo)1/2, = the intrinsic impedance of free space, =y jo =_the propagation constant in the air-filled waveguide connected to the sample holder. /6o and'- are given by go = 2[1_ ( )2]1/2 (3.4) 2A r A a = a + jp. = 2[(A0)2 _ E]1/2 (3.5) Ao Ac where AX = a/2 is the cutoff wavelength of the guide of width a (for TElo mode). From measurements of /Tm/ and m,, it is possible to determine a and A, from which the real and imaginary parts of E may be determined: (2 [() - (a2 - p2)], (3.6) "= ( )2 (2cf3l), (3.7) In practice, because of the nonlinear relationships between the measured quantities I/Tm and'k and the quantities a and f,, an iterative procedure is used to solve for a and P. The details of the procedure are given in Hallikainen et al (1985).

3.1.2 Free-Space System As shown in Fig. 3.2, the free-space transmission system is basically similar to the waveguide system. The only difference is the utilization of two antennas and a sample holder, in the form of a dielectric slab, instead of waveguide sections. Consequently, the analysis is the same if we set 1/A. = 0 in ( 3.4), ( 3.5), and (3.6). Again, an iterative procedure is used to determine E. 3.2 Reflection Techniques The problem here is to measure the reflection coefficient at the end of a transmission line (both amplitude, IPml and phase, Am) and to try to relate it to E of an unknown medium. Reflection techniques have, in general, two major problems: first, since the reflection coefficients for most natural materials are very close to unity, great care has to be taken in measuring 1pml, and second, the mathematical expressions relating Pm to e are usually derived for an infinite sample, a condition that can not be satisfied in practice. In the next two subsections a brief description will be given for two measurement systems based on the reflection technique. 3.2.1 Slotted Line System This system was used by Broadhurst, as discussed earlier in Section 2.5, and it is shown schematically in Fig.3.3 (Broadhurst, 1970 ). The measurement of dielectric constant can be related to the measurement of the admittance of a

lexible Cable' I Transmitting Horn Attenuator Pulley Systeml' |9 ~ Abso rbi ng Sheets Sample Holder ti 8 (Styrofoam) irectional Coupler \ Receiving Horn L -,,Flexible Cable Variable Attenuator Attenuator Attenuator Sweep Network Oscillator Analyzer Amplitude Phase Pen Recorder Figure 3.2. 3-18 GHz free-space transmission measurement system. 44

COAX WAVE GUIDE r,; SAMPLE EFFECTIVE OPEN _____ I POSITION VOLTAGE STANDING WAVE PATTErN WITH OPEN AT Q r ~~~~~~~~2 )WITH SAMPLE ATO Figure 3.3. A schematic diagram of the coaxial wave guide used for the leaf measurements and the corresponding standing wave patterns assumed in the derivation of the working equations [Broadhurst, 1971]. 45

coaxial transmission line with a specimen of the material occupying some of the space between the coaxial conductors (Broadhurst, 1970). The measurement of the admittance of a coaxial line is equivalent to the measurement of reflection coefficient at the same plane of reference. The characteristic admittance YE of a section of the line filled with an unknown material of permittivity E = c'- j" is given by (Kraus and Carver, 1973) Y'r VE (3.8) = 60 ln(a/b) where a and b are the outer and inner radii of the line. Similarly, for an air-filled coaxial line, the characteristic admittance and propagation factor are given by = 60 l(a/b)' (3.9) And the propagation constants y, and yo are given by.WoE (3.10) and 0Yo - 3 — (3.11) where c =speed of light = In the following mathematical treatment, it will be assumed that the operating frequency is low enough for the line to propagate in the TEM mode only. 46

The admittance YM at point M, refer to Fig. 3.3, can be expressed in terms of the admittence YL at point L, YO, and -yo as follows: YM = Y YL + Yotanh(-oI) (3.12) Yo + YLtanh(-yol)' where I is the length of line between M & L. Since it is impossible to achieve an open circuit at the end of the line, an extra length, 11, is determined where the actual open circuit is located. Using equation ( 3.12) to transform the effective open circuit to point I, YI = Yotanh-yo(ll - 1) (3.13) If we transform this admittance from point I to point L (through the sample), we can show that YL = Y Y1 + Y~tanh('yl,) (3.14) or YL = E Yotanhyo(lI - 1,) + Ytanh(yl.) (3.15) Y, + Yotanhr-o(ll - I.)tanh(^ll(.) Substituting Y, = YoV/ and y- =,oV/E and simplifying we obtain YL = O tanh[yo(l1 - 1,)] + /tanh( ol,)316) 0+YL = Yoi + 4tnanho(I - 1.) (3.16) 47

Equation ( 3.16) relates a measureable quantity, the admittance YL, to the unknown dielectric constant of the sample e. The relationship, however, is not simple and suitable approximations must be used. Broadhurst used frequencies up to 4.2 GHz (A = 7.1cm) and samples of thicknesses less than.04 cm. 1l was found experimentally to be about.3 cm. Hence the maximum values of the above arguments can be shown to be less than.26. Using equation ( 3.16) and the approximation tanh(u); u, leads to YL ~Y YO 0(l -1- 1) + l E1 (3.17) The resulting error is about 7 percent or less. Using the above argument, we can also neglect the second term in the denominator, leading to YL - YO[-o(11 - 1l) + E'ol,] (3.18) Using equation 3.18, E can be calculated from the measured value of YL, 1 YL e,= oL[ -M ~ - 14 (3.19) It should be noted here that equation ( 3.19) is only valid under the following assumptions: (i) Pure TEM propagation mode.

before higher order modes start to propagate, as f = 9.5/ij5 (3.20) shown in Chapter 4). 3.2.2 Probe System Open-ended coaxial lines can be used successfully in measuring the permittivity of unknown materials (Burdette et al, 1980; Athey et al, 1982; Stuchly et al, 1982). A complete description and analysis of this system will be delayed until the next chapter. However, a brief discussion of the theory of operation is given here for the sake of completeness. Figure 3.4 shows a block diagram of the measurement system. It is basically a standard reflection coefficient measurement system with the probe tip acting as the termination load (either immersed or in contact with the sample). The input reflection coefficient at the probe tip, p, is given by P= 5 zo' (3.21) Ths imt epnd n hecoxil ie imnson a wl a E(a 49lb

A; swap Netlwoork terfocW I ollcrl OscIllator Amlyzer Clt - -r Counter Ffrequncy Convertir IP nc / VOU trlect o Mn I Test Cougler Pl)4) D tCruOMI Cam lrI U (AC-7) Led Figure 3.4. Block diagram of the probe dielectric system. Frequency coverage is 0.1-20 GHz. 50

where Zo is the line impedance (50 11 usually) and ZL is the load impedance given by (Deschamps, 1962; Burdette et al, 1980) ZL(w, E) ZL(y Iw, o) (3.22) where t70 and rt are the intrinsic impedances of free space and the measured dielectric medium respectively, co and E are the complex dielectric constant of free space and the medium under test respectively, and w is the angular frequency. For a non-magnetic medium where A =, o, ZL simplifies to 1 ZL(U, E) = -ZL (EWI,EO). (3.23) If the probe equivalent circuit can be modelled analytically, the medium dielectric constant can be retrieved from the measured reflection coefficient; sometimes an iterative solution is required depending upon the complexity of the form of ZL. It is possible, albeit difficult, to relate the measured reflection coefficient directly (e.g., the Method of Moments, MOM)to the unknown E (Gajda and Stuchly, 1983). The analysis, e.g. MOM, and processing time would be enormous using this approach. On the other hand, if we choose the frequency range and the line dimensions such that the field distribution around the probe-tip is dominantly capacitive we could develop a lumped-element equivalent circuit which would facilitate the analysis and data precessing. The equivalent circuit elements could be chosen on the basis of the line dimensions and the operating frequency. In this section only the low frequency

equivalent circuit will be analyzed and the complete one will be discussed in the following chapter. The input impedance for the low frequency equivalent circuit is given by ZL = l/jw(Cf + CO) in free space, and ZL = 1/jw(Cf + ECo) in the medium. where, Cf is the fringing field inside the teflon, and Co is the fringing field outside the teflon and inside the medium. The reflection coefficient can then be expressed as =1 - jwz(Cf + ECo) (3.24) 1 + jwZo(C1 + ECo)' and, solving for E we get = 1-p _ Cf (3.25) jwZoCo(1 + p) Co This equivalent circuit is only valid at frequencies where the line dimensions are small compared to A; i.e., only the reactive field exists with no radiation. Cf and Co are not known and should be estimated using calibration against a standard material such as distilled water. This technique is quite attractive because E can be computed from p in a straightforward manner. 52

3.3 Resonance Technique In the following two sections a brief description will be given of the use of resonant cavities in the measurement of the microwave dielectric properties of matter. 3.3.1 The Filled-Cavity Approach A block diagram of a typical cavity measurement system is shown in Fig. 3.5. A complete theoretical analysis of this problem was given by Harrington (Harrington, 1961). The basic idea is that the dielectric constant of a material filling a cavity is determined by the shift in the resonant frequency fo and the change in the quality factor Q (Russ, 1983). An air-filled cavity is assumed to be the reference with fo and Qo; while the dielectric-filled cavity has f, and Q,. The dielectric constant can then be calculated from 4= (Jo/f.)2, (3.26) and, rQ Q Jt (3.27) The quality factor Qi is in general given by Qi = fi/Afi (3.28)

I _,_ __1 I CAVITY l 1 VARIABLE MCROWAVE TEMPERATUE OSCILLATOR I ETER DIViDER Figure 3.5. Schematic diagram of the measurement set-up for microwave cavity measurements.

where fi is the resonant frequency and Afi is the 3-db bandwidth. Equations ( 3.26- 3.28) are evidently very simple and easy to use, yet there are two problems encountered: 1. If E, is too high, an undesirable large frequency shifts and/or reduction in the value of Q would preclude an accurate measurement of f8 and Q,. 2. For some materials, such as vegetation, it is very difficult to fill the cavity with solid material without some air pockets remaining. This complicates the inference of the dielectric constant of the material. 3.3.2 The Partially-filled Cavity Approach This technique is also called the perturbation technique. Small resonant frequency shifts are attainable by the proper selection of the sample size. The perturbation analysis is given in details in (Harrington, 1961; Russ, 1983). These derivations were based on the assumption that either the sample volume or its dielectric constant are small enough so that the field structure in the cavity is not substantially changed by the insertion of the sample. The shape of the sample is an important factor in determining the appropriate approximate formula to be used. Spheres, discs, and needles are the most commonly used shapes, and among these the needles are the most popular. Let us take, as an example, a TMolo cylindrical cavity with d < 2a (3.29) where, d is the cavity length and a is the cavity radius.

For a cylindrical sample of radius c and length d, (Russ, 1983) shows the derivations leading to w' -WO = -1.855(E - 1)()2, (3.30) WO a 2WS W, -w + j 2Q (3.31) et — 5- w + 1, (3.32) 1.855w,V, and,_ wo 1 1 3.71w ( Qv Q 1 (3.33) where equations 3.32 and 3.33 were derived using equations 3.30, which is only applicable for a needle-shaped sample, and 3.31, which represents the resonant frequency for a lossy circuit. Data processing in this case is very straightforward. However, special care should be taken in the following cases: (i) If the sample length is not equal to the cavity length, a different set of equations is valid (Parkash et al, 1979). (ii) If the sample volume is very small, the changes it produces may not be detectable, and if the sample volume is very large, it could modify the fields, thereby destroying the validity of the perturbation equations. 56

3.4 Comparison Table 3.1 provides a summary of the pertinent features of the various microwave dielectric measurement techniques. An analysis of these features will be given next. 3.4.1 Usable Frequency Band (i) The Waveguide Transmission System L, S, C, and X band systems are possible frequency bands for the measurements, yet for each band a separate waveguide system is needed. This fact makes measurements across a wide band, e.g. 1-12 GHz, discontinuous due to calibration problems. Also, packing an X-band waveguide is very difficult and it is hard to achieve a homogeneous sample. One of the major limitations of the waveguide system is the possible propagation of higher-order modes in the guide, especially in the upper end of the range. Above X-band, the waveguide size becomes impractically small to use. (ii) Free-Space System The free-space system was used successfully in measuring dielectric properties of wet soils and snow samples over the 3-18 GHz (Hallikainen and Ulaby, 1983). The lower frequency limit was imposed by the required sample size and the upper limit by the cut-off frequency of the antennas. A similar system at 37 GHz was also constructed and calibrated. The only high frequency limit seems to be the required smoothness of the sample surface (surface rms roughness should be less

than A/10). (iii) Slotted Line System Since this system utilizes a TEM cell in a coaxial line, it has a much larger bandwidth compared to a waveguide system (Broadhurst, 1970). Broadhurst reported a slotted line system that operated from 100 kHz to 4.2 GHz but he also concluded that excessive scatter in the data above 1 GHz was due to highorder mode propagation. For the coaxial line used in his experiment the cutoff frequency of these modes is given by f= 9.5//i;, which means that a moist leaf can be measured up to 1 or 2 GHz without the occurence of moding problems. (iv) Probe System Since the probe system is basically an open-ended coaxial line, the usable bandwidth is expected to be as high as that of the slotted line system. In the course of this study, however, it was only attempted to operate the system from 100 MHz to 20 GHz. Reduction in the system sensitivity was observed in the low frequency range and an increase of higher-order mode propagation in the high end. A statisfactory compromise can be achieved by using larger probes at low frequencies and smaller probes at high frequencies as will be discussed in the next chapter. (v) Resonant Cavity Systems

The frequency of operation is limited to only one single frequency for each cavity. 3.4.2 Measurement Accuracy and Precision (i) Waveguide System The relative measurement errors Ae'/E' and AE"/E" were estimated on the basis of the precision specifications of the network analyzer /phase gain indicater. They were compared to those observed during the course of measurement and found to be in complete agreement. The results may be summarized as follows: (a) Ae' <.15 and AE" <.17 for all samples tested. (b) (Ls'/E') <.9% at 1.4 GHz and <.7% at 5 GHz for all samples tested. (c) AE"/E" decreases from 37% at low values of e" to 6% for high values of'". The 37% relative precision was observed for e" =.06 and the standard deviation was Ae" =.022. So, even though the relative precision is large, the absolute precision is small. (ii) Free-Space System The total calculated worst case error bounds were plotted against frequency for different sample lengths and for various dielectric constant magnitudes for both E' and E" and were found to be around 10% (except for very low loss materials where the error can be as high as 60 %). The error bounds include uncertainties in both the equipment and in sample preparation. The system was calibrated for absolute accuracy using polymethyl methacrylate (a low-loss material) and water (a high-loss material) and the errors were within the worst case bounds.

It was found that the system accuracy improves with increasing frequency, magnitude of E, and sample thickness. (iii) Slotted Line System The accuracy of measuring the real part was within 10%o, while for the imaginary part sizeable errors were reported (Broadhurst, 1970). It was found generally that the accuracy improves at low frequencies. A check of the precision of leaf measurements was conducted by packing the sample, measuring it, unpacking it, then packing it and measuring it again. The previously mentioned procedure was repeated several times for different samples and at different fre- quencies and an analysis of variance was conducted to separate the instrumental errors from those due to sample variations. The uncertainties in the leaf- thickness measurements amounts to 5 - 10%. In general, the total uncertainties in the measurement system was much better than 20%. (iv) Probe system Athey et al (part 1, 1982) grouped the errors in their measurement system into two types: (1) Systematic errors and (2) nonsystematic errors. The systematic errors, which are due to the network analyzer system, were assumed to be A pI -.003 and =.30. The estimated uncertainties around 1 GHz were found to be within 2% for E' and 8% for E". The nonsystematic errors, on the other hand, were attributed to repeatability of connections, temperature drift, noise, nonperfect probe connector, dirt, imperfect contact with the sample, and inhomogeneities in the substance under test. The system overall accuracy depends on how far the

probe capacitance is from the optimum capacitance value (a discussion of this condition will be given in the next chapter). The nonsystematic errors can be avoided if proper care is exercised during the measurements and by repeating suspicious data sets. According to Athey (1982), the overall system accuracy and precision were within the limits estimated on the basis of the systematic errors alone. (v) The Cavity Systems The precision of the filled cavity measurement system is almost perfect especially if care is taken in replacing the cover and tightening the bolts using a torque wrench. The measurement error for QL for a partially filled cavity is ~1.25%o ( for QL ~ 500) and ~7% fort QL = 200) (Chao, 1985), which means that the measurement error is negligible for E' and less than ~2% for c" (compared to 37% in the waveguide system ). However, the smaller the sample volume the larger are the errors associated with E' and E" due to dimensions measurement errors. These errors can be as large as 10%. 3.4.3 Dielectric Values Limit It is probably a general rule that the higher the magnitude of e is, the better becomes the accuracy and precision of the measurements, as long as the values of e do not allow higher-order modes to propagate. 61

3.4.4 Practical Aspects (1) Sample Size and Preparation From a vegetation dielectric-measurement-system point of view, the waveguide, the free-space, and the cavity techniques are not suitable because it is impossible to achieve a unity filling factor (because of unavoidable air voids inside the measured sample). Also it is impossible to achieve the smooth surface required for free-space system samples. Slotted line and cavity perturbation measurements on a vegetation sample will always suffer from inaccuracies in thickness measurements. The probe system on the other hand, requires a relatively thin sample (at most a few leaves-thick). However, special care has to be taken to insure that the pressure applied by the probe against the sample is high enough to ensure good contact, but not too high to cause squeezing of fluid out of the vegetation tissue or changing the vegetation bulk density (as will be discussed in the next Chapter). (2) Temperature Measurements The best system for the purpose of making dielectric measurements as a function of temperature is probably the free-space system because there are no metal parts in contact with the sample. The waveguide is probably the hardest because large pieces of metal would need to be insulated. The probe system (as will be shown in the next chapter) operates satisfactorily with regard to temperature measurements.

(3) Field Measurement The probe system, no doubt, is superior to any other system for field operation because it is the only nondestructive tool capable of measuring samples without destroying them. Technique Waveguide Free-Space Slotted- Probe Filled- PartiallyFeature System System Line System Cavity filled Usable 1-2,2-4, 3-18 100 KHz-.05-20.4 single single Band 4-8,8-12 1 system 4.2 GHz 1 system, frequency frequency (GHz) 4 systems 2 systems 2 probes per cavity per cavity Accuracy reasonable reasonable bad bad the very Low best good loss Accuracy very good good good Does not good high good work loss Sample small at HF large at HF reasonable small small at HF small Size large at LF large at LF Sample Easy but hard and easy easy hard/ hard/ Preparation lengthy tedious impossible impossible temperature hard perfect hard easy perfect perfect Field hard hard hard easy hard hard Measurements Table 3.1 Comparison between different microwave dielectric measurement techniques. 63

Chapter 4 Open-Ended Coaxial Probe System 4.1 System Description As previously discussed in section 3.2.2, an open-ended coaxial line and a short monopole probe are found to be viable sensors for dielectric constant measurements at microwave frequencies. We shall restrict the discussion here to only open-ended coaxial line probes. As shown in Fig. 3.4, the main part of the system is the microcomputer-controlled network analyzer (HP 8410C) which is employed to measure the input impedance at the probe tip. The probe translates changes in the permittivity of a test sample into changes in the input reflection coefficient of the probe. The automation of the reflectometry system made data acquisition, correction, and processing a straight forward task in addition to the achieved speed of operation. Indeed, the development of such a system would have been impossible only 15 years ago, since the concept of automated network analyzer measurements was introduced recently.

The open-ended coaxial line probe system operates over a very wide frequency band. The.141" probe model, for example, covers the range extending from.5 GHz to 20 GHz. The overall error bounds for both E' and E" were found to be within 10 %o of the measured values. The 10%o figure is very conservative and in some cases it is even better than 1%. Also, since the rounding error in E' and E" is ~.1, at low dielectric values the relative errors can be too large. The lower frequency limit is set by the degraded sensitivity while the upper limit is determined by the cut-off frequency of the next propagating high-order mode as will be discussed later is section 4.3.2 and 4.3.3. Besides the wide frequency band of operation, the probe has the capability of measuring the dielectric constant of test materials nondestructively and rapidly. 4.2 Analysis The analysis of the probe system can be divided into the following steps: error correction, equivalent circuit modeling, and calibration and the inverse problem. 4.2.1 Error Correction There are certain inherent measurement errors when the network analyzer system is used for microwave measurements. These errors can be separated into two categories: (a) instrument errors and (b) test set/connection errors (HP application Note and Burdette, 1980). Instrument errors are those related to random variations due to noise, imperfect conversions in such equipment as the frequency converter, crosstalk, inaccurate logarithmic conversion, nonlinearity

in displays, and overall drift of the system. Test set/connection errors are due to the directional couplers in the reflectometer, imperfect cables, and the use of connector adaptors. Among these two error sources, the latter is the major source of error at UHF and microwave frequencies. These uncertainties are quantified as directivity, source match, and frequency tracking errors. The analytical model used for correcting test set/connection errors is based on the model used by Hewlett-Packard for correcting reflectivity measurements (HP Application note). This model accounts for the three types of systematic errors. Each of them is shown schematically in Fig. (4.1). The measured reflection coefficient can be derived as Piim = S11 + S22P11a (4.1) 1- S22Plla S11 is the directivity term and is due to (a) direct leakage of the incident signal into the test channel via the reflectometer directional couplers and (b) to further degradation by connectors and adaptors. S22 is the source match term and is caused by multiple reflections into the unknown load. The product (S21S12) is the frequency tracking term and is due to small variations in gain and phase flatness between the test and reference channels as a function of frequency. The reflection coefficients pllm and Plia are the measured and actual reflection coefficients, respectively. These three error factors can be determined and calibrated out using three known standard loads with known Plia across the required frequency band. Hence, Pla can then be determined from

L9 ~s0oza uo!,auuo las I9sa,.oj pasn sapom 9 ouW'LT' ant ZLSLZS + (LLS - L Ld) ZZS L L I.. u L'"d eI Ld eL LdZZS. L ~S 4 — (LsLS)eW[d=U4Ld (3) ~ Id.,., i. i d Z}S LZS (q) tI. wld ~~KZ i Z Z I eCl I I,,.l.d 11S ~1 "~" / /1

(Pum - Sir) = S22(Pllm- S) + S12S21) S11 can be determined separately using a sliding matched load termination. The reflection coefficient of the load can be eliminated by multiple load measurements at different path lengths. The loci of these points form a circle whose center is the true directivity error vector. Using short-circuit and open-circuit loads, S22 and S12S21 can be determined (S12 and S21 were lumped together because they always appear as a product). Since the open-circuit condition is hypothetical, because of radiation and fringing fields, a correction to (P1a)O.C. is always made. Also, since the calibration should be done with the probe tip as the reference plane, and since there is no standard short circuit for that situation, liquid mercury has been used as the short circuit termination. This approach proved successfull as long as care is taken to ensure an approximate phase shift of 1800 from the open-circuit reading. A final remark that should be made here about SI, is that its determination is made at the APC-7 connector reference plane and it is used at the probe tip reference plane. This approach neglects the reflections due to the APC-7 connector and any other reflections along the probe especially due to the bent, along the probe line, and any inhomogeneity in the teflon. This approximation is justified by assuming that the APC-7 connector and the probe line are free of defects. This approximation is probably accountable for most of the system errors (accuracy), while instrumental errors can be greatly reduced by data averaging.

4.2.2 Equivalent Circuit Modeling In general, there are two approaches to handling the probe analysis: an exact electromagnetic treatment or an approximate modeling approach. The exact electromagnetic treatment uses either the variational or the moment methods. These approches are exact, but they have a few problems: 1. Computer- time consuming, 2. The exact inverse problem is impossible, and 3. The loss of accuracy due to the approximate inverse problem is high. On the other hand, the approximate modeling treameant is less accurate and more efficient in terms of computer time. The model used to describe the probe behavior has, as shown in Fig.(4.2), the following equivalent circuit parameters (Marcuvitz, 19511; Tai, 1961; Kraszewski and Stuchly, 1983; Gajda and Stuchly, 1983): 1. Co, the fringing field capacitance, 2. Cf, the fringing field (inside the teflon) capacitance, 3. Bw2, the increase in the fringing field capacitance with frequency because of the evanescent TM modes excited at the junction discontinuity, and 4. A, the factor representing the radiative discontinuity field.

, pn k6.6 mm 2.2lom G mmd2.0 mm Longitudlnl gh Frequency Pro Low Frequency Probe Cross Section High Frequency Probe Low Frequency Probe (a) DIelectric Probes Y *% I- c. CR%, C 0. %. AC,,' YR (b) Probe Equivalent Circuit Figure 4.2. Coaxial probe (a), and its equivalent circuit (b). 70

These four parameters are a function of the transmission line dimensions. The admittance in free space is given by Y(E = 1) = jw(Cf + Co + Bw2) + Aw4 (4.3) when the load is a lossy dielectric medium with complex dielectric constant E, Y(E) is given by: Y(e) = jw(C! + CoE + Bw2E2) + Aw4E2.5 (4.4) This is a linear equation with four unknowns Cf, Co, B, and A. In order to determine the equivalent circuit unknowns, two standard materials need to be measured to provide two complex equations or four real ones. Usually distilled water and methanol were used for calibration in this work. Equation ( 4.4) can be solved for the unknown equivalent circuit parameters by solving the matrix equation(4 x 4). It is possible to solve this equation for Cf, Co, B, and A using standard matrix techniques (e.g. diagnonal method). After calculating the equivalent circuit paramaters, the system will be ready to process the reflection coefficient data for the unknown materials. 4.2.3 Calibration and the Inverse problem In calibration we need to solve a (4 x 4) matrix for the equivalent circuit parameters, but in calculating the unknown E of the material under test Equation

( 4.4) should be solved for E. This equation is a complex equation of the fifth order. It was found that an easy method for solving it is through an iterative routine. The algorithm used for correction, calibration, and data processing is given in Fig.(4.3). 4.3 Probe Selection The overall accuracy and precision of any probe system depends on the frequency range of operation, the accuracy of the dielectric constant of the calibration materials, the value of the unknown dielectric, and the nature of the sample under test. 4.3.1 Optimum Capacitance It has been shown (Stuchly et al, 1974) that for a given accuracy of the reflection coefficient measurement, the accuracy in determining the permittivity E is greatest when Co = (4.5) wZox/VE'2 + d'2 where Zo is the characteristic impedance of the line. The expression strictly holds only when the uncertainties in the magnetude and phase of the reflection coefficient are approximately the same, i.e., A~p _ A,. For other cases the optimum value of Co is different for E' and e"; nontheless, in general the value given by ( 4.5) is a good compromise. Figures 4.4(a) to (d) show the calculated optimum capacitance for a variety of materials plotted against frequency. Since the

positions to determine Si, Measure Po.c.. PS.C.. PD.w. PWI Pmat Assume initial values for C,, CO, and A use Po.C., pS.C.' and SI -> calculate S121 and S22 Corredt PD., Pm and I Use PD.w.l Pmeaot, rt O.W.and emethanol tO calcuate new Cu, C,and A (4 X 4) matrix id Cf,, C.., No_ Use obtained Cf. co. B.,and A converge?' 1 ajdAasinitial values Use equivalent circuit parameters and P,,taei to calculate cmta by inspec on Print equha.,nt circuit param,.s.e,,,, and me error in the iteration procedure Stop Figure 4.3, Calibration algorithm for the full equivalent circuit parameters, C1, Co, B, andA.

Optimum Capacitance 2.0 1.8 Methanol \1.6 Low Frequency 1.4 1.2 1.0 o 0 0.8 0.6 0.4 0.2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Frequency (GHz) Figure 4.4(a). Calculated optimum capacitance for methanol(O.1-1 GHz).

Optimnlnum Capacitance 0.12 Methanlol 0.10 High Frequency 0.08 0.06 0 0.04 0.02 0.00. 1.. 1 __ I 1......... 0. 2. 4. 6. 8. 10. 12. 14. 1 6. 18. 20. Frequency (GHz) Figure 4.4(b). Calculated optimum capacitance for methanol(1-20 GHz).

Optimum Capacitance 1.00 Distilled Water -80 \Low Frequency 0.60 0 0.40 - 0.20 0.o0 0.1 0.3 -A 0.. _0I I 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Frequency (GCHz) Figure 4.4(c). Calculated optimum capacitance for distilled water(O.1-1 GHz).

Optimum Capacitance 0.05 -_ Distil led Water 0.04 High Frequency 0,03 0 0.02 - 0.01 0.00 * I I. I I I 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. Prequency (GHz) Figure 4.4(d). Calculated optimum capacitance for distilled water(l-20 GHz).

capacitance of an open-ended coaxial line is typically between.02 and.04 pf, the optimum capacitance condition is satisfied for only some materials over a limited frequency range (e.g., distilled water above 2 GHz). The practical situation is not really that stringent and a typical probe can operate satisfactorily over quite a wide band of frequency and range of dielectrics as will be discussed in the next section. The optimum capacitance condition is only useful as a design guideline because the probe would still function satisfactorily in completely different situations, albeit with some degradation in performance. 4.3.2 Sensitivity The probe translates variations in the permittivity of the test material into variations in the measured amplitude and phase of the reflection coefficient. The variation in the measured phase depends on e" as well as e'. However, the effect of e" on Acp is of less importance compared to the effect of e' specially at low frequencies. Thus, A = f(E', E) f(E) - A similar argument for AA can lead us to AA = f(E', e") f(E") We can define S',, the probe phase-sensitivity to E', as r = ~limita [ i9AP/i] (4.6) AE'/e' el apo =( > ) ~~~~~~(4.7) 7 8a,

We can interpret the sensitivity S, as the ratio of the fractional change in the function Vp to the fractional change in the parameter a', provided that the changes are sufficiently small (approaching zero). Similarly, S can be defined as tans dco S t=(- C8tane5 (4.8) St'n" = ( )atan(4.8) A third sensitivity term Se= (: ) (4.9) may also be defined for f". The corresponding relations for A, where A is the magnitude of the reflection coefficient, can be defined as follows: -' aA VS =(-A)a c -(4.10) tanS aA Stan8 =( A 8tan6' (4.11) and d' aA Se" = ( " (4.12) Figures (4.5)-(4.12) show plots of Sw', Sf, S,., and SA, versus frequency for 4 different materials: distilled water, methanol, 1-butanol, and l-octanol. The following conclusions can be drawn: 1. SeA, has the highest value especially at low frequencies (Fig.4.6). This shows that E" has a large sensitivity to the amplitude measurements, and shows how critical the amplitude is in this type of measurements. 2. Se~ is larger than Se at low frequencies and for high loss materials (Fig.4.8). As the frequency increases, S, decreases while S! increases and they become equal around 5 GHz (for distilled water). This trend continues as 79

DISTILLED.WATER 7, - SPP (REAL TOASE) SW IM TOAE) 6. 5. - 4. z7 1. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.9 1. FREQUENCY (GHz) Figure 4.5. Calculated probe sensitivity for distilled water (0.1-1 GHz). 80

DISTILLED.WATER 6. = S(PREAL TO PHUE) IS MAG TO PM Pj - SA (IMPG TO AP.) 5. F 4. Z 3.C~A 2 0. I I I I 0.0 2.0 4.0 6.0 8.0 10.0 12.0 FREQUENCY (GHz) Figure 4.6. Calculated probe sensitivity for distilled water (1-20 GHz). 81

METHANOL 3. SPPREAL T. SPA h SPA (REAL AlP. SEP IMP)A 3. 2. 2. z 1. 0. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FREQUENCY (GHz) Figure 4.7. Calculated probe sensitivity for methanol (0.1-1 GHz). 82

METHANOL 3. -e- SWP IMAG TO U -* S(M I up.) 2. HF 2. 1.., cr 0. 0.0 2.0 4.0 6.0 8.010.012.014.016.018.020.0 FREQUENCY (GHz) Figure 4.8. Calculated probe sensitivity for methanol (1-20 GHz). 83

1 -BUTANOL 0. - SPRAL Mm PHASE) -e- SI1MAG 10 PHASE) o. Cl Im~0. O e3 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0,7 0.8 0.9 1.0 FREQUENCY (GHz) Figure 4.9. Calculated probe sensitivity for 1-butanol (0.1-1 GHz). 84

1 -BU TANOL 7. x- SPA(AL TOD 6. 5. 4. CI) V: 3., 0.0 2.0 4.0 6.0 8.010.012.014.016.018.020.0 FREQUENCY (GHz) Figure 4.10. Calculated probe sensitivity for 1-butanol (1-20 GHz). 85

1 -OCTANOL 1. — L SPA TO Ai. 0 — SPMA TO k).) x SA IMAG TO.) H_ 1.1 C,.) 0. O. 0.0 0. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FREQUENCY (GHz) Figure 4.11. Calculated probe sensitivity for 1-octanol (0.1-1 GHz). 86

1 -OCTANOL 7. -— ~HASE) -- - SPA EAL TO MP4 6. 5. > ~-0 4. ~) 3. 0.0 2.0 4.0 6.0 8.010.012.014.016.018.020.0 FREQUENCY (GHz) Figure 4.12. Calculated probe sensitivity for 1-octanol (1-20 GHz). 87

the frequency increases, and Si becomes larger than S$. This observation shows the increased importance of the amplitude measurement at high frequencies. In other words, E' at low frequencies depends mainly on p, while at high frequency it is more sensitive to A. This is due to the increased role of the radiation term Aw4 in Eq. ( 4.4) with increasing frequency. 3. S9, is generally higher than SA (e.g., Fig.4.7), which shows that e" is more sensitive to p than E' is sensitive to A. 4. For l-Butanol and l-Octanol (Fig.4.10 to 4.13), SeI and So.. increase with frequency, S, is roughly constant with frequency, and SA is almost zero. 5. The sensitivity of the probe generally increases with an increase in its diameter (and hence its lumped capacitance and radiation resistance). 4.3.3 Higher Order Modes Open-ended coaxial lines can be modeled as a simple capacitance, Co, especially at low frequencies (where the free space wavelength is much larger than the line cross-sectional dimensions). When the frequency of operation increases, the line starts to radiate and the energy is not concentrated in the reactive fringing field any longer. In this situation Co increases with frequency due to the increase in the evanescent TM modes being excited at the junction discontinuity. An expression of the form Co + Bw2, where B is a constant dependent on the line dimensions, should be used in place of the constant value Co. Futhermore, when the medium has a high dielectric constant, these modes may become propagating 88

modes. The first of these modes is the TMol mode which can propagate when Ae < 2.03(a - b), where A, is the wavelengh in the medium, and a and b are the outer and inner line radii. Table (4.1) shows the cut-off wavelengh for the probe types used in this study along with their line dimensions (Athey, 1982): Cable type a( mm) b( mm ) a/b AX (mm).085" Teflon.838.255 3.282 1.177.141" Teflon 1.499.455 3.295 2.129.250" Teflon 2.655.824 3.222 3.764.350" Teflon 3.620 1.124 3.221 5.067 Table (4.1): Dimensions and cut-off wavelengths for the TMo0 mode for the probes used in this study. If the frequency is high enough such that the wavelength in the medium is shorter than A,, moding will occur. To calculate the wavelength in the medium, the following equation can be used (Ulaby et al, 1982): Ao 89

where A6, A0, E' and 6 are as defined earlier. In order to avoid the moding problem, care must be taken when materials with high dielectric constants are measured. Usually this probem is encountered in two situations: 1. distilled water and saline solutions at high frequency, and 2. thin samples placed against metal background. Table (4.2) shows the calculated wavelength in the medium A, as a function of frequency for distilled water: f(GHz) 1 2 4 6 9 10 20 30 40 (A,)c(mm) 33.7 16.9 11.7 5.825 4.05 3.70 2.21 1.75 1.49 Table (4.2): (A.). for distilled water. From this table we can conclude the following: 1. The.085" probe may be operated at frequencies higher than 40 GHz, 2. The.141" probe may be operated at f < 21 GHz,

3. The.250" probe may be operated at f ~ 9 GHz, and 4. The.350" probe may be operated at f < 6 GHz. It was found experimentally, however, that this theoretical limit does not strictly apply. The practical cut-off frequencies are slightly lower than the calculated values. It should be noted that whereas a smaller probe can operate over a wider frequency range, its sensitivities are smaller in magnitude than those of larger probes. 4.3.4 Contact and Pressure Probem The calibration procedure involves measuring two standard liquids (usually distilled water and methanol). The open-ended coaxial line (with or without a ground plane) is suitable for measuring liquids as long as care is excercised to avoid air bubbles at the probe tip. Also, the fact that the calibration was carried out using liquids made the probe more suitable and more accurate for measuring liquid and semi-liquid materials. Semi-solid materials can also be measured accurately since the surface can deform to comply with the probe tip and achieve a good contact (an example of semi-solid materials is cheese). On the other hand, solid materials are very hard to measure using ordinary probes. When measuring the dielectric constant of a solid material, it is crucial to achieve a perfect contact with the mterial under test particularly in the immediate vicinity of the probe tip. As will be discussed later in this chapter, some new probe designs with very smooth surfaces and ground planes were built, tested

and found suitable to measure solid materials. Measuring vegetation materials, particularly leaves, is usually a problem since any deformation of the plant part would cause an immediate cellular rupture and possible flow of the included liquids, in addition to the change in density with increasing pressure. It was found that for each vegetation material and plant part there is an optimum pressure above which the part will be crushed and below which the contact will not be perfect. This optimum pressure is found experimentally for each part and should be maintained constant during the experiment ( a digital scale was used to check pressure). Usually a pressure of few hundred grams applied on the.141" probe tip (a.lcm2) is sufficient. 4.4 Probe Calibration 4.4.1 Choice of Calibration Materials The overall performance of the system depends on the choice of calibration materials as well as the accuracy with which we know their dielectric properties. This section gives few guidelines regarding the selecting of proper materials for a particular application. During the course of this work only distilled water and methanol were used for calibration. The dielectric constant of water is the highest known in the microwave band and that of methanol is approximately one half of it. For wet vegetation materials, it is a good idea to use water as a calibration material. On the other hand, for dry vegetation materials, a different combination may be better. Butanol, e.g., can be used in place of water since its

dielectric constant is about half that of methanol. The calibration liquids should have, in general, the following features: 1. their dielectric properties should be known fairly accurately as a function of frequency and temperature. 2. both must have a reasonably large imaginary part (any lossless material is not suitable for calibration). 3. the dielectric properties of the two materials should be significantly different (e.g., it is not recommended using two saline solutions with different salinities). 4. the two materials should have dielectric values that cover the expected range of the material under test. 4.4.2 Error Analysis A measurement system usually suffers from three major sources of error, namely the systematic, the random, and the illegitimate errors. The errors in the probe measurement technique can be summed up as follows: 1. Systematic Errors (a) System S parameters (S11, S12, S21, and S22), (b) Probe model accuracy, (c) Experimental conditions and standards, and

(d) Conditions of the sample under test. 2. Random Errors (a) Network analyzer precision, (b) Harmonic skip problem, (c) Noise, and (d) Sample conditions. 3. Illegitimate errors (a) Blunders, and (b) Chaotic. Before proceeding into quantitative estimation of errors, the following assumptions will be made: 1. The error correction procedure is perfect (for the system S parameters). 2. The sample conditions problem does not exist for liquids (since they are homogeneous and since care was taken to avoid air bubbles at the probe tip). 3. The harmonic skip problem is cured through averaging (of 4 sweeps and 4 independent measurements). 4. Since each time the computer reads the A/D board it actually reads it 30 times, the noise is eliminated.

5. Illegitimate errors can be detected and eliminated by inspection. Comparing this list to the errors' list, the remaining errors are: 1. Model accuracy, experimental conditions, and standards. 2. Network analyzer precision. In this analysis, it was assumed that 1. AE =2.%, 2. AA = ~.05dB, 3. AO =.30, and 4. Since the number of independent samples is 4, then AE (4 independent measurements) = AE (1 measurement)/2. The estimated precision and accuracy of the probe system were evaluated and plotted as shown in Figs. 4.13-4.18 for yellow cheese (.141"), white cheese (.141"), 1-octanol (.250"), 1-octanol (.141"), 1-butanol (.250"), and 1-butanol (.141"), respectively. In order to evaluate the probe performance; several standard materials were measured and plotted along with the calculated values. An example is shown in Figs. 4.19 and 4.20 for 1-butanol. From this error analysis, it was found that the overall system accuracy and precision are within 10.% (including system and sample errors). The estimated precision and accuracy of the probe system were evaluated and plotted as shown in Fig.(4.19)-(4.20) for l-Butanol.

.14 1 "NGP-YELLOW -CHEESE 4= -- REAL PART PRECISION IMAG PART PRECISION -- REAL PART AmURACY --- IMAG PART ACCURACY 3 ~ / iC 2I rf 0 \ 0.0 5.0 10.0 FREQUENCY (GHz) both accuracy and precision. t le - --

141 "NGP -WHITE- CHEESE -- REAL PART PRECISION - IMAG PART PRECISION -e- P PART ACCURACY XxIL PAr A-CURAEY E-43 1 2 0. |L,, 0.0 5.0 10.0 FREQUENCY (GHz) Figure 4.14. Estimated relative errors % for measurements on white cheese both accuracy and precision. 97

35 \ REAL PART PRECISION \ - IMAG PART PRECISION \ - REAL' PART ACCURACY - IMA PART ACCURACY 30;a 25 20-'5 z \ \ 10 M5 0. I 0.0 0.2 0.4 0.6 0.8 1.0.o FREQUENCY (GHz) Figure 4.15. Estimated relative errors % for measurements on 1-octanol both oth accuracy and precision using the 0.250" probe. 98

- REAL PART PRECISION -- IMAG PART PRECISION 25 REAL PAoR ACNRAC II RMAG PA ACfCURACY 20 15 10 0 0.0 5.0 10.0 15.0 FREQUENCY (GHz) Figure 4.16. Estimated relative errors % for measurements on 1-octanol both accuracy and precision using the 0.141" probe. 99

25 25REAL PAR PRECISION - IMAG PART PRECISION -e- REAL PART ACCURACY - IMAC PART ACXURACY 20 C 15 accuracy and precision using the 0.250" probe. 100

~ REAL PART PRECISION 10 IMW PART PRECISION REAL PART ACCURACY - IMAG PART ACCURACY 0 8 >a- 6 4 2: O. _._ i, I 0.0 5.0 10.0 15.0 FREQUENCY (GHz) Figure 4.18. Estimated relative errors % for measurements on 1-butanol both accuracy and precision using the 0.141" probe. 101

1-Butanol (Prob System Calibration) 20. 18a. C Real 14. 4. ~~~~~~~~~~~Ref.2 12.' Measured 0 *-4 10. cn 8. 6. 2. 0. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. Frequency (GHz) Figure 4.19. Comparison of calculated [ref. 2 is Bottreau et al, 19771 and measured data using the 0.141" probe for 1-butanol (real part).

1-Butanol (Prob System Calibration) 8. Imag I _ Ref.2 Measured 5. F-A~~~5 ~ O*0 (.0) 4. 3. 2. 0. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. Frequency (GHz) Figure 4.20. Comparison of calculated (ref. 2 is Bottreau et al, 1977J and measured data using the 0.141" probe for 1-butanol (imaginary part).

4.4.3 Thin Sample Measurements The sample under test was assumed to be a semi-infinite medium. This assumption is impossible to achieve practically; however, it was found that the fringing and radiating fields decay rapidly with distance away from the probe tip. A simple experiment was designed to show the validity of the semi-infinite assumption. A stack of paper sheets, with variable thickness (1 up to 30 sheets), was measured against two different backgrounds. The background materials were selected to be plexiglass and metal in order to provide a large contrast (refer to Fig. 4.21). The results of this measurement are shown in Fig. 4.22(a) to (c). The following observations can be made regarding these figures: 1. One sheet (~.1 mm)is too thin and does not satisfy the semi-infinite medium condition. 2. At 1 GHz, at least 30 sheets are required to satisfy the thick sample condition (3 mm). 3. The higher the frequency, the less stringent this condition becomes (at 8 GHz it is about 2 mm). 4. Since paper sheets are practically lossless, this condition is even easier to satisfy for lossy materials. 5. By intuition, we can state that the larger the probe diameter is, the thicker the required sample gets. 104

PrOt \E field To A V reflectwiwter *I —---- Very thict layer of dielectric c (a) Prob against seei.tnfinits layer Thin layer riglass Thin layer of material of mrterial (b) Probe gainst thin laye withs O different baPkr ms Figure 4.21. Probe technique for measuring dielectric of (a) thick layers and (b) thin layers. 105

F= 1.OGHZ(PAPERS) 12. 11. x PAPER OVER MEAL 0 PAPER OVER PLEXYCLASS x 10. 9. L 8. 5. 4. x 3 _ x. 2.1. 0. O. _I i I....' I i x'; 0.2. 4, 6. 8.10.12.14. 16.18.20.22.24.26.28.30. NUMBER OF SHEETS Figure 4.22(a). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=l GHz. 106

12. F=5.OGHZ(PAPERS) 11. x PAPER OV METAL o PAPM OV PLEXYLASS 10. 9. -x 8. 7. x 6. x 5. 4. 3. xX 0o o x [ 0 o0 2. 1. 0. 2. 4. 6. 8.10.12.14.16.18.20.22.24.26.28.30. NUMBER OF SHEETS Figure 4.22(b). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=5 GHz. 107

12. F=8.0GHZ(PAPERS) 12.. 11. x PAPER OVER METAL o PAPER OVER PLEXYCIASS 10. 9. 8. )1' 7. - x 6. 5. 4. xI 3. o ~0 O O O~x x 0000 0 0 0 2. 0. O. 1 I I I 0. 2. 4. 6. 8.10.12.14.16.18.20.22.24.26.28.30. NUMBER OF SHEETS Figure 4.22(c). Comparison of a measured stack of sheets against a metal background and against a plexiglass background versus the stack's thickness at f=8 GHz. 108

As a rule of thumb, the sample thickness should be approximately equal to the probe radius. The previous discussion has shown that a sample 3 mm in thickness is suffcient (using the.25" probe) to satisfy the semi-infinite condition for any material and across the entire frequency band of interest (.1-20 GHz). For dielectric measurements of vegetation leaves, however, a single leaf does not have sufficient thickness to satisfy the above conditions. So, a stack of leaves, usually 8 or more, is used and 2 measurements are taken against plexyglass (or teflon) as background and another 2 measurements are taken with a metal background. It is advisable to check that these 4 measurements are consistent and that the variations, if any, can be attributed to sample conditions (and not to sample thickness). In order for the probe to be useful for measuring live or intact plants, it should be able to measure samples that are thinner than the minimum thickness required (3 mm). A semi-empirical formula was developed, tested, and has proved to work satisfactorily over the frequency band of interest. The exact mathematical analysis was fairly complex and hence we took a semi-empirical approach. Assume that a TEM signal is propagating in medium 1 and impinging on a dielectric slab of known thickness d and known permittivity E2. The slab is terminated in a semi-infinite medium of dielectric constant C3 (as shown in Fig. 4.23). If all multiple reflections are considered, we end up with the following general equation for the input impedance at the interface between media 1 and 2 (Ulaby et al, 1982): 109

medium 1 Z Probe ->Z ~J medium 2 ~2 —> Z2 Y2 Unknown material R 2 medium 3 3 — > Z3, 3 Background material Figure 4.23. Thin sample configuration against a background material (known).

1+ R2e-j372d Zin = Z2( R2 e-j'7d (4.13) where, R2 + - Z2 (4.14) Z3 +Z2' 2- A o2r, (4.15) and Z1, Z2, and Z3 are the effective impedances of media 1, 2, and 3, respectively. Equation (4.13) can be rewritten as: e-Y2d (Y - Y+ )(Y2 + Yin) (4.16) Y2 - Ys Y2 + Yin where Y2, Y3, and Yin are the admittances for media 2, 3, and the input admittance respectively. This equation can be solved for Y2 by iteration if we know the thickness d, Ys of a known background, and the measured Yin. The material under test is generally very thin (e.g., a vegetation leaf), so the error in measuring d can be large, in addition to the fact that the solution is oscillatory and a very strong function of thickness. It was suggested to use two different background materials to eliminate the errors associated with the thickness measurement. We will denote the two different backgrounds by the superscripts 1 and 2; hence, e i2d - (Y2 + Yl)) (Y2 l)) (4.17) (Y2 - y3(l))(y2 + Y, )) also, 111

(y2 +'(2))(r: (2)) ( )(Y2 + y()) (4.18) (Y2 3 (Y2 + Ytn) After straightforward manipulation we obtain the general equation: y y()y(2) (y(1) _ y(2)) + y(l)y(2)(y(2) _())(4.19) (y(2) - Y)) - (Y(2) _ y3()) This equation is valid for any 2 media with known Y(1) and y(2) and 2 known measured input admittances Yi() and Yi). A special and useful case can, however, be deduced by putting Y,(') = oo (i.e., medium 1 is metal). Y2, in this case, will be given by Y2 = YYi y) + y(2)(y(2) - ()) (4.20) The admittances of the media are those seen by the probe; hence, they depend on the probe equivalent circuit. A special case can simplify the last expression by assuming the simplest equivalent circuit, which is a capacitor. 62, in this case, is given by 62 = (1) (2) (2)(E2)-)) (4.21) = rn iin +" where 62, e(2),, ), and e,2) are the relative dielectric constants for the sample under test, the second background medium (the first is metal), the measured input e for background material 1 and material 2, respectively. It was found experimentally that Equation ( 4.21) is valid only at low frequencies, while Equation ( 4.20) is valid across the entire frequency range of interest (except when the frequency is high enough to cause moding). The validity of this semi-empirical approach 112

1.0 GHz 90. - 70. 0 s50U) 40. < 30. 30. (.) 20 10. 0 - t X I I' I i 1 O. 10. 20. 30 40. 50. 60 70. 80. 90 E' MEASURED Figure 4.24(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 1 GHz(real part). 113

1.0 GHz 40 - 35 - U 30 25 D U 20 10. 5. 0 0. 5. O. 75. 20. 25.30, 35. 40, 45 E" M EASU REO Figure 4.24(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 1 GHz(imaginary part). 114

8.0 0G-!z 90 70 C tO. - 50 - J < 30 20 - 10. 0.1 0. 2.30 40. 50. 60. 70. 30. 90 E' MEASURED Figure 4.25(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 8 GHz(real part). 115

45. 40 3.5 L0 30 25 U 20. U 1 10 Li' iX".. I I iI I I 0. 5 1 0. 15. 20. 25. 30. 35. 40. 45. E'' MEASURED Figure 4.25(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.250" probe at 8 GHz(imaginary part). 116

1.0 GHz 90. - 70. - @ 60. < 50. -. 10. 0. 0.10.20.30 40. 50. 60 70.80.90 E' MEASURED Figure 4.27(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 1 GHz(real part). 117

1.0 GHz 45. 40 35. w 30. - 4 25. - D U 20. - U 15. 10. 5. -. I' " l l l'l'' 0. 5. 10. 5. 20. 5. 30. 35. 40. 4.5. E"' MEASURED Figure 4.26(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 1 GHz(imaginary part). 118

8.0 GHz 90. 70. Li 60/0. I < X50 () 40..30. 20. 10. 0. 10. 20. 30 40. 50. 60. 70. 8O. 90 E' MEASURED Figure 4.27(a). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 8 GHz(real part). 119

8.0 GHz 45. 40..35. Q U 30 25 U 20. _j:) 1.5., 10. 5.' X I I I t" I' I I 0. 5. 1 O. 15. 20. 2 5. 30 35. 40. 45 E"'' MEAU RED Figure 4.27(b). Evaluation of the thin-thick sample formula (refer to text) for the 0.141" probe at 8 GHz(imaginary part). 120

9/12 FRESH CORN LEAVES 0.141" 100 - EP ONELEAF/PL c. 9 EPO4E ONE L 90 -s- EP LAVEA /PLX. * EP FOrIJLA z 4080 20 10- _,0 - L s...L _ _.. 0 I.2 4. 6.. 10. 12. 14. 16. 1. 20. FREQUENCY (GHz) Figure 4.28(a). Spectra of measured one leaf/metal, one leaf/plexiglass, and thick stack/plexiglass along with the calculated values from the thin-thick formula (real parts). Aborve 11 GHz high-order modes propagation (upper 2OO~121 121

9/12 FRESH CORN LEAVES 0.141" 50 ED ONE LA PUG. 45 =' — ED ONE [Buffs E 45 - ED 11 LEAV/PLX. -- ED FaRKLA 40 35 30 NO 25;, ti 5 -a -. F'. —. —-_ —--— ~ ---. o!, I I' i 1__~ J 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. FREQUENCY (Gliz) Figure 4.28(b). Spectra of measured one leaf/metal, one leaf/plexiglass, and thick stack/plexiglass along with the calculated values from the thin-thick formula (imaginary parts). Above 11 GHz high-order modes propagation (upper curve) causes large errors. 122

was tested for a wide frequency range, wide range of dielectric values, and for the.141" probe (Table 4.3). The results were found to be very satisfactory as shown in Table (4.3). Figures (4.24) to (4.27) show how well this approximate model works. Figures 4.28(a) and (b) show spectra of an example of these measurements for thin and thick samples against various backgrounds. The data above 11 GHz was plotted to show how high-order modes can propagate when we use a metal background and a very thin sample. To avoid this problem, however, we can use either a thicker sample or a background material other than metal. f(GHz) 1 2 4 8 # points 24 25 25 25 El slope 1.0265 1.0078 1.0026.9594 E' intercept -2.03 -1.2728 -1.0795 -.5036 ca variance 15.03 11.51 8.90 7.81 d p.9776.9829.9858.9849 e" slope 1.0306 1.0351.9834.8726 E" intercept -.0707 -.3509 -.2225.2683 e" variance 4.38 1.70 1.43 2.34 e' p.9610.9684.9660.9601 123

Table (4.3): Evaluation of the thin-thick formula for the.141" probe. 4.4.4 Comparison to the Waveguide Transmission System As was discussed earlier in Chapter 3, the transmission technique is, in general more accurate than the reflection technique. A comparison between both systems provides a useful confirmation of the validity of the probe-system accuracy. The choice of material was a problem since the sample requirements are different for the two techniques. Yellow cheese was finally selected because it is suitable for both systems. As shown in Fig. (4.29) the agreement is very good and the error is within the expected ~5%o bounds. This evaluation test gave us confidence in our measurement techniques to go ahead and start measurements on vegetation samples. 4.5 Probe Usage and Limitations-Other Probe Configurations The standard probes were found to have the following features and limitations: 1. Wide frequency band (.5 - 20 GHz for the.141" and.05 - 9 GHz for the.250"). 2. Accurate to within ~5% for all values of e' and to within ~10%o for all values of E" except for low loss materials (because rounding error is ~0.1). 3. The system is very suitable for temperature measurements. 124

30 o C-band Guide 28 x X-band Guide 26 * Dielectric Probe 24 Material - Yellow Cheese T = 25~C 22,me 20 I,_ 14 1 o 4 | C-band Guide 2 L X-band Guide 0 1 2 3 4 5 6 7 8 9 10 11 12 FREQUENCY (GHz) Figure 4.29. Comparison between the probe and the waveguide systems.

4. The system is very suitable for measuring liquid or semi-liquid materials but is difficult to use with solid materials. 5. The probe is suitable for non-destructive and in-vivo measurements. Other Probe Configurations For standard cables, the ratio r z.3 and is kept constant in order to maintain Z0 constant (refer to Fig. 4.2). In order to build an "optimum" probe, it may be necessary to change this ratio to increase the probe sensitivity over a particular frequency band and a given range of c. The cut-off frequency of the first higherorder mode is proportional to (r2 - i) while the sensitivity is proportional to the probe tip area, i.e. to w(r2 - r2). Thus we have two major objectives with 1 2 opposing requirements: 1. To avoid moding (r2 - rl) should be small. 2. To increase the sensitivity, Ir(r2 - r) should be large which means (r2- r1) should be large too. Preferrably, the ratio (a) should be kept constant in order to keep the cable characteristic impedance matched to the probe tip. 126

Chapter 5 Measurement Results This chapter presents the experimental results obtained using the open-ended coaxial probe system. Gravimetric moisture content M. was used in this chapter, instead of the volumetric moisture content M, because it is a directly measureable quantity, while M, is dependent on vegetation density. Vegetation density is very hard to measure, especially for leaves, and the density data measured in this study represents an approximate estimate at best. For the most part, the dielectric data presented in this report will be the actual measurements derived from the probe measurements. In some cases, however, the measured variation of E as a function of moisture will be presented in the form of plots based on regression equations generated using actual data. This is done for the purpose of making presentations clearer in cases where multiple plots are included in a given figure. It should be noted that these regressions provide excellent fits to the data and probably describe the moisture dependence of E better than the actual data. The data presented in this chapter is a subset of that presented in Appendix A. The primary purpose of this chapter is to acquaint the reader with 127

the observed dielectric behavior. Interpretation and modeling of the data are the subjects of Chapter 6. 5.1 Plant Type, Part, and Location 1. Plant type Plant types (species) vary depending on the following parameters: (a) density, (b) salinity, (c) bound water content, and (d) how the vegetation material shrinks when it dries out. Salinity and bound water effects are more dominant at low frequency, while density effects are more obvious at low moisture levels. Figure 5.1 shows a comparison between corn (Zea Mays) leaves and soybean leaves at 1 GHz. Corn leaves have, in general, higher values of c' and E" than soybean leaves. The difference can be attributed either to measurement errors in the dielectric constant and moisture content or to physical and physiological differeces. Figure 5.2 shows another comparison between corn stalks and black spruce tree trunk to test the effects of plant type on high density plant parts. The tree samples were measured at moistures less than 40% (graviometric). Corn stalks have a lower E for dry samples, which can be attributed to density effects. 2. Plant part In order to illustrate the differences between plant parts, we will test two different parts from the same species. Corn leaves and corn stalks are compared at 1 GHz in Fig. 5.3. These two plant parts show comparable 128

45. - CoTlaves al) CornLeaves Imac I.) 40. _L =eaq) 35. C 30 f = 1 GHz T = 22~C o 25. Q 20. 15. 10. 5. 0. 0o. 0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure 5.1. Comparison between corn leaves and soybeans leaves. Curves were fitted to measured data using a second order polynomial fit. 129

zo 5orrsealks (Ral) orrrst. 1k (Laag. ) 15. f 1= GHz 0 T = 220C 10.... 5. 0.0 0.1 0.2 0.3 0.4 0.S Gravimetric moisture Figure 5.2. Comparison between corn stalks(measured on the inside part) and tree trunk (Black-Spruce). Curves were fitted to measured data using a second order polynomial fit. 130

45. rnrLeaves e1) 40.~ dCor s ) 35. fG I GHz VI TT=220C o 25. 20. C) 131 15. 0. 0.0 0.2 0.4 0.6 0.8 Gravimetric moisture 131.

trends and magnitudes for both E' and E" in spite of the fact that their densities are different. 3. Part location It was observed that plants have a moisture distribution profile, especially tall plants like corn. Figure 5.4 shows the dependence of e', E", and Mu on height (above the ground) for a corn stalk of a fresh plant. The measured dielectric constant varies quite significantly as a function of height while the measured volumetric moisture exhibits a weaker dependence. This behavior may be explained by the fact that when the probe is used to measure the dielectric of a corn stalk from the outside sheath, it actually measures e of the sheath (leaf) material surrounding the stalk, and not the stalk itself (because the fringing field of the probe has an effective penetration depth of only few millimeters). The moisture determination, however, is performed for the stalk including the sheath and the inside. Hence, Fig. 5.4 should not be considered quantitatively and the general trend only matters here. 5.2 Frequency Dependence Figures 5.5 and 5.6 show the frequency behavior of the dielectric constant of corn leaves at different volumetric moisture levels. The trends in these two figures can be compared to those of saline liquid water ( refer to Fig. 2.1 ) and to those of bound water ( refer to Fig. 5.18 ). The low frequency behavior of e" is similar to those exhibited by both saline and bound water. At high 132

FRESH aCN STALKS 60 T-25.0 F l.OGHZ |-.[PS. (REAL PARIT) O50 EPS. (IIAG. PART) I OOXMV VOLUMETRIC MOISIUR[ ( 1001 1 40 ELECTRIC NSTANT 30 EPS. 0 0 50 100 150 200 250 HEO11HT Ab1E RORJND (CtM) Figure 5.4. Measured dielectric constant and calculated volumetric moisture for fresh corn stalks as a function of height above the ground (cm).

10/15tl/1985 O. 1 41 " NGP NEW CORN LEAVES YS. FREQUENCY P.400.0 GMS 30 MYs 25 HY 20, EPS(REAL PART) 2S 95 0 -' 10'B' _ __, — - 0.336 0.288 ~S +_== o.z28 "-a ~ 0.13 - -- -.x 0.029 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ) Figure 5.5. Measured spectra of the dielectric constant of corn leaves with volumetric moisture M, as parameter (real parts).

p40. 141onNO NEW CORN LEAVES VS FREQUENCY 1 4 I 0 EPSOMAFGINARY PART)) 6~~~~~~~~~~~~~~~~~.3 2~~~~~~~~~~~~~~~~~.2 0 2 4 6 a I 0 1 2 1 4 1 6 18 0 2 FREQUENCY (GHZ) Figure 5.6. Measured spectra of the dielectric constant of corn leaves with vl umetric moisture M. as parameter (imaginary parts).

frequencies, however, f" increases with f because of the free water component. For the medium to low moisture samples (M. <.2), f1 does not increase with increasing f, but stays rather constant or decreases slowly with f. This behavior is attributed to bound-water domination at low moisture levels (because the bound relaxation frequency is below.2 GHz and its Cole-Cole shape factor is.5, e" exhibits a very slowly varying dependence on f for f > 2 GHz, as illustrated in Fig. 5.18). The dielectric loss factor e" has a minimum around 2 GHz and this minimum becomes less sharp with decreasing moisture content. This minimum separates the low frequency region (where losses are dominated by conductivity and bound water) from the high frequency region ( where losses are dominated by free water relaxation with fo = 18 GHz at room temperature). At f < 3 GHz, the permittivity E' decreases with increasing frequency at a rate comparable to that observed for bound water. This is discerned from a comparison of Fig. 5.5 with Fig. 5.18. Similar frequency behavior were observed for other vegetation types and parts (refer to Appendix A). Figure 5.7 shows plots for Crassulaceae Echeveria (which has succulent leaves) on an expanded scale covering the.2-2 GHz range. This material has a relatively low salinity (the measured salinity of the extracted liquid was 4 parts per thousands). The real part is almost constant indicating that there is no relaxation process in this frequency range, which means that the bound water content is neglegible and the dielectric loss is dominated by ionic conductivity. 136

i 1112/850 SK I 8.25' NOGP Tr 22 DEO C 50 50 * *..REAL 45 + 40 35 EPSILON (EP) 30 25 20 15 o o IMAGI NARY 10 o Co o 0.0 0.2 0.4 0.6 0 8 1.0 1.2 1.4 1.6 1.8 2.0 FREQUENCY (OHZ) Figure 5.7. Measured spectra of the dielectric constant (real and imaginary parts) at the low frequency band (.1-2 GHz) for Crassulaceae Echeveria leaves.

5.3 Water Content Dependence Since the main constituent of a plant is liquid water, its dielectric properties are driven by the dielectric properties of liquid water. Liquid water exists in plant tissues in two forms: free and bound. In addition, the free water component usually has a certain amount of dissolved salts, which leads to an ionic conductivity term. It was generally found that E' and E" are both monotonically increasing functions of water content. Figure 5.8(a) shows the dielectric constant for corn leaves versus M2 at 1, 4, and 17 GHz. As expected, E' increases steadily with increasing M. and decreases steadily with increasing f. On the other hand, E" increases steadily with M. and has a peculiar frequency response: at low moisture levels, E"(1 GHz) > E"(4 GHz) > E"(17 GHz), while at high moisture levels, e"(17 GHz) > e"(1 GHz) > E"(4 GHz). The reason we choose to report dielectric data as a function of gravimetric moisture rather than volumetric moisture is, as discussed earlier, because M. is not a measureable quantity and it depends on the assumption we make about the dry vegetation density and the manner by which plants lose water (i.e., whether or not they shrink). In some cases, E' was observed to decrease with increasing moisture content at very high moisture contents. An example of this behavior is shown in Fig. 5.8(b). No explanation is available at present for this unexpected behavior. 138

CORNLEAVES 1,4, 17GH 40 REAL PA (1.CHG - REAL PART [4.Hz/ REAL PART 17/Hz - IMG PART (1.C - IMG PAI 4. z ~35 -I NG PART( 30 25 i / 20 z. 15 0 0.00.20.40.60.80 Gravimetric moisture Figure 5.8(a). Measured dielectric constant of corn leaves at 1, 4, and 17 GHz, respectively, with frequency as parameter. 139

.141" NGP SOYBEANS B I / 1 7/86G T=22 OEG REALS 35 30''->(\., 25 - I - -. ",,:, MV=0.537 20 C: EPSILON (EP) | * - -- I MV=0.434 15 10 1 ScscaOo o 0 L I —- -0 6 ~-_ __ MVY0.238 0 2 4 6 6 10 12 FREQUENCY (GHZ) Figure 5.8(b). Measured spectra of the dielectric constant of soybeans leaves with volumetric moisture M. as parameter (real parts).

.141 " NG P SOYBEANS'8 1/17/86G T=22 OEG IMAGINARIES 14 I-~~~~~~~~ ~~MV-0.537 12 0 0 -y EPSILON (EP) 8 eej~",e$_...e0 6 - 0] 4 2 * __| rVI0. 1 25 O..,,_ —i -.... —------....~-....~ MV+-O. 12 0 t- ~ t.0 2 4 6 8 10 12 FRQ(OUENCY (GHL) Figure 5.8(c). Measured spectra of the dielectric constant of soybeans leaves with volumetric moisture M. as parameter (imaginary parts).

5.4 Salinity Effects The equivalent NaCI salinity, in parts per thousand, is defined as the number of grams of NaCi dissolved in one kilogram of distilled water. The imaginary part of the dielectric constant, e", can be expressed as: E+ fE + fib (5) C ++ (5.1) where the subscripts c, b, and f denote the conductivity, bound, and free water terms, respectively. Below 1 GHz, fei and 4' are, in general, much larger than Ef, while above 4 GHz, C" is the dominant factor. We can summarize the loss mechanisms as follows: 1. conductivity term fi- a 7! ac (5.2) C WEO f where acff is the effective conductivity in Siemens/mn and a, (a, = reff/27rEo) is in sec1. 2. bound water term (refer to Sec. 5.5) (Esb - fob) b (1 +() (5.3) where E,b and Eoob are the static and optical limits for the bound water dielectric constant and fob is the resonance frequency (the spread relaxation parameter a was assumed to be.5). 142

3. free water term (few- ~ + for~ )2~ ~(5.4) where Ec,, oof, and fo0 are, as defined earlier, the relaxation parameters for free water. At frequencies in the 1 GHz range, these terms can be approximated as: 1. -", 2. jb -(f >oe), and 3. - _ F (f < ffor) where C, B, and F are constants. This approximate approach helps in studying and understanding the low frequency behavior of E" qualitatively. Unfortunately, both o' and 4 terms decrease steadily with increasing frequency, although Ed decreases more slowly than does c', which makes it difficult to separate the contribution of these two terms. In order to resolve this problem, we extracted fluids from different plant parts at different moistures and measured their dielectric constant. Table 5.1 shows the measured salinity of included liquids for corn leaves and stalks that had been growing at different heights locations on the corn plant. 143

moisture fresh plant one day two days location part P(tons) S(ppt) P(tons) S(ppt) P(tons) S(ppt) upper leaves 20 6 20 11 25 20 upper stalks 10 4 20 8 12 6 middle leaves 15 6 20 14 25 29 middle stalks 5 5.5 7 7 5 7 10 5 17 7.5 12 8 lower leaves 10 6 20 23 25 29 lower stalks 3 5.5 5 7 5 6 6 5.5 10 7 10 6 8 6.5 Table 5.1: Measured salinity of liquids extracted from corn plants at different pressures (in tons per unit area) and at different plant heights. The data in Table 5.1 was obtained for three different corn plants from the same canopy. The first was measured while still fresh, the second and the third were measured one and two days later, respectively. Each plant was divided into three parts: upper, middle, and lower sections. Then, liquids from leaves and stalks, in each section, were extracted and measured separately and the 144

extraction pressure was recorded in tons per unit area. A modified hydraulic press was used to squeeze the juices out of the plant parts. The gravimetric moisture of different sections were measured and the estimated averages of S (ppt) and M. are given in Table 5.2: leaves stalks Mg S (ppt) M, S(ppt) by measuring e by measuring e.351 29.669 6.396 29.674 4.521 23.691 8.525 20.733 5.605 11.739 7.5.624 14.742 7.646 6.757 6.657 6.779 6.675 6.789 7 Table 5.2 Salinity and gravimetric moisture for corn leaves and stalks. The following observations are offered: 145

1. It is very difficult to extract liquids from relatively dry leaves (Mg <.3). 2. Salinity increases with decreasing moisture content, which indicates an increase in concentration of ions with moisture loss. 3. The smallest reported Mg was.35 for corn leaves, while that for corn stalks was.67. Figure 5.9 shows the measured salinity (in parts per thousands) of corn leaves as a function of volumetric moisture (assuming pDv=.33); the maximum measured salinity is around 30 ppt, while the lowest is about 5 ppt. A best fit line for this set of data is shown also; a linear equation relating S to M2 is given by: S = 37 - 46Mg.........(ppt), (5.5) or, aOff = 57- 71M,.........(m Siemens/cm), (5.6) or a, = 103 - 130 Mg.........(as defined in Eq.(5.2)) (5.7) Because of the limited range of Mg for stalks, it was not possible to adequately relate S to Mg for stalks. The previous three equations should be taken only as approximate estimates of S,af11,and ao because the variability among different species is quite large. Furthermore, large differences in salinity were observed among samples of the same species depending on the stage of growth and geographic location. As 146

CORN L[AU[S 25 _.. 20 1 - 1- 1 -I.1 S (0/00) 13 0.10 01 00 0X. 0X.0 0.35 0.405 Mu Figure 5.9. Measured salinity in (ppt) for extracted fluids from corn leaves at different volumetric moisture levels, plants were excised and naturally dried.

an example of this variability, the measured salinities of extracted liquids from fresh corn leaves (Ulaby and Jedlicka, 1984 ) grown near Lawrence, Kansas, were measured to be about 12 ppt. As shown in Table 5.1, the measured salinities of fresh corn leaves grown near Ann Arbor, Michigan, were measured to be about 6 ppt. This large difference can not be attributed to measurement errors or equipment calibration alone. A comparison between different measurements on corn leaves grown in Kansas (1984) and in Michigan (1985) is given in Table 5.3 (both measured using the same technique, the open-ended coaxial line probe system ). where when Mg f(GHz) E I e" J tan(6) Kansas 1984.736 1 33.8 17.50.653 1 30 15.50 Michigan 1985.835 1 46 18.5.4.645 1 27 9.33 Table 5.3: Comparison between measured corn leaves grown in Kansas and Michigan. Another experiment was conducted in Michigan (December, 1985 ) on corn leaves and stalks (grown at the University of Michigan Botanical Gardens). The dielectric constant of corn leaves and corn stalks was measured as a function of 148

frequency for freshly cut plants. Simultaneously, extracted liquids from the same plants were measured in two different ways: (i) Conductivity (mSiemens/cm), using a conductivity meter and (ii) e, using the open-ended coaxial probe, and then by comparing this data to that calculated for saline solutions, an estimate of the effective NaCl salinity can be made. Table 5.4 shows a comparison between these two different approaches: plant part P(tons) S(ppt) S(ppt)conductivity meter leaves 12 8 6.5 stalks 3 8 6.63 stalks 10 7 6.63 Table 5.4: Comparison between salinity measurements using conductivity meter and using dielectric measurement. Figures 5.10 to 5.12 show spectra of the dielectric constant of extracted liquids along with that for saline solutions with S = 7 and 8 ppt. The effective salinity inferred from the measured dielectric constant of the liquid is about 20% higher than that measured by the conductivity meter. The latter represents the actual density of free ions present in the solution, whereas the former represents an effective value based on the observed loss factor. The difference may be at149

CL (LIOUID) REA~L & IMAO1INARY RMA 1 6 1~~I0 1 2 1 4 16 re 2 FREOUENC',"' (GH42) e extracted fluids from corn leaves. The data pit solid lines are calculated from [Stogryn, 197')fo with 8 ppt salinity.

12/03/85 G REAL I.INARY I tGI NARY 14 16 18 20 22 im corn stalks. The data points ulated from [Stogryn, 19711 for

12/03/85 G REAL II MAI NARY 4 16 18 20 22 i stalks. The data points from [Stogryn, 19711 for ressure guage showed 10 *).

not sought in this work: it was our objective, rather, to test plants with different ionic contents and to try to relate their measured salinities to their overall dielectric behavior. An attempt was made during the course of this study to test plants with exceptionally high ionic contents. We were advised to try desert plants because.1'I 1I.,. I 11 I I I 1* I1

part liquids from leaves leaves plant s (ppt) e' " tan(6) e' e" tan(6) l MC 5 72.1 18.4.255 53.7 12.5.233 CM 10 73.1 33.451 36.6 20.2.552 LH 52.6 24.5.466 SK 4 73.6 15.8.215 22.6 7.2.319 Table 5.6. Freshly cut desert plants ( at 1 GHz). Table 5.7 presents the results of a test made to compare e for potatoes, apples, and tomatoes and to relate the measured e to the salinity of the extracted liquids. part _ solid liquids material l E" ttan(5) El En s(ppt) tan(6) potatoes 64.1 24.7.385 71.3 24.1 7.338 tomatoes 73.5 16.3.222 74.5 16 4.215 apples 63.5 8.7.137 72.2 6.4.8.089 Table 5.7: Dielectric of potatoes, tomatoes, and apples (Mg >.8 and f = 1 GHz). 155

It is observed that tan(6) of the solid plant material is generally higher than that for the extracted liquids, which may be due to the added losses contributed by bound water. Figure 5.13 illustrates the effects of salinity by comparing the dielectric constants of potatoes and apples as a function of frequency. 5.5 Bound Water Effects As discussed in the previous section, the effects of bound water and salinity are similar and they tend to mask each other, especially in the 1-5 GHz frequency range. Therefore, two steps were taken to remedy this problem: 1. The measurement frequency range was extended down to.1 GHz, and 2. Special circumstances were sought that would allow the study of boundwater effects in isolation of salinity effects. To achieve the first step, the dielectric system was modified and the probe section was calibrated so that it could operate at as low a frequency as 50 MHz, as discussed in Chapter 4. In order to study the bound water without the "shadow" of the ionic conductivity, it is necessary to use a material with known bound water concentration. Sucrose (table sugar) is such a material (Sayre, 1932). It was reported that each molecule of sucrose can bind to six molecules of water. Since the molecular weights of water and sucrose are known to be 18.01534 and 342.30 respectively, we can write, Xb = 6( )X = ( )X (5.8) 342.30 19 156

POT4-APP.MG>O.8 70 I Pa In -- It,~:; Pi'r,tao. -e- PAr aple 6O,-, 5050 4 40 30 10 O o F 1. 2. 3. 4. 5. FREQUENCY (GHz) Figure 5.13. Measured spectra of the dielectric properties of potatoes and apples. The measured salinity of the extracted fluids were 7 and 0.8 ppt, respectively. 157

where Xb is the mass ratio of bound water to total water and X = - is the ratio of sucrose weight to water weight. So, given X, we can calculate Xb and Xf, the mass ratio of free water to total water, as: Xf = 1- (6)X. (5.9) Volume-Fraction Calculations 1. Dissolve S(gm) of sucrose into W(gm) of distilled water. Hence, X W (5.10) 2. A, the concentration (per cent), is given by: A- 100s % (5.11) S+W' 3. Use a Chemistry Handbook to read p(the density in g/cm3) corresponding to A. 4. The total volume of solid sucrose is: V =S W(p- 1) cm3 (5.12) 5. The total volume of water is: V,,, = W, cm3 (5.13) 6. The volume fraction of solid sucrose is: V8 V V, +v (5.14) 158

7. The volume fraction of water is: v, = VW (5.15) 8. The volume fraction of bound water is: Vb =VW ( X) (5.16) 19 9. The volume fraction of free water is: f=,(1 -6 X). (5.17) 19 Table 5.8 gives the volume fractions of some of the sucrose solutions measured in the course of this work. II sucrose# X v, vb Vf En tan(6) fo(GHz) water 0 0 0 1 79.1 4.1.052 18 A.5.239.120.641 65 10.154 8.4 B 1.385.194.421 51.9 14.270 3.9 C 1.5.485.244.271 40.2 15.4.383 2.2 D 2.559.279.162 31.1 14.4.463 1.1 E 2.5.613.306.081 23.4 12.1.517.44 F 3.655.327.018 18.5 9.9.535.21 G 3.17.667.333 0 17.4 9.3.534.178 Table 5.8: Volume fractions and dielectric constants of sucrose solutions at 1 GHz. 159

Samples A though G were prepared such that they cover a wide range of the bound-water volume fractions that may exist in a plant material. A peculiar, yet useful, observation is that the ratio v,/Vb is always equal to 2. In Chapter six, this feature will be used to calculate the volume fractions for vegetation samples. The dielectric properties of these samples were measured as a function of frequency at two different frequency bands: 1. Low band.2-2 GHz using the.25" probe, and 2. High band.5-20.4 GHz using the.141" probe. A sample of the results is shown in Figs. 5.14 to 5.17 for sucrose solutions A, D and G. The dielectric loss factor e" is relatively small for distilled water at.2 GHz, but it increases rapidly as vb is increased. Conductivity measurements were carried out on these samples to test their ionic contents and the results showed no dissolved ionic concentrations. It is clear that these high losses are caused by a dipolar relaxation mechanism and not by conductivity effects. Table 5.8 shows the measured E1 and E" at 1 GHz for different sucrose concentrations. Also given is the relaxation frequency fo corresponding to each concentration, calculated using an optimization program (BMDP) that fits the spectral data to a Cole-Cole equation of the form: ~E= Eo1 + (Ef/fo)'L (5.18) For sucrose solution #G, which contains no free water, 160

0. 1 41 NGP HF SUC ROSE'A 0.250ONGP VLF 12/1 7/1985GH 80 YSsO.239 YBoO. 120 70 O YVsO.641 60 EPSILON 40 30 a 200 ~~Cjl~OC 0 0 2 4 6 8 10 12 14 FREQUENCY IN GHZ Figure 5.14. Measured spectra of the sucrose solution (A) with x=O.5. Two probes were used to measure the lower (.25") and upper (.141") bands. V., Vb, anddV1 are sucrose, bound, and free water volume fractions, respectively.

O0 1 41'NGP HF SUCROSE AD 0.250"NGP VLF 12/1 7/1 985G,H 50 YSSO.SS59 4YB0O.279 45 * YFO.1 62 40 35 Cr~ 30 EPSILON 2520 15 I0 5,t.....- --- F —— I 0 5 10 15 20 25 FREQUENCY IN GHZ Figure 5.15. Measured spectra of the sucrose solution (D) with x=2. Two probes were used to measure the lower (.25") and upper (.141") bands. V, Vb, andV/ are sucrose, bound, and free water volume fractions, respectively.

SuCROSE 0 O.S41OMNGP VI 12/17/1985GH 35 y5.o.667 Y660.333 VF 00.000 30yruOO 25 20 EPSILON 10 0 10 12 14 16 18 20 2REQUENCY INGHZ Figure 5.16. Measured spectra of the sucrose solution (G) with x=3.l7* Two probes were used to measure the lower (.25") and upper (.141") bands V,,Vb,andVf are sucrose, bound, and free water volume fractions, respec

0.141 "NGP HF YS0.559 SUCROSE D 0.250"NGP YLF YB-0.279 YfO.11 2 1 2/7/1985G,H 14.5 13.0 EPSILON 12.5 12.0 11.5 11.0 10.5. 10.0. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 FREQUENCY IN GHZ Figure 5.17. Measured spectrum of the imaginary part for sucrose solution (D) with x=2. The peak is at around 1 GHz. The agreement between the two sets of data produced by two different probes is fairly good.

=2.9+ 56(5.19) 1 + (jf/.178)5 (5.19) where f is in GHz and the relaxation parameters a is.5. Figure 5.18 shows Eq. ( 5.19) plotted with the measured data points. This type of frequency response is rarely observed in plants because salinity effects are present also, and what we observe is the result of the combined spectra of both, especially in frequency range below 5 GHz. The observed spectrum of sucrose solutions is not really unique; a similar type of behavior was observed for the following materials: 1. Dextrose Fig.5.19 shows the spectrum of a dextrose solution of concentration X = 2. This curve, when compared to sucrose solution D (Fig. 5.15), is found to bear strong resemblence in shape, although the two are slightly different in magnitude. 2. Silica gel, Fig. 5.20 shows the spectrum for silica gel of concentration X =.5. This curve is to be compared to that of sucrose A. Again they are similar but vary slightly in level and in the frequency at which e' and E" intersect (silica gel at 20 GHz and sucrose A at 13 GHz). 3. Gelatin, Fig. 5.21 shows the spectrum for gelatin at a concentration of X = 1. Comparing this figure to that for sucrose B shows large differences indicating that sucrose and gelatin have different binding properties. 165

Boundwater#g 35 * REAL PART (measured) * IMAO PART (measuredi) -e- REAL PART ca culat edi -- IMAC; PART calculated) 30 25 zi p 0< 20 0 II 15 I, 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 5.18. Spectra for the sucrose solution (G) with x=3.17. The data points are measured and the solid lines are calculated using Equation 2.18 in the text.

I12/9/850&HH 0.250"'NOP LF 0.141 "HOP HF 60 50 EP 40 EPSILON 50 20 10 0 10~~~~~~~~~~~~~2 0 FREQUENCY IN 0$!Z Figure 5.19. MessUred spectra for dextrose solutiOl with x=2. Two probes were used to measure the iower(.25") and pper(.141") bands

.141 NGP 80 2/20/85H *+,*.,.* REPEAT SILICA GEL'X3 70 60 50 EPSILON (EP*) 40 -...._...., 0 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ) Figure 5.20. Measured spectra for Silica gel (X3) with x=O.5. Figure 5.20. Measured spectra for Silica gel (X3) with x=0.5.

.141" NGP 60 12/19/85 H 55 11BGELATIN JX I (X= 1.0) 55 50 45 40 EPSILON (EP*) 35 30 25 20 105 I 0 I -- 0 2 4 6 8 10 12 FREQUENCY (GHZ) Figure 5.21. Measured spectra for Gelatin (X1) with x=1. Two probes were used to measure the lower(.25") and upper(.141") bands.

4. Starch, Fig. 5.22 shows the spectrum of a starch mixture at X = 1. This figure is to be compared to sucrose B. It can be observed that starch can bind more water than sucrose can (for the same concentration). 5. Accacia, Fig. 5.23 shows the behavior of accacia (arabic gum) mixture with water at X =.8. Similar to starch, accacia shows a larger binding capacity compared to sucrose solutions. 6. Natural honey, Fig. 5.24 shows the spectrum of natural honey. If we compare this spectrum to sucrose G, we note that E, at e.g. f =.5 GHz, drops from about (26-jll) for sucrose G to about (14 - j7) for honey. This behavior is governed by the molecular arrangement by which water binds itself to the host molecule. 7. Miscellaneous materials including egg white, egg yolk, and human skin (finger tips) as shown in Figs. 5.25 to 5.27, respectively. Table 5.12 summarizes these measurements at f = 1 GHz. 170

.141 NGP 35 12/20/85 H REPEAT STARCH *X I 30 i9 25 EPSILON (EP*) 20 I 0 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ) Figure 5.22. Measured spectra for starch solution with x=1.

O. 141"NOP 1/8/19860 ACCACIA (0.8A) 35 30 25,., 20 EPSI LON 15 I0 O 2 4 6 8 10 12 FREQUENCY IN GHZ Figure 5.23. Measured spectra for Accacia (Arabic Gum) solution with x=0.8.

HF —O. 14 1" NGP; VLF —0.250" NGP NATURAL HON 1/28/86 G 20 T 14 16 14 4 12' U. EPSLON(EP) 10 m'+ 0 l-~ 0 5 10 15 20 25 fRE(UENCY (GHz) - NATURAL HONEY -- NATURAL HONEY,- NATURAL HONEY o- NATURAL HONEY (REAL)-VLF (0.250 (MAG6.)-VLF (REAL)-f (IMAG.)-f NCP) (0.250 NGP) (0.141 "NGP) (0.141 "NGP) Figure 5.24. Measured spectra for natural honey. Two probes were used to measure the lower(.25") and upper(.141") bands.

HF —O. 141' NGP; VLF —0.250' NGP EGG WHITES 1/28/86 G 80.0 0 70.0 Iia 60.0 50.0 (EP') 40.0 30.0 o 20.0 Vl0 10.0 0.0 0.0 5.0 10.0 15.0 20.0 250 FREQUENCY (GHZ) Figure 5.25. Measured spectra for egg white. Two probes were used to measure the lower(.25") and upper(.141") bands. - E6G6 WHES - ES EGG TES GG'ITES 13- EGG IITES (REAL) —f (IHrA.)- HF (REAL)-VLF (IrAG.)-VLF (0.14 I" NGP) (0.141 " NGP) (0.250" NGP) (0.250" N,3P)

0.141 NGP EGG YOLKS 1/17/86 35 25 Ln EPSILON (EP) 20 20 10 0 2 4 6 8 10 12 14 16 18 20 E6G YOLK (REAL).o- EGG YOLK (IMAGINARY) Figure 5.26. Measured spectra for egg yolks.

11/5/85. 41" NGP SKIN1 T 22 DEGC (FINGERS) 35 " 30 REAL EPSILON (EP') 20 015 \ (I MAGINARY * * 10 r o o o o o o o 55 0 fREQUENCY (GHZ) Figure 6.27. Measured spectra for human skin (finger tips). Two probes were used to measure the lower(.25") and upper(141") bands.

material LX e " i tan(6) distilled water 0 79.1 4.1.052 sucrose#A.5 65 10.154 sucrose#B 1 51.9 14.270 dextrose#X3.5 67 7.5.112 dextrose#X1 1 62 12.5.093 gelatin#X3.5 55 12.218 gelatin#X1 1 44 12.273 starch#X3.5 57 9.158 starch#X1 1 28 7.5.268 accacia.8 31 9.290 natural honey 11 5.455 egg white 70 20.286 egg yalk 31 10.323 skin 23 12.5.543 Table 5.9: Measured E' and E" of various materials (some with known waterbinding capacity, X=solid weight/water weight)at 1 GHz. 177

5.6 Temperature Effects A temperature experiment was devised and conducted to study: 1. the dielectric properties of plants at temperatures above, below, and at the freezing-point discontinuity, and 2. the properties of bound water as a function of temperature. A.Free Water Before we start discussing the data measured for plants, it is useful to first review the dielectric properties of liquid water because the latter govern the behavior of the former. Figures 5.28 to 5.30 show the dielectric properties of liquid water as a function of temperature (above freezing) for different frequencies (1, 4, 8 and 20 GHz) and salinities (0, 4 and 8 ppt). The following observations may be made: 1. aO (at 1 and 4 GHz) is, in general, small in magnitude and negative in sign. 2. @a" (at 8 and 20 GHz ) is large and positive in sign. 3. I is small and negative (S is salinity in ppt). 4. The relaxation frequency, fo, decreases with T. 178

T1118/1965 CALCULATED D W.VS T(I.4,8.20 GHZ) 90 REAL IMAGINARY 80 80 6HZ AL NW4 GHZ AL AL 70 60 t 200 GHZR AL 0 50 EPSILON 40 200 6HZ IrA3 30 lo- L A _~ 1.0 GIZ InAG. 0 5 10 15 20 25 30 35 40 45 50 tErPERATURE IN DEG C. Figure 5.28. Dielectric constant behavior versus temperature with frequency as parameter for distilled water (s=0 ppt). Calculated from [Stogryn, 19711

11/18/85 CALCULATED 90 S S-4.0 PP r VS. T. - - AL & IAG. ~~~~~~~~~~80. l~~~~~~~1.0 6HZ 4.0 GHZ 00oo,7,. 60 20.0 6HZ 40 EPS ILON 50 i A2I5, =>=.200 GHZ 8.0 6HZ 4.0 GHZ t- - - 10- I 0 0 10 20 30 40 50 TEMPERA TURE (DEG C) Figure 5.29. Dielectric constant behavior versus temperature with frequency as parameter for saline water solution (s=4 ppt). Calculated from [Stogryn, 19711.

S - 80 PPT. VS. T. 11/18/85 CALCULATED go REAL & IM1AGINARY 1.0 GHZ REAL 4.0 GHZ REAL 0 Ad8. 20.0 GHZ REAL EPSILON 50 1.0 G3HZ IrlAG.,,20c...~~~ ~ - ~' 20.0 GHZ I1A, 8.0.3HZ IfIAG - - ~ -2 *"" —--- _.__$_, =, ~ 4.0 GHZ IMAG -10 0 10 20 30 40 50 TErIPERRATRUE (DEG C) Figure 5.30. Dielectric constant behavior versus temperature with frequency as parameter for saline water solution (s=8 ppt). Calculated from [Stogryn, 1971].

5. E"(at 4, 8, and 20 GHz) is driven mainly by the free-water relaxation process; it has a negative temperature-coefficient, j'9, below resonance and a positive one above resonance. 6. E" is very sensitive to conductivity at 1 GHz, aa" (at f=1 GHz and S=O) is negative because f < fo, while d'a (at f=l GHz and S=4 and 8 ppt ) is positive due to conductivity effects. Table 5.10 summarizes the temperature properties of water in its different forms: free-water relaxation conductivity bound-water relaxation,t |a f < fo f = fo f > fo f < 4GHz f < fo f = fo f > fo (fo -- 18 GHz) __ I_ (fo —.178GHz) f in GHz -ve zero +ve +ve -ve zero +ve 1 GHz small -ve large +ve large +ve 4 GHz medium -ve medium +ve medium +ve 10 GHz large -ve neglegible small +ve 20 GHz small +ve neglegible small +ve Table 5.10: Liquid water temperature coefficients. 182

B.Bound Water As shown in Table 5.10, the dielectric properties of free-water and bound-water as a function of temperature are similar, except in that the relaxation frequency is a 100 times smaller and the spectrum is more flat for bound water(a =.5). The dielectric behavior of bound water is studied through the study of concentrated sucrose solutions. Figures 5.49 to 5.51 show the measured dielectric properties of a concentrated sucrose solution as a function of temperature. The general behavior of bound water agrees with that expected in Table 5.10. C.Vegetation Material experiment # 1 Fatshedera leaves were used for the first temperature experiment. The temperature inside the environmental chamber was measured accurately but the stability of the temperature sensing circuit is only ~.50C. The temperature sensing devices, i.e. the thermistor and the thermocouple, were placed as close as possible to the sample under test, and sufficient time was allowed so that the chamber may reach equilibrium before e is measured. The steady state condition is hard to identify, since there is no way by which we can check the temperature difference between the sample and the surrounding air. An air blower was used for this purpose, but blowing air, especially hot air, increases evaporation from the sample. The longer we wait, to attain steady-state conditions, the larger is the moisture loss from the sample and of course the more tedious the experiment becomes. It was found that waiting for 30 minutes, after resetting the temperature, 183

before taking the dielectric measurement is an acceptable compromise. Figures 5.31 to 5.34 show plots of e versus T at 1, 4, 8, and 20 GHz. The gravimetric moisture of the sample was.745 before the experiment started and.711 after the measurements were completed. The sample lost 5% of its original M2 during the experiment. The following observations may be made: 1. The freezing-point discontinuity takes place at well below 0~C. Freezing actually happens at around -70C, which is attributed to a super-cooling (or under-cooling) effect (Levitt, 1956). Figure 5.35 shows reported data on corn plants with and without Pseudomonas Syringae (Bacteria that act like ice nuclei between -2 and -5~C). The untreated plants were able to withstand temperatures as low as -80C before significant damage was observed. 2. a (1 GHz) is small and negative, 3. o' (4 GHz) is small and positive, 4. a(8 and 20 GHz) is large and positive, 5. a'(1 GHz) is large and positive, 6.'9' (4 and 8 GHz) is small and negative, and 7. e"(20 GHz) has a minimum around 20~C. Comparing these properties to liquid water shows great similarity, except for the imaginary part at 20 GHz. The imaginary part e" at 20 GHz is not similar to 184

1 1/8 /1 P8 FZ*t Fe 1.0 OHZ O.141"NOP TH KK S AV"PLE /?1T AL 30 25 00 20 EPSLON 15 10 -U40 30 ft2 -10 0 10 20 30 TEhPORATURS iN' t4 *. C. Figure 5.31. Measured dielectric constant versus temperature from -400C to +300C at 1 GHz for Fatshedera leaves. M,(before) = 0.745 and M9(after) = 0.711.

11 /8 / 1905 0.41 "NOP F4.0 OHZ THICK SAItPLE/r TAL 30 25 20 Co ~PS. LON 1 5 -40 -30' 20 -10 0 10 20 30 TEiPERATU* IN DO. C. Figure 5.32. Measured dielectric constant versus temperature from -400C to +300C at 4 GHz for Fatshedera leaves. M,(before) = 0.745 and M,(after) = 0.711.

II/e/1965 FZ~ID 0.141 "NOP F4.0 OH THICK SAMPLE/METM2 20 EPSLON -40 -K0 -20 -0 -10 0 10 20 50 TEMPERATL II O. C. Figure 5.33. Measured dielectric constant versus temperature from -400C to +300C at 8 GHz for Fatshedera leaves. M,(before) = 0.745 and M,(after) = 0.711.

It /I/I "5 FZ*I O.1 41 NOP F20.0 OH THICK SN'PLE/tITAL REL 16 14 12 10 OP LON co 9~~ 8 IMAG. W[PERATUWE IN DCO. C. Figure 5.34. Measured dielectric constant versus temperature from -400C to +300C at 20 GHz for Fatshedera leaves. Mg(before) = 0.745 and Mg(after)

I-,b;,= -I < 0o - -2 -3 -4 -S -6 - - -9 -10 Frost damnai as a function of temperature to corn)n seedlings uith ard witht leaf populations of PseudomonaL; syringae. Plants were sprayed with P. syringae suspensions ( 0.5 mi/plant) of 3 x 1j8 cel ls,'inl (0) or 3 x 105 cells,'ml (A) and incubated in a mist chamber for 24 hours. Other plants remained untreated (S). Then the plants were placed in a growth chamber at 0O C and Coo0ed at 0.050 C/minute. Groups of plants were removc-d from thle cIInamber at the temperatures shown ont the abscissa. Data are represented as means + standard error (vertical 2bars).. Figure 5.35. [Levitt, 1956J. Figure 5.35. [Levitt, 1956].

that of liquid water. Figures 5.36 to 5.38 show the frequency response of e, both real and imaginary, at different temperatures (-400C < T < +300C). Note the sudden change in level between the spectra measured at T > -50C and those measured at T < -100C. Experiment # 2 The fact that the Fatshedera leaves freeze at around -100C poses a question: Do other plants have similar freezing behavior?. To answer this question, a leaf sample from the plant (a tropical banana-like plant) with M,=.839 was tested. This time, care was excercised to allow more time for the chamber to reach steady state and, also, e was sampled more frequently at temperatures around freezing (25 times). Figure 5.39 shows E versus T (-450C < T < 500C) at 10 GHz. Since, for this experiment, we really do not care about the frequency response, only the 1 GHz data is shown. The rest of the data is given in Appendix B. Figure 5.39 shows the usual above-freezing behavior of e at low frequencies; a is small and negative and aa is large and positive. The freezing temperature is below -80C and the change in level, as shown in Fig. 5.39, is very steep. Below freezing, however, E" continues to have a non-zero value down to -250C. Below -300C, E' is almost zero (indeed we should always bear in mind that the data processing procedure has a ~.1 accuracy due to rounding error alone ). But, in spite of the poor overall system accuracy at low E values, conclusive evidence shows the existence of unfrozen water in plants below the freezing temperature of free water. Figure 5.40 shows an example of e versus f at T = -150C, it is clear 190

0..141 NGP 1 1/8/19 REAL PARTS 35W |30* FZIVS.FRE)T-+30 o FZ I.FQ(R AL)Tm +20 20~0 ~ o * 0 1 FZ1VS.FO(R[AL)T+10| 20 ~000o * * | o FZe1VS.FQ(REAL)TC)O | Ao 0DO * 0 FZ*'1VS.FRC)T.0 1.5 A A 0 FZ 1 VSY.FOREAL)T —15 EfS oC~ A A Ao o 1b5 ~ i ~FZIYSFQ(RLT.2 A 4;; ^ ^ A.s ^ A A A ^ 7 # A * I FZ VSFQ(RCAL)Tm- 1I 0 0 2 4 6 10 12 14 16 10 20 FRE.UECY IN (OHt) Figure 5.36. Measured spectra for Fatshedera leaves with temperature as parameter (real parts) M,(before) = 0.745 and M9(after) = 0.711. = 0.711.

0.141'NOP zeI I1/8/19 IMAO. PARTS 15 14 - I 1VSF'Q(MfA.)T-+I.SG1- FZe1 S.I O(.)T, 0 PSLON 11 - FZ_1_S1 freezing as parameter (imaginFZary parts) M,1efore) = 0.745 and M(after) 10 0.711 0 2 4 & S 10 12 14 1& ISl 20 FREOECY IN (0HZ) Figure 5.37. Measured spectra for Fatshedera leaves with temperature above freezing as parameter (imaginary parts) M9(before) = 0.745 and M9(after) = 0.711.

0 141 "OP ~~~fl12@~~~~~~~~~ 11,/1/I9 HtAO. PARTS &.0 B.LO FREEZ NO I 2.0. FZVSfC~tlAO)Ts_1O CPS LON I.$ no IeT=-20!t~ G-N~ v ~f~ell~G VF1SItA. )T=-25 1.0 " 4 ~ I v O(AO- 0.5 0.0 - 0 2 4 6 0 10 12 14 1& 18 20 Figure 5.38. Measured spectra for Fatshedera leaves with temperature below freezing as parameter (imaginary parts) Mlgf(before) = 0.745 and M,(after) = 0.711.

O. 41"NGP 11/11/198SG FZ 2VS.T(.0GHZ) 60 4T50- —.., * —. 40:pa EPSILON 30 I 0000 o-. 0-..0-0...;.: -. -50 -40 -30 -20 - 10 0 10 20 30 40 SO TEMPERATURE IN DEG.C. Figure 5.39. Measured dielectric constant versus temperature from -450C to +500C at 1 GHz for a tropical tree leaves. M,(before) = 0.839 and M,(after) = 0.818.

.141 NGP 15 D/850 I010 9 8.7i. v REAL EPSILON (EP) S5 4 IMAOINARY,C. 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (0HZ) Figure 5.40. Measured spectra for a tropical tree leaves at -15C.

that Ec has a much larger value than that of ice. Figure 5.39 also shows that the terminal value of e below -400C is about (5-jO). Since E of dry vegetation (bulk vegetation + air ) is - 1.7 - jO, and e of ice is - 3.15 - jO, e of the mixture can not be larger than that of ice unless liquid water is present. The observed value of Ec' 5 is attributed to E' of bound-water ice. It has, probably, a value much higher than that of free-water ice (- 10!). Experiment # S In the previous two experiments we have shown the similarity between the dielectric spectra of liquid water and plant materials. Also, the low freezing temperature of plant samples, the super-cooling effects, was briefly discussed. The third experiment was designed to test a plant sample undergoing two cycles of freezing and thawing. Again, we chose Fatshedera leaves with high moisture content (M,=.736 before and =.718 after the experiment). Figures 5.41 and 5.42 show the general behavior of e versus T at 1, 4, and 8 GHz. Above freezing, the temperature dependence of e' is consistent with that of free water. Below freezing, e'(1 GHz)> E"(8 GHz)> E"(4 GHz), but the levels are too close to the lower limit of the system's measurement capability to make quantitative comparisons. Figures 5.43 and 5.44 show a freezing cycle side by side with a thawing cycle. The hystresis behavior was completely unexpected because it implies a different freezing temperature for water in the two directions. Hence, another experiment 196

O. 141"NOP 1 1/14/19850 FZa 4VS.T 35. 1.0 OHZ 8.0 GHZ'.0@~~~~~~ 20 EPSILON 1 5 REAL PARTS 10 -40 -30 -20 - 10 0 10 20 30 TEMPERATURE IN DEO.C. Figure 5.41. Measured dielectric constant versus temperature from -400C to +300C with frequency as parameter for Fatshedera leaves (real parts). M,(before) = 0.736 and M9(after) = 0.718.

0.141"N~P I11/14/19850 FZ#v4VS.T 14 0.100HZ 00, 8.0 oHZ EPSI LON 4.0GHZ IMAG. PARTS -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO.C. Figure 5.42b Measured dielectric constant versus temperature from -400C to +300C with frequency as parameter for Fatshedera leaves (imaginary parts). M,(before) = 0.736 and M9(after) = 0.718.

0. 14 INOP 11/14/19850 FZ*4VS.T 1.0 0HZ 35 FREEZINC'3 ~ ~ ~ ~ ~ ~ ~ ~~~~~~3 25 20 (PSI LON 15 REAL PARTS I 0 ~~~~I I I L -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEO.C. Figure 5.43. Measured dielectric constant versus temperature from -400C to +300C at 1 GHz for Fatshedera leaves. A freezing-thawing cycle is shown for the real part.

0.141 "NP F~Zf~VS~.r 1 1/14/1985G I.0 GHZ 10 I- f' FREEZING I " 7t r 7 t / rTHAWING EPSI LON IMAG. PARTS -40 -30 -20 -10 0 0 20 30 40 TEMPERATURE IN DEO.C. Figure 5.44. Measured dielectric constant versus temperature from -40~C to +300C at 1 GHfz for Fatshedera leaves. A freezing.thawig cycle is shown for the imaginary part.

was conducted with particular concentration on the freezing region. Experiment # 4 During this experiment, freezing, thawing, and refreezing cycles were conducted very slowly on corn leaves with high moisture, Mg(before)=.835 and M,(after)=.781. The dielectric constant behavior versus temperature for f=1, 4, and 8 GHz is plotted in Figs. 5.45 and 5.46. The following observations may be made: 1. Above and below freezing, the behavior is close to that observed for Fatshedera. 2. The freezing point discontinuity occurs between (-5.30Cand- 7.70C), similar to Fatshedera leaves. Figures 5.47 and 5.48 show the freezing, thawing, and refreezing cycles at 1 GHz. The hystresis pattern observed earlier in Figs. 5.43 and 5.44 were apparently real but exagerated. The difference in level is, probably, due to loss of moisture during the experiment. Experiment # 5 As mentioned earlier, the behavior of bound water in biological tissues is not well understood. This shortcoming is attributed, at least in part, to the following reasons: 201

0 141 "NOP FZU, 14 1S.T REAL PARTS FRESH CORN LEAVES 12/06/19850 55.45 FREEZING CYCLE 40 4.00HZ EPSI LON / 20 15 I 0 -40 -30 -20 -10 0 10 20 30 TEMPFRATURE IN DEG. C. Figure 5.45. Measured dielectric constant versus temperature from -350C to +300C with frequency as parameter for corn leaves (real parts). M9(before) = 0.835 and M,(after) = 0.781.

0. 141 "PNOP FZ i1 1 VS.T IMAG. PARTS FRESH CO.RN LEAV ES985 12/06/1985G FREEZI NG CYCLE EPSI LON " | _. 8.0 HHZ 100 -30 -20 -10.0 40HZ 5 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEOG. C. Figure 5.46. Measured dielectric constant versus temperature from -350C to +300C with frequency as parameter for corn leaves (imaginary parts). M,(before) = 0.835 and M,(after) = 0.781.

fZ I IVS T( 10 OHZ)REAL 0. 141 "NOP FP$EH XlON LEAVES 12/06/198,55 i u FREEZENG,40". REFREEZINO EPSILOH1 THAW. Itf) -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure 5.47. Measured dielectric constant versus temperature from -350C to +300C at 1 GHz for corn leaves. A freezing-thawing-freezing cycle is shown for the real part.

0. 141 NYP FZ1 1IS.T( 1.0 OHZ) I MA&G fRESH CORN1 CLEAVES 12/06/19850 20 FREEZI NO N) T HAWW I NO EPSI LON -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure 5.48. Measured dielectric constant versus temperature from -350C to +300C at 1 GHz for corn leaves. A freezing-thawing-freezing cycle is shown for the imaginary part.

1. It is impossible to isolate or obtain pure bound water (otherwise it would not be bound ), so we usually measure the combined properties of bound water, the binding surface material (e.g. sucrose), and other materials (e.g. free water) at the same time. 2. We do not know for sure whether bound water has unique properties, irrespect of the binding material, or not. So, measured properties for one material may not be generalized to others. For example, compare the spectrum of sucrose solution #B to that of starch sloution #X1 (Table 5.9). 3. Bound water relaxation takes place at frequencies well below 1 GHz. Unfortunately, in this band losses due to ionic conductivity are very large, which makes it difficult to separate the two processes. Our approach, as will become evident in Chapter 6, is to study the dielectric properties of bound water in sucrose solutions and assume that these properties represent bound water in plant materials. In order to study the temperature behavior of sucrose solutions, a concentrated solution was prepared (with VpF =0, VB=.33, and vs=.67) and it will be referred to as sucrose #9 (it is similar to sucrose #G that was reported in previous sections). Figures 5.49 and 5.50 show the temperature behavior of sucrose #9 as a function of T (-15~C < T < 550C) for f=.2,.6, 1, and 1.9 GHz. The reason bound water was measured at these low frequencies is to be able to study its relaxation properties. Figure 5.49 shows that the real part has a monotonic increase with T. On the other hand, Fig. 5.50 206

0.250"NOP 35 12/07/198&5 SUCRAOS5E 9VS. T _._._.__.__. 0.6 0HZ 30 EPSILON 201.9HZ -20 -10 0 10 20 30 40 50 60 TEMPERATURE IN DEO.C. Figure 5.49. Measured dielectric constant versus temperature from -200C to +500C with frequency as parameter for sucrose solution (#9 or C) for the real partrs.

UCtOSE* 9'VS. T IMA*O. PAP-TS 12/07/1955 0. 250 "ONOP 1 2.. 0. 2 GHZ 10 00 EPSILON 0.60HZ 1.0 0HZ 1.90HZ.? -20 -10 0 10 20 30 40 50 60 TEMPERATURE IN DEO.C. Figure 5.50. Measured dielectric constant versus temperature from -200C to +500C with frequency as parameter for sucrose solution (#9 or G) for the imaginary partrs.

shows that the imaginary part has a peak at a frequency-dependent temperature, e.g. e"(.2 GHz) peaks at 00C, E"(.6 GHz) peaks at +150C, e"(1 GHz) peaks at +250C, and e"(1.9 GHz) peaks at +550C. In order to study the effects of deep freezing on sucrose solutions, another experiment was performed on sucrose #9 over the range -800C < T < +300C, and the results are shown in Fig. 5.51. It is interesting to note that there is no sharp freezing point discontinuity and that E(T = -800C) = 6 - jO. 5.7 Density Effects A quantitative definition of density will be given in Chapter 6, and for the time being, the term density will be used in the qualitative sense. In order to compare the effects of density variations, we will need to compare either different parts of the same species (e.g. corn leaves and corn stalks) or the same parts from different species (e.g. corn stalks and Black Spruce tree wood). Comparison between corn leaves and corn stalks, at 1 GHz, is shown in Fig. 5.3. These two parts have similar dielectric properties except, perhaps, at the dry end. When MgO, corn stalks have a higher dielectric constant than corn leaves. Comparison between the dielectric constants of corn stalks and the trunk of a Black Spruce tree at 2 GHz are shown in Fig. 5.53. There are obvious differences in the general trend, but again E' at M,=O is larger for the tree sample, which has a higher density. The density effects are not well understood because it is very hard to measure the density, especially that of a leaf, accurately. 209

0.250"NGP YLF 12/11/19851 FZ 12(1.OGHZ)F (SUCROS E 9) 35 30 REAL 25 C:) EPSILON 15 -100 -80 -60 -40 -20 0 20 40 TEMPERATURE IN DEG.C. Figure 5.51. Measured dielectric constant versus temperature from -800C to +300C at 1 GHz for sucrose solution (#9 or G). The measured solution in this case is not exactly (#9 or G) because of solid sucrose precipitation at low temperatures.

Measurements conducted on a poplar tree trunk showed large variations between measured e at various parts on the trunk cross section. It was observed that e increases inwardly while the moisture content (Mg) was found to be constant. The only explanation of this phenomena is density variations of wood from one ring to the other, increasing in density inwardly. Table 5.11 shows a summary of the results at 1 and 5 GHz, respectively. f(GHz) location E El i tan(6) Mg 1 bark(side) 7.5 1.3.173.48 1 bark(section) 17.73 5.07.286.48 1 first ring 23.17 4.7.203.49 1 second ring 21.95 6.01.274.50 1 central ring 32.8 8.3.253.50 1 average 20.63 5.08.246.49 5 bark(side) 7.1 1.5.211.48 5 bark(section) 14.4 5.5.382.48 5 first ring 20.3 6.9.340.49 5 second ring 19 6.7.353.50 5 central ring 29.2 10.343.50 5 average 18 6.1.339.49 Table (5.11): Measured data for Poplar tree trunk at 1 and 5 GHz. 211

Chapter 6 Modeling Efforts In order to model the dielectric properties of vegetation parts, e.g. leaves, we must first examine: (i) the dielectric properties of the vegetation constituents, (ii) their volume fractions, and (iii) the proper mixing formula by which the information from (i) and (ii) may be combined to calculate the dielectric of the mixture E. These pieces of information will be discussed separately in Sections 6.1 to 6.3. Section 6.3 contains the results of different physical, semi-empirical, and empirical models. Also, the use of statistical regression to model the dielectric behavior of vegetation independent of plant type or part is considered. No attempt will be made to model the temperature dependence of the dielectric constant of vegetation; such a development would require further work, both experimentally and analytically. 212

6.1 Liquid Water Dielectric Properties 6.1.1 Distilled Water For pure water, it is assumed that the ionic conductivity is zero which means that there are no free ions to contribute to the total loss (especially at low frequencies). The frequency dependence is given by the Debye equations (2.13)(2.15): = E+ - woo (6.1) 1 + jwr where Es,, and cwOO are the static and optical limit of the dielectric constant of liquid water, respectively, and r is the relaxation time constant. The importance of liquid water at microwave frequencies stems from the fact that its relaxation frequency (fw = 1/27rr) lies in the microwave band. For example, fw(O0~C) 9GHz (6.2) and f,(20~C) 17GHz (6.3) 6.1.2 Saline Water A saline solution is defined as a solution that contains free ions, whether or not these ions are organic in nature. The salinity, S, of a solution is defined as the total mass of dissolved solid salts in grams in one kilogram of solution. An equivalent Debye-like equation could be used to represent saline solutions in the 213

following modified form E - eWOO + Ew-WO (6.4) = fEO + )2 and it (ESo. - Eeooo)(y..) ai ew- = l+(7L) + ef (6.5) 8W +(;1 + ( )2 2-0of where the subscript sw refers to saline water, vi is the ionic conductivity in Siemens/m, and Eo is the free space dielectric constant (Eo = 8.854 x 10'12f/m). 6.1.3 Temperature Effects For any relaxation process, temperature affects E, coo,, and fo. However, the change in Ec, is negligible, that in s, is small, and that in fo is of major importance. Referring to Sec. 2.1.1, we can write Eq. (2.18) to (2.20) as r = Aexp( RT) (6.6) a(ln r) _ AH (67) T)(6 7)'(t-) R r= KT exp( R )exp(-T) (6.8) KirT R RT where the notation used here is the same as elsewhere in this text. Referring to (Ulaby et al, 1986), we can write the equations for liquid water as a function of temperature (~C) and salinity (ppt) as: e00- 4.9(__ independent of temperature and salinity), (6.9) 214

27rrw,(T) = 1.1109 x 10-1~ - 3.824 x 10-12T + 6.938 x 10-14T2 - 5.096 x 10-16T3 (6.10) Eo(T) = 88.045 - 0.4147T + 6.295 x 10-4T2 + 1.075 x 10-5T3, (6.11) E,,o(T, S,,) = E,,wo(T, 0)a(T, S,,), (6.12) Efmo(T,0) = 87.134 - 1.949 x 10-1T - 1.276 x 10-2T2 + 2.491 x 10-4T3, (6.13) a(T, Sw) = 1.0+1.613x 10-5TSw-3.656x 10-SSw+3.210x 10-5S,2w -4.232x 10-7WS, (6.14),r w(T, S,=) r=.(T, O)b(T, Sw), (6.15) b(T, Sw) = 1.0+2.282x 10-5TSw -7.638x 10-4S,, -7.760x 10-6S,2+1.105x 10-8S3w (6.16) ai(T, S,,) = ai(25, SJ,,) exp -b, (6.17) 215

ai(25, S,,) = Sw[0.18252 - 1.4619 x 10-SS, + 2.093 x 10-5S2w - 1.282 X 10-73w], (6.18) A = 25 - T, (6.19) and b = A[2.033 x 10-2 + 1.266 x 10-4A + 2.464 x 10-6A2 - S.w(1.849 x 10-5 - 2.551 x 10-7A + 2.551 x 10-8A2)]. (6.20) 6.1.4 Bound Water According to the results presented in Chapter 5, the Cole-Cole equation provides a reasonable fit to the dielectric data measured for sucrose. The Cole-Cole equation is given by E.b - Eoob Eb = eob + + (jf /fob)() (6.21) where ab is a Cole-Cole relaxation parameter. For the volume fractions vb =.33, vf =0, and va =.67, the relaxation parameter was found to be ab =.5, fob.178, Eob =2.9, and Eb =59, in which case ( 6.21) may be rewritten in the following form: (E+b - fob)(1 + /fob-Voob-+ I ( 2fo + (6.22) 216

E~ = (Efb - foob)V/2/ob =b (eab (6.23) 1+ 202() The assumption made in this chapter is that the dielectric properties of the sucrose solutions may be generalized to other materials, e.g., other carbohydrates and starches. As discussed earlier in Chapter 5, this assumption is not always valid, but in the absence of detailed information about the dielectric properties of all of the major organic and inorganic constituents of vegetation material, the assumption shall be considered adequate for the time being. 6.1.5 Temperature Effects (Bound Water) The temperature measurements conducted for sucrose solutions were discussed in Sec. 5.6 (experiment#5) and the results were shown in Fig. (5.49) to (5.50). This data will now be used to model the temperature-dependence of the parameters in the Cole-Cole equation. From fob = 1/2irr and Eq.( 6.8), h -AS AH T = KTexp( )exp( ) (6.24) K'T' we can write fob AfTexp Bf, (6.25) p T where Af Kexp A B (R), and T is in K. A linear model was assumed for E,, Eo,, and ab as follows: 217

Es = As + BT, (6.26) ~E- Ax + BoT, (6.27) and ab = Aa + BaT. (6.28) Using regression techniques (BMDP software library), the constants were estimated and the model can be represented by: Eb(f, T) = Eoob(T) + 1 + [(f/fT (T)' (6.29) Eb(T) = 35.461 + 0.262T(~C), (6.30) Eoob(T) = 6.457 - 0.146T(~C), (6.31) ab(T) = 0.207 + 0.007T(OC), and (6.32) - 1882.238 fob(T) = 1.296T(K) exp T(K) (6.33) An evaluation of the overall accuracy of this model was performed and the results are given in Table 6.1. 218

The quantities in the table are: RSS Residual sum of squares, EMSE Estimated Mean Square Error, N -number of data points, p = correlation coefficient, b -- intercept(scatter plot), a E slope(scatter plot), where, for a given variable X, a and b have the following meaning: X(predicted) = aX(observed) + b. (6.34) For sucrose solution #9, the frequency range was.2GHz< f < 2GHz, the temperature range was -60C < T < 300C, and the volume fractions were: v, =.67, vb =.33, and vf = 0. RSS EMSEu N L b a' 340.1 1 1.447 237.984 -.090 1.005 I "I 114.494 237.932.688.904 Table (6.1) Statistics associated with the regression fits given by (6.30) to (6.33). 219

The strategy used in this optimization procedure, similar to that used elsewhere in this chapter, was to rely on the fact that the model is more sensitive to E" than it is to E'. Six parameters were optimized using the E" data; they are Af, Bf, A., B, Aa, and Ba. Then, A, and Bo were optimized using the E' data and the other six parameter values already determined. The relaxation parameters calculated from the equations given in this section at room temperature should match those for sucrose#9. The fact that they do not quite match may be due to a slight change in the sucrose solution concentration. The overall fit is reasonably adequate for our purposes but a more elaborate model may be needed for future work. 6.2 Volume Fraction Calculations 6.2.1 Assumptions and Definitions The density measurement of plant materials is, in general, tedious and inaccurate. Furthermore, the density of the bulk vegetation material with no air present is not known. So, certain assumptions have to be made in order to model the vegetation medium. The most important assumption is the one related to the question of whether or not vegetation material shrinks in volume when it loses water. For a material like a corn leaf, the assumption is made that the volume occupied by the bulk vegetation and by air is independent of the moisture content of the leaf, and that when a leaf loses moisture, its volume shrinks by the volume of the lost water. 220

Some of the terms used in this chapter need to be defined, although some of them were used in earlier chapters with or without proper definition. The gravimetric moisture (wet basis) M,, may be determined from knowledge of the wet weight of the plant sample WV and its dry weight Wd, (Wv - Wd) (635) mg WV (6.35) Wv The vegetation density (wet basis) p,, can be determined by measuring the weight W, and the volume V. of the vegetation sample, p, = W,/Vv. The volume may be determined using a displacement technique in which the leaf is inserted in an oil bath and the increase in volume is measured (McKinley, 1983). The volumetric moisture (wet basis) Mo is given by MV = Mpv. (6.36) The dry vegetation density PDv is the density of the dry material and is usually less than 1 g/cm3. The bulk vegetation density PBV is the bulk density of the vegetation material without air. In the next section, we shall derive expressions for the various volume fractions used in the dielectric models in Sections 6.3. These and related quantities are defined as follows: 7 _ PD2V PBV v, (Max) = volume fraction of solid vegetation, 221

vb(Max) = maximum volume fraction that bound water can occupy, vV = volume fraction of solid vegetation that actually binds some water, vu, = volume fraction of solid vegetation that does not bind any water 0 < vV < vlu(Max), vb — volume fraction of bound water, vf volume fraction of free water, va = volume fraction of air, and vub volume fraction of the total vegetation-bound water mixture(= vb + vu). 6.2.2 Volume Fractions For a Sample That Shrinks Volumetric moisture can be derived for a vegetation sample with known Mg and PDV as follows: water weight water weight Mg = (6.37) total weight water weight + dry vegetation weight Since the density of water is 1g/cm3, water volume water volume + PDV(total volume - water volume) or, M Mv (6.39) from which we can obtain: 222

M M, M (6.40) This expression was used throughout this text to calculate. The otherPDV This expression was used throughout this text to calculate M,. The other relevant expressions are: v (Max) =.(1.- M- ), vb(Maz) = v,(Ma; where x = 2 for sucrose solutions and may vary for different materials(see Sec. 6.2.4); this formulation implies that water exists only as bound water for gravimetric moisture equal to or less than.2 and that bound water can not exceed this value, Vb = Vb(Maz) if M, > vb(Max), vb = Mv if M, < vb(Max), V! = Mu — Vb, Vv = XVb, Vub = Vv + Vb& v= 1 - v,(Max) - M,, and 223

vr = vv(Max) - vv. Figures (6.1) to (6.3) were calculated assuming PDV =.33 g/cm3, PBV = 1.60 g/cm3, and x = 2. Figure (6.1) shows v,, vf, Vb, and v, plotted versus Mg; figure (6.2) shows Mv,vf, vb, and v, plotted versus Mg; and Fig. (6.3) shows Mv,, v,,, v,,r and v, (Max) plotted versus Mg. 6.2.3 Volume Fractions For a Sample That Does Not Shrink In this case, when the sample loses water (due to evapotranspiration), an equal volume of air is acquired (may be through the pores). The volume of the sample stays constant throughout the drying process. This situation does not seem realistic, but the shrinking assumption may not be exact either, and the actual case probably lies somewhere between these two limits. Again the volumetric moisture can be derived from M, and PDV as follows: water weight water weight total weight water weight + dry vegetation weight (6.41) but the weight of dry vegetation is constant (independent of moisture, since the volume fraction of the bulk vegetation, v,, does not change), and dry vegetation weight = PBVV, = PDv hence, water volume water volume + pBv(bulk vegetation volume) (6.42) Again, by dividing by the total volume, we will get 224

- VA VF -*- wB W ~~ I 0. 0. 0.0 0.2 0.4 0.6 0.8 1.0 Graviometric moisture Figure 6.1. Calculated volume fractions for a vegetation sample that shrinks. V., Vf, Vb, and V, are the volume fractions of air, free, bound water, and bulk vegetation material that binds water, respectively. 225

1.~ VF - VB 0.47 s Ia/ 0.0 0. 2 0. 4 0.6 0. 8 1.0 Graviometric moisture Figure 6.2. Calculated volume fractions for a vegetation sample that shrinks. M,, Vl, V,, and V, are the volume fractions of water, free water, bound water, and bulk vegetation material that binds water, respectively. 226

1. -'MV - VVR S.V] ~ ~~ xW 0. I 0. 0.0 0.2 0.4 0.6 0.8 1.0 Graviometric moisture Figure 6.3. Calculated volume fractions for a vegetation sample that shrinks. M,, V,, V,7, and Vm are the volume fractions of water, bulk vegetation material that binds water, remaining bulk material that does not bind water, and the total or maximum bulk material, respectively. 227 227

M M, (6.43) MV + PDV and Mu will be, M= MgPDV (6.44) 1 1-Mg The expressions given previously for Vb(Max), Vb, Vf, Vv,, vvb, Va, and vvr remain unchanged; the only changes are: 1. M9 has an upper limit, Mg(Max) = 1xDV and 2. v (Maz) =. Figures (6.4) to (6.6) were calculated assuming PDV =.33 g/cm3, PBV 1.60 g/cm3, and x = 2. Figure (6.4) shows v.,,Vf,Vb, and v, plotted versus Mg; figure (6.5) shows M,,vf,vb,and vv plotted versus Mg; and Fig. (6.6) shows MV,Ivu, Vvr, and vv, (Max) plotted versus Mg. 6.2.4 Volume Fractions For Sucrose solutions As discussed earlier in Sec. 5.5, the volume fractions for a sucrose solution of S(g) sucrose and W(g) water are given by: X=sA= 100S = 10OX S+W X+1 from The Chemistry Handbook (1986), the density p(g/cm3) is tabulated in terms of Ao, 228

1.. -- VA -- VW 0. C o T. Gravimetric moisture shrink. V., V1, Yb, and V, are the volume fractions of air, free, bound water, and bulk vegetation material that binds water, respectively 229 229

I - -EVF e VB 0.lei O.~/ 0 L " 0.O 0.2 0.4 0.6 0.8 Gravimetric moisture Figure 6.5. Calculated volume fractions for a vegetation sample that does not shrink. M, V, IVb, and V. are the volume fractions of water, free water, bound water, and bulk vegetation material that binds water, respectively.

1. -M- w - WR 0. 0. p. 0.4 0. 0.0 0.2 0.4 0.6 0.8 1. Gravimetric moisture Figure 6.6. Calculated volume fractions for a vegetation sample that does not shrink. M,, V,, V,,, and V,,m are the volume fractions of water, bulk vegetation material that binds water, remaining bulk material that does not bind water, and the total or maximum bulk material, respectively. 231

Vs = S-W(p- (Cm3) Va = Vw W(cm3), VW V.L V-+VW As Vb = vW('1)X, and f= v-(l -_6)X. Table 5.8 shows these volume fractions for different solution concentrations. We observe that the ratio 2L is always a constant, approximately equal to 2. 6.3 Models 6.3.1 DeLoor's model, Discs, and e*- = Em As discussed in Sec. 2.2.1, DeLoor's mixing model depends on the following parameters: (1) the depolarization factors, A,, of the included particles, and (2) E*, the effective relative dielectric constant near an inclusion-host boundary. According to Tan (1981), DeLoor's model with parameters E* = Ch and A, = (0,0,1) provides a good fit when compared with the measured data for grass samples. He treated vegetation as a two component mixture consisting of dry vegetation and free water. Tan's data set, however, was limited to singlefrequency measurements made at 9.5 GHz. For this study, we shall assume that vegetation materials consist of four components: (1) air, (2) free water, (3) bound water, and (4) bulk vegetation. Knowing that bound water is held by bulk vegetation materials (e.g. Carbohydrates and Starches) and assuming a constant 232

ratio between v,, and Vb (e.g. = 2 for sucrose solutions, as shown in Table 5.8), we can reduce the components into three: 1. If M. > vb(Max), the three volume fractions are: va, 9Vb = v + Vb, and vf, 2. If M, < vb(Maxz), the three volume fractions are: va, Vvb = v + Vb, and vvr. As discussed earlier, v,, = v,(Max) - v. while vf = 0. DeLoor's model for disc-shaped, randomly-oriented, and randomly-distributed inclusions (Ai = 0,0,1) and e* = Em was found to fit our measured data better than Deloor's other models. This model is known to give the upper limit of E, while sphere-shaped inclusions with E* = Eh gives the lower limit (refer to Eq.2.34). The equation describing the upper limit is given by: Em = Ch + Z - (E - Eh)(2 + (6.45) or for a three-component mixture: Ea + 2 Vvbb(Eb - Ea) + lVf(Ef- E) (6.46) 1 - lve&(1 - I ) - Vf(l -f for M, > vb(Max). DeLoor's model is asymmetrical, and the choice of the host material is not completely arbitrary. The host material should be the material with the largest volume fraction among the constituent components. In Eq. (6.46), Eh was put equal to E, since air has the largest volume fraction. On the other hand, when M, < v&(Maz) we can use: 233

eCa +I sub (eb- Ea) + 2V r(E,- a) (6.47) 6 - kVE(1 - (6.47) 1 - 1v~(1 -1' —) where o = 1,, =ge 4.1 (this value was rep orted for solid sucrose and was defined earlier in this chapter. A regression analysis on measured data for corn leaves was conducted to optimize the model parameters. These parameters were PDV, PBV, s(- V), Sm (maximum salinity), and S. (slope of salinity curve, s = S,,- SMg). The optimized values are as follows: PDv =.322, PBV =.978, x. - 2.398, Sm = 30.307 ppt, and S = 34.417 ppt. Ef and ib were calculated for each sample given T, f, and s using the equations listed in Sec. 6.1. Table 6.2 shows the model accuracy for the data measured on corn leaves for M, _.7,.7GHz < f < 20.4 GHz, and at T = 220C. 234

L RSS EMSE N p b a I' 3883.82 J5.745 676.981.179.821 e" 245.1.365 676.979.197.949 Table 6.2 Model accuracy for corn leaves, DeLoor's model with Aj = (. 0,01) and e* =,m at T = 220C. It is obvious from this last table that the model fits E1 much better than it fits E'. Again, it was our strategy to use the model sensitivity to En to optimize all the model parameters. The model was then evaluated for E'. Figures (6.7) to (6.9) show frequency spectra of the model compared to the measured data for three different moistures (M =.681,.333, and.168). 6.3.2 Debye's model (two relaxation spectra) Since the dielectric properties of plants are controlled by the dielectric properties of water, in its various forms, and since Debye's equations can adequately model water properties, it was assumed that a Debye-like equation is suitable for modeling the dielectric properties of vegetation. The proposed model is: = oo + (f -'foo)f + (l b -'oob )j,, (6.48) fo2 235

35, REAL PART measured) IMPC PART measured) -e- REAL PART calculat)i - IMAG PART caloulated) 20c:_3q i - 15; | i 10 0 5 10 15 20. FREQUENCY (GHz) Figure 6.7. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=22~C for M9=0.681. 236

CORNLEAVESA9 15 REAL PA measured) I PART measured) -- REAL PA calclated) -t- PAKT calculated) - x _ 0 I 0. 5 10. 15. 2. FREQUENCY (GHz) Figure 8.8. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=2200 for M9=O.333.

CORN 10 AtRT (cal cuated) < I p.-'.5.I...' 0. 5. 10. 1 S 2 0 FREQUENCY (GHz) Figure 8.9. Comparison of calculated and measured dielectric spectra for corn leaves using DeLoor's model for randomly oriented and randomly distributed discs at T=220C for M,=0.168. 238

where EO = A + BMW, Eof, Eoof, for, and aeff are free water relaxation parameters as defined in Sec.6.1.1, CEb, foob, fob, and ab are bound water relaxation parameters as defined in Sec.6.1.4. This model was tested on data taken at room temperature; from Section 6.1.3 and 6.1.4, (Esf - CoE) - 75, fof - 18GHz, (Cab - Eob) - 55, and fob -.178 GHz. The conductivity term f was written in a slightly modified form, as,C Vf (6.49) Furthermore, the conductivity term, which is proportional to salinity, can be expressed as: a, = P - Qvf (6.50) where P and Q are constants that depend on the plant type (or in general depend on the ionic content of the sample). This conductivity term was found to vary between different species and even for the same species grown in different geographic locations, as discussed earlier in Sec. 5.4. This Debye-like model was found to fit the data very well in terms of magnitudes and trends. The optimized parameters for c" (i.e., PDV, PBV, x, P, and Q) were used as constants when optimizing the remaining parameters of c' (A and B). The optimized values are: PDv =.238, PBV = 1.255, z = 2, A = 1.861, B = 12.913, P = 53.506, Q = 121.041, and ab =.501. Hence, Eq. (6.48) becomes: 239

75. 53.506- 121.041vf ( 55. ) -= (1.861+12.913M,)+(1 + j 3l *.0 -t)v( 1. + j 18.0 f + (0.178) (6.51) Table 6.3 shows the model accuracy for the data measured on corn leaves (Mg <.7,.7GHz< f < 20.4GHz), and at T = 220C). RSSI EMSE N p b a [i 1412.21 1.947 676 1.983 1.292.969 en 254.9.379 676.978.084.968 Table 6.3 Model accuracy for corn leaves data, Debye-like model at T = 220C. Comparing Table 6.3 (Debye's model) to 6.2 (DeLoor's model) shows that Deloor's model provides a slightly better fit for e", whereas the Debye-like model provides a much better fit for e'. Figures (6.10) to (6.12) show frequency spectra of the measured data and the values calculated according to the Debye-like model. Also, Fig. (6.13) to (6.16) show the dielectric properties of corn leaves (measured and calculated) as a function of Mg for f =1, 4, 12, and 20 GHz. These plots, indicate that the model is in good agreement with the data over the frequency 240

35 EPM REAL PART ( EO IMA PART -E C REAL PART CC - EDC IMPG PARTC) 30. 25" 2015 Z,, 150. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. FREQUENCY (GHz) Figure 6.10. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T=220C for M,=0.681. 241

CORNLEAVESA9 35s EM REAL PART EM I PART -- EPC REAL PARTL - EDC IMWG PART 30 - 255 i00. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. FREQUENCY (GHz) Figure 8.11. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T=220C for M,=0.333. 242

CORN 10 E0 PM REAL PART FREQUE~-NMC P PA1R )._.. —-! 7. 0. 2. 4. 6. 8. 10. 12. 14.. 18. 20. FREQUENCY (GHz) Figure 6.12. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with two relaxation spectra at T=220C for M,=O.168. 243

30 CORNLEAVES( 1.OGHZ) 30,... EPM PART ~ 9De MPART -x- C R- PART 2520 L r15OI O - i 0. 0.0 0. 1 0.2 0.3 0.4 0.5 Volumetric moisture sus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=l GHz). 244

30 CORNLEAVES(4. OGHZ) 25 ~' 20, ~15 - 10L _~~~~I~~~! 1~/ 7 i 0.0 0.1 0 2 0 3 0.4 0.5 Volumetric moisture Figure 6.14. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with two relaxation spectra (f=4 GHz). 245

3CORNLEAVES( 12.OGHZ) 25 c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ p~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~T

PART - REAL PART IWND )4 -* REAL PAIRT R/GI.) 30 _O 20 z 15 rt 10 0. S. 10. 15. 20. FREQUENCY (GHz) Figure 6.17. Calculated real parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra (M, = 0.681 ). 249

30 25 2015i z 1 I i 0..5. 10. 15. 20. FREQUENCY (GHz) Figure 6.18. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (M, = 0.681) 250

C ORNLEAVE SA9 15 IMREAL PART REAL, PARTn RA) m RM PT ~,AIn.CI. ) \ I _i \ 10 V,.. 10... FREQUENCY (GHz) Figure 6.19. Calculated real parts spectra of all components for corn leaves using a Debyelike model with two relaxation spectra. (M = 0.333 ). 251

C O RNLEAVE SA9 _- IwC 5s9 0 5 15. 20 FREQUENCY (GHz) Figure 8.20. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (Mg = 0.333 252

CORN -- I- _70 0 0. 5. 10. 15. 20. FREQUENCY (GHz ) Figure 6.21. Calculated real parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (M, = 0.168 ). 253

CORN _ I m7o24 % 0. 5. 10. 15 2. FREQUENCY (GHz) Figure 6.22. Calculated imaginary parts spectra of all components for corn leaves using a Debye-like model with two relaxation spectra. (MO = O.168) 25,

5. Ei increases with frequency and it has a broad peak around 18 GHz. 6. cd decreases with frequency but with a much slower rate than E". Since bound-water relaxation has a relaxation parameter ab =.5, the spectrum of Ei is very broad (the half-peak points are separated by about 80 decades!). 7. In general, free water dominates at high moistures, while bound water dominates at low moistures. 6.3.3 Birchak model (Semi-empirical) The Birchak model is one of the most attractive semi-empirical models because it is simple and symmetrical. It is given as: -- = vaea + Vvr,, + viee +,vbEbE, (6.54) where the variables are as defined earlier, and a is a free parameter. If a =.5, it is called the refractive model. Again, we tested this model using the measured dielectric data for corn leaves with the following assumptions: PDV =.33, PBV 1.60, and z(= 1 ) = 2. Equation 5.5 was used for salinity, s = 37 - 46Mg. The only parameter to be optimized in this case was a and it was found to be.873. For these parameters, Table 6.4 shows the model accuracy when tested against the measured data. 255

RSS EMSEI N p b a j 1772.02 2.621 676.984 -.182 935 413.612 676.975.264 1.030 Table 6.4 Model accuracy for corn leaves, Birchak model (a =.873) at T = 220C. The model accuracy in this case is very good especially if we remember that only one free parameter was used to fit the data. Figures (6.23) to (6.25) show examples of the frequency spectrum of the model compared to the measured data. 6.3.4 Polynomial fit (empirical model) Polynomial fits are usually very versatile, easy to use, and they can be made to fit almost any set of data (provided that the order of the polynomial is suitable). On the other hand, these models have, in general, no physical significance and they require that many coefficients be estimated. The following polynomial expressions were found to fit the corn leaves data very well: E = (.429 +.074f) + (14.620-.834f)Mg + (39.396-.616f)MM2 (6.55) and 256

35 *RE PAl(mrasrit PE masured) e- REAL PA (calculated - IMG PART (calculated 30 20 I'I_, 0. 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.23. Comparison of calculated and measured dielectric spectra for corn leaves using Birchak's model ( Mf = 0.681 ). 257

CORNLEAVESA9 15 * REAL PAT (measured) IMPG PART Cm.re) - REAL PART caliulated) - IMG PART (calculated) I0 <,W-4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 0 S 1~0: 0 15 20 lasusn'mol58 _ I, 0. 5. 10 15. 20. FREQUENCY (GHz) leaves using Birchak's model (.M9 = 0.333 ). 258

CORN 10 REAL P measre) 1IM PART elasiad -- REAL PA( caloulat.1)? A)I 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.25. Comparison of calculated and measured dielectric spectra for corn leaves using Birchak's model M g, = 0.168). 259

I.977 9.368 lE = (6.590 - -.559f)Mg + (.463 + + 1.617f)M2. (6.56) f f The expression for c" was obtained after several trials to determine which powers of f are the most appropriate. Table 6.5 shows the model accuracy for the polynomial fit. I RSS EMSEI N p b a I 885.8 1.322 676.989.210.978 I"! 235.4.351 676.980.230.943 Table 6.5 Model accuracy for corn-leaves data, Polynomial fit at T = 220C. It is surprising how well this model fits the measured data, albeit it includes 12 coefficients whose values were selected by regressing the model against the data. Figures (6.26) to (6.28) compare spectra calculated using the polynomial model with the measured data. 260

30 L-x ARrIlasoated) 325~eq,; sC 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.26. Comparison of calculated and measured dielectric spectra for corn leaves using a polynomial fit ( M, = 0.681 ). 261

CORNLEAVESA9 15_. * REAL PART asured e REAL P P cal culat) - IMAL PART calculatad r ^41. 0. 5 1 5 20. 0 0. 5 o. 1015 FREQUENCY (GHz) 262

CORN 10 * PART Ia:1 Fir 8mcalecti a fr d) 263 bowI

6.3.5 Single-Phase Single-Relaxation Spectrum Debye Model In the previous sections, a vegetation sample was considered as a heterogeneous mixture with four components: (1) vegetation bulk material, (2) air, (3) free water, and (4) bound water. A different approach is adopted in this section which assumes liquid water to have one phase which is neither free nor bound. It is difficult to satisfactorily define what is meant by bound water. It is generally agreed (Sayre, 1932) that bound water is that portion of the total water content that does not show some of the common properties of liquid (bulk) water. Since the binding forces generated by solid materials, like e.g. sucrose, are continuous and decay with increasing distance from the surfaces of their molecules, bound water actauly exists under various conditions of binding forces. The first layer of water, being the closest to the solid molecules and consequently the most tightly held by their surfaces, is considered to represent the "real" bound water. The further apart water molecules are from solid molecules, the weaker the attraction forces become. At a sufficient distance (corresponding to a sparsely concentrated solution), these attraction forces become small enough so as to consider all the water as free. In this section we will consider the liquid water in a plant tissue as having a uniform single-phase spectrum with effective characteristics that are neither those of free water nor those of bound water. The attraction forces exerted by solid molecules on water molecules, in general, limit the mobility of the free dipoles and their ability of alignment with a time-varying electric field. Consequently, 264

the effective resonance frequency of a sucrose solution is less than that of free water. This effect may be treated as if the solution has an effective temperature lower than its physical temperature. 1. Sucrose Solutions Let us choose a parameter that represents the concentration of a solution: Y = v./M. (6.57) where v, is the volume fraction of the solid material (solute) and Mu is that of the solvent. We may assume, arbitrarily, that the effective temperature depression AT caused by a concentation y is AT = -ATY (6.58) where AT is a constant that depends on the solute type but is independent of concentration. The effective temperature, T,, of the solution is then defined as T, = TT + AT (6.59) where Tp is the physical temperature of the solution. Now, having the effective temperature, we can calculate the resonance frequency fo,(T6) 265

using the formulation derived by Stogryn (1971) for free water (see Section 6.1.3). The quantity A,( — E, - oo) for liquid water is assumed to vary linearly with effective temperature, A, = AA- BAT (6.60) where AA and Ba are constants and T, is in Kelvins. The values of AA and Ba are derived from Equation 6.12 by considering only terms to first order. Similarly, the Cole-Cole relaxation spread parameter a is assumed to vary with y as: = A(1 - exp -Ba!y) (6.61) where A. and Ba are constants. The Debye model for a single-phase liquid is given as: e = ev,[ + [ 1 + (j/fo,,)1-]M (6.62) Using the data measured for sucrose solutions A through G, regression analysis provided the following results: AT = 67.290, AA = 195.110, 266

BA =.371, A4 =.509, B, = 1.035, c, = 2.442, and E~ = 1.0. Table 6.6 lists the statistical measures of the model fit to the data. RSS EMSE N p b a E1 741.4 2.463 302.997 -.630 1.027 e' 254.5.857 302.980.454.962 Table 6.6 Model accuracy of Single-Phase Debye Model as applied to the sucrose solutions data at T = 220C. Figures (6.23)-(6.29), which show the measured and calculated data for various sucrose solutions, indicate that the model is in very good agreement with the measured data. 2. Corn Leaves To test the single-relaxation Debye model for vegetation data, we shall use the same parameter y to represent the tissue volume fractions, in exactly the same manner it was used for sucrose solutions. Consequently, we shall use the same expressions obtained from the sucrose-solutions optimization 267

SUCROSE#A 75 70 _A, A meas red) -e- REAL PAR (caloilated) 65.%, — IMAG PARcalculated 60 55, — 5X50l 45p4 5 40 35 30 _-, 2 50 205 15 10 5 O. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.29. Comparison of calculated and measured dielectric spectra for sucrose solution (A) using a Debye-like model with a single variable relaxation spectrum (V. = 0.239 and Mu = 0.761). 268

65.....SU.CROSE#B 60 Od P asrci3 -- REA P calculate) -- IMPG PA~r (calUolat.) 55 50 < 45, _ *E 401<: 35 30 5 A 0. 5. 10 15. 20. FREQUENCY (GHz) Figure 6.30. Comparison of calculated and measured dielectric spectra for sucrose solution (B) using a Debye-like model with a single variable relaxation spectrum (V. = 0.385 and M, = 0.615). 269

SUCROSE#C 60 ~ + REALU PAWI' tA -5 - is pa (Cal.latled) 50 OW 45 40 35 30 Fp. 25 20 __ o15!O 5 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.31. Comparison of calculated and measured dielectric spectra for sucrose solution (C) using a Debye-like model with a single variable relaxation spectrum (V, = 0.485 and M, = 0.515). 270

50 SUCROSE#D 50 REALP?Fmasured 45 -- REAL PAr calea1ti -- IMPG Pi (calculated 40 3530 25 2 0 0 5. 0 ~ 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.32. Comparison of calculated and measured dielectric spectra for sucrose-solution (D) using a Debye-like model with a single variable relaxation spectrum (V, = 0.559 and M, = 0.441). 271

~40 SUCROSE#E 40 *REALP P er mas-urei) e REAL P cTuallar ted 35, x IMPl PARTcalculated 30 25 _20 15 5O. o. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.33. Comparison of calculated and measured dielectric spectra for sucrose solution (E) using a Debye-like model with a single variable relaxation spectrum (V, = 0.613 and M, = 0.387). 272

SUCROSE #F 35 -- REAL PART calculat) -*t IMPG PART (cairatd1) 30 25 101 -5 10 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 8.34. Comparison of calculated and measured dielectric spectra for sucrose solution (F) using a Debye-like model with a single variable relaxation spectrum (V. = 0.655 and M. = 0.345). 273

SUTCROSE#G REAL PART (msurd) IMP PART maur:d),4 -e- REAL PARr calcalatit) 0 -* IMAMPG PART calculated 30 4 0o,25 2 ei 0I 0. 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.35. Comparison of calculated and measured dielectric spectra for sucrose solution (G) using a Debye-like model with a single variable relaxation spectrum (Vs = 0.667 and M,, = 0.333). 274

10.Ii 3.02. 00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Gravimetric moisture Figure 6.36. For the single phase model, y(Vv,/Mv) is plotted against gravimetric moisture Mg. 275

to model the data for corn leaves. These expressions are: y = v,/Mv, (6.63) AT - -67.290y, (6.64) T, = Tp + AT(K), (6.65) fow(T,) is according to the expressions given in Stogryn (1971), A, = 195.110-.371T,(K), and (6.66) =.509(1 - exp — 1.035y). (6.67) The Expressions for the volume fractions are: Me= mg + (6.68) PDV and v, = v (Max.) = r/(1 - M.). (6.69) In order to calculate v, and M, we have to assume values for PDv and PBV. 276

7= PDV/PBV. (6.70) The model may be written in the following form: - = coo + [I ()// o) -jaof/]Mv (6.71) 1 + (jf/fO;)'where coo = Ao + BooMv and a, = A, - BM,,. Using corn leaves data and regression analysis (BMDP), the following values were selected for the unknown parameters: PDV =.154 g/cm3, PBV = 3.978 g/cm3, A0o = 1.656, Bo = 24.374, Af = 37.396, and B, = 18.892. Table 6.7 gives the statistical parameters associated with fitting the model to the data. RSS EMSE N p b a E1 1063.99 1.579 676.987.230.976 E1i 390.60.580 676.969.439.923 277

Table 6.7 Model accuracy for corn leaves data, Single-Phase Debye Model, T = 220C. Figure (6.30) shows a plot of the parameter y as a function of gravimetric moisture, and Fig. (6.31) shows how the resonance frequency varies with gravimetric moisture. When M, = 1 (pure water), fo = 18 GHz while when Mg = 0, fo = 0. The volume fractions calculated using the optimized values of PDV and PBV are shown in Fig.(6.32). Figure (6.33)-(6.43) show frequency spectra for corn leave, at selected moisture conditions, plotted against the model. Similarly, Figs. (6.44)-(6.51) show dielectric plots for corn leaves as a function of M,. The model, in general, fits the measured data very well (at least as good as the two-phase Debye model does). Tables 6.8 and 6.9 provide comparison of the overall performance of the five models considered in this Chapter. 278

25f0 25tt 15 r-O pow 5 -O 20,4 A/' o / 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Gravimetric moisture Figure 6.37. The effective resonant frequency fo(GHz) of the single water phase versus gravimetric moisture M,. 279

lo 0. ) VA o.3E - 0 o. 0./ O.0.o 0. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Gravimetric moisture Figure 6.38. Volume fractions of corn leaves as calculated from the single phase model. Mr,, V,,,,, Va, and V,,, + V,, are the volume fractions of water, bulk vegetation material, air, and dry vegetation material, respectively. 280

35 P WL, measured -O- REAL PART calculati3 -E — IMAC PART calculated 30 I 5 20I X,. 15 7 x 0. 5 10. 15. 20. FREQUENCY (GHz) Figure 8.39. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, " 0.681. 281

CORNLEAVESA3 30 * REALPAt (ua saed) PW na.men.ured) * P PART calculalart) - ItMA PART (calculated) 25 4!m4 20 - 1 S 4>5 2o 10 I'0. 5 10. 15. 20. FREQUENCY (GHz) Figure 6.40. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.605. 282

30 iART(calculated) MC PART calculoated) 25 2 0. 2OC15 51 i6 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.41. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.601. 283

CORNLEAVESA7 20 -- 15=, Btam - I. FREQUENCY (GHz) Figure 6.43. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.472. 285

CORNLEAVESA9 10 REAL -4- REAL P caloulated) - IMPG PAr calculated) 8FREQUENCY (GHz) Figure 6.44. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M. = 0.333. 286 2861

CORN 10 -31- IMa P calclated) <08 z rIw 0. 1, 0. 5. 10. 15. 20. FREQUENCY (GHz) Figure 6.45. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.258. 287

CORN 10 REAL PAiT calaclated) -- I MAC PART calolated) 8 7. I j * 0. 5. 10. is. 20. FREQUENCY (GHz) Figure 6.46. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M_ = 0.252. 288

CORN AmeasLred F-RE RQ C (caGclatid e 6. Co calculatedarcspct /_ IX _.' I i I _! *, ~!: 0. 5. 10. 1 5. 20. FREQUrENCY (GHz) Figure 6.47. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.168. 289

CORN A (calculat1 ) x-I- ~ PART (calculated) 43 3' 4.'e. 0. I 10 15 20 FREQUENCY (GHz) Figure 6.48. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.074. 290

CORN 3 - P REAL PAK Pcalculatld) -e- IMPC P2a (caliolated) _ I V., ams rQ ~ ~ ~ ~ ~ FREQUENCY (GHz) Figure 6.4g. Comparison of calculated and measured dielectric spectra for corn leaves using a Debye-like model with a single relaxation spectrum (variable) for M, = 0.041. to ~ FEUEC.,~z Fiue84.Coprsno cacl a e anmasredilcrcsctafron le_ e uin&Dey-iemdlwt&silerlxtospcrmvaabe

CORNLEAVESO.7GHZ 35 * EM RE ALPA AS) * E' 1eMP PAI I -- EC REAL PA I" -ED C 14MPG PAPT(CART) 30 / 25 I 0 20e rGravimetric moisture O. o.o 0s.2 0c3 0.e4 0f S 6 0 07 08 Gravimetric moisture Figure 6.50. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 0.7 GHz. 292

CORNLEAVES 1.OGHZ 35. IMAPC e O SC REAL P.4T,'Ca --- EI IMP; PA 30 < 25 20 15 05 - 0 -,. o. O o 0. I 2 o.3 0.4 0.5 0.6 0.7 0. 8 Gravimetric moisture Figure 6.51. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 1 GHz. 293

CORNLEAVES2.OGHZ 35 ~ EM REAL PAnr - EDC EAL PA 30,~ 25 20 15 ~ill lo 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Gravimetric moisture Figure 6.52. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 2 GHz. 294

CORNLEAVES4.OGHZ 35 -3- EC IMPC PA (CAIL 30 25 20..15 I ~ 0.0 0.1 o.2 0.3 0.4 0.5 0.6 0.7 0.8 Gravimetric moisture Figure 6.53. Comparison of caklculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 4 GHz. 295

CORNLEAVES8.OGHZ 30 EPM REAL PA S E tIM~C PARTG e — EC REAL PART ---- EC IMN PArW 25 20 15 10 oe 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Gravimetric moisture Figure 6.54. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 8 GHz. 296

CORNLEAVES 1 7.GHZ 30 -* EREAL P -- EDC IMG PRT C 25 20 151 0 5 0. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 Gravimetric moisture Figure 6.55. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 17 GHz. 297

CORNLEAVES2O.4GHZ 30 E*M REAL PA a o E2 IMPG PAST -0 EC REAL PART -*- EDC IMAG PART CA 25 r - 20 15 Z a 10 51 0.f 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Gravimetric moisture Figure 6.56. Comparison of calculated and measured dielectric constant versus moisture for corn leaves using a Debye-like model with a single variable relaxation spectrum for f = 20.4 GHz. 298

model DeLoor's Debye Birchak Polynomial Debye (Single) #parameters E' 0 2 0 6 2 RSS 3883.82 1412.2 1772.02 885.8 1063.99 EMSE 5.745 1.947 2.621 1.322 1.579 N 676 676 676 676 676 p.981.983.984.989.987 b.179.292 -.182.210.230 a.821.969.935.978.976 Table 6.8 Comparison between different models for corn leaves data at 220C (real parts). model DeLoor's Debye Birchak Polynomial Debye (Single) # parameters e' 5 5 1 6 4 RSS 245.1 254.9 413 235.4 390.60 EMSE.365.379.612.351.580 N 676 676 676 676 676 p.979.978.975.980.969 b.197.084.264.230.439 a.949.968 1.030.943.923 299

Table 6.9 Comparison between different models for corn leaves data at 220C (imaginary parts). 300

Chapter 7 Conclusions and Recommendations This chapter provides a summary of the major conclusions reached during the course of this study and proposes recommendations for future work. 7.1 Conclusions 7.1.1 Measurement System Open-ended coaxial probes were found to be viable sensors for making dielectric constant measurements at microwave frequencies. They have the following features: 1. They can be operated over a wide frequency band ( e.g.,.05-20.4 GHz for the.141" probe). 301

2. They are easy to use; no sample preparation, in general, is required. 3. They provide results in near real-time (when used with an automatic network analyzer). 4. Non-destructive measurements of plant parts (or any living tissue) are possible. 5. Temperature measurements are easy. 6. Measurement accuracy is fairly good (5% or better for liquids). 7. The sample thickness need only be comparable to the probe diameter. 8. It is possible to deduce E of a thin sheet of material from two independent measurements made against two known background materials with infinite electrical thicknesses. 9. The probe system is very sensitive to contact and pressure at the probe tip. It is extremely accurate for liquids where contact and pressure are not crucial problems. For semi-solids, like plant parts, it is possible to use a pressure guage to control pressure and use care to insure good contact between the sample and the probe. However, because of errors caused by imperfect contact between the probe tip and the material under test, the variability of the measured e was found to be about 10% (alt/ =.10). By designing the experiment to fit the required precision of the data, a choice of N (number of independent measurements) can be made. 302

7.1.2 Measurements 1. The measurements covered a variety of plant types; some of them were not reported because of time and space limitations. 2. The overall frequency band of the measurement system was.05 to 20.4 GHz; however, most of the measurements on plant parts were performed from.7 to 20.4 GHz. Higher-order mode propagation determined the upper end of the frequency range while probe sensitivity governed the lower end of the frequency range. 3. Plants were measured at various moisture levels from freshly cut to very dry. 4. Also, the salinity of the fluids extracted from leaves and stalks was measured by a conductivity meter. 5. Temperature measurements were conducted on different plant leaves between -400C and +500C. These samples were found to freeze at temperatures below 0~C ( between -5 and -100C) due to supercooling effects. Some of these temperature experiments involved exposing the sample to a freezing-thawing-freezig cycle to investigate a hysteresis-like behavior. 6. In order to study bound water effects in plant materials, a series of dielectric measurements were conducted on sucrose, dextrose, starch, and other plant constituents known to form chemical bonds with water molecules. 303

Various sucrose solutions of different concentrations were measured as a function of frequency and temperature. The knowledge gained from these measurements confirmed the existence and importance of bound water in living tissues, and the technique made it possible to study this form of water in the absence of the effects of salinity on the dielectric constant of the water-vegetation mixture. 7.1.3 Modeling The dielectric properties of liquid water in all its forms (free, bound, and saline water) were summarized. The volume fraction models were established for a vegetation sample that shrinks and for one that does not. Both models were tested and we concluded that although the real situation lies between these two extremes, the shrinking model is closer to reality. Given the dielectric constant and the volume fractions of the sample constituents, various mixing models were tested and compared to dielectric data measured for corn leaves at room temperature (T = 220C). DeLoor's mixing model fits the data when E* = Em and (Ai = 0, 0, 1) which is the model for randomly-oriented and randomly-distributed disc-shaped inclusions (known as DeLoor's upper limit). Birchak model was tested and found satisfactory. Debye's model was tested (with one and with two relaxation spectra) and found to yield very good results. Also, a polynomial fit was developed for easy calculations. Because our knowledge about the physical properties of plants is still limited, we had to use free parameters in the models. The fewer these free parameters are, the more useful the model becomes. 304

7.2 Recommendations 7.2.1 Measurement System 1. The use of the HP8510 network analyzer will enhance the system capabilities: * Frequency band.01 to 20.4 GHz in one sweep. * The time domain feature will help eliminate the reflections from the various discontinuities (e.g., connectors and bends), while allowing the measurement of the reflection from the probe tip (using FFT and a time gate). Consequently, the system will have better overall accuracy. * Similarly, measurement precision will improve because of the general built-in high quality features of the HP8510 such as automatic frequency-locking (no harmonic skip problem). * Easy to program and fast data acquisition and processing. 2. The calibration algorithm can be modified by replacing the equivalent circuit model with an exact electromagnetic solution ( e.g., MOM), which will improve the overall accuracy of the system. 3. The frequency range may be extended beyond 20.4 GHz by using.085" probes with connectors that operate at millimeter wavelengths. 4. New probe tip configurations may be developed to better suit the measurement of solid materials (e.g., rocks). 305

5. The possibility of using open-ended waveguides to perform dielectric measurements should be explored. 7.2.2 Measurements and modeling Extensive measurements and modeling efforts need to be performed on plant materials to: 1. Generate a database of plant dielectric properties as a function of: * plant type, part, and location, * plants with very high moisture contents, * plants with low salinity (may be fresh water aquatic plants), * plants with very high salinity content, * temperature for -400C < T < +500C with freezing-thawing-freezing cycles. 2. Develop a complete dielectric model for bound water (one or two relaxation spectra) as a function of concentration, frequency, temperature, and the binding material. 3. Investigate, more thoroughly, the freezing point discontinuity, the under (super) cooled effects, and the hysteresis-like behavior observed in E - T curves. 4. Further investigate the single-phase model of liquid water (refer to Sec. 6.3.5). This model suggests that liquid water exists in solute and colloidal 306

solutions as one continuous phase with an effective temperature lower than room temperature by a value that is proportional to the type and concentration of the solid material. The effective temperature calculated for a particular solution has a corresponding oE and fo for the liquid water phase. The model fits the sucrose solutions and the corn leaves data (at least as good as the two-phase model). Another approach to the single-phase model can be suggested as follows: since, according to Debye's relaxation formulation, the ability of the molecular dipole to orient itself with a time-varying electromagnetic field depends on the viscosity of the medium, it is possible to consider that solutions have viscosities that are different from that of free water. Consequently, solutions have dielectric relaxation spectra that are different from that for pure water. 5. Conduct experiments on pressure-volume curves: Pressure-volume (P-V) curves can be generated on roots, shoots, or leaves using two methods: (i) samples are dehydrated inside a pressure chamber, and the sap is collected and weighed as the pressure is incremently increased, or (ii) excised samples are allowed to dry outside the pressure chamber by evapotranspiration, then they are weighed periodically to determine sap loss, and their corresponding balance pressure is determined in a pressure chamber. These two methods were compared in (Ritchie et al, 1984). Such an experiment is important because the extracted sap samples may be used to determine: 307

(a) the salinity distribution (by measuring ionic content of the extracted fluids using a conductivity meter) as a function of pressure, and (b) the bound water distribution (by measuring the dielectric constant of the extracted liquids) as a function of pressure. The two methods described earlier for generating (P-V) curves are tedious, time consuming, and destructive. We can investigate the possibility of using the probe dielectric measurement system to predict the (P-V) curves without actually destroying the sample. The probe system, in this case, can be used as a fast and non-destructive tool to monitor plant physiological parameters such as volume-averaged osmotic potential at full turgor (0i~ro) and volume-averaged water potential at zero turgor (tz). 6. Study the dielectric constant profiles in plants as a function of height above the ground surface. Also, more measurements should be conducted to study the azimuthal profiles of the dielectric constant of tree trunks. 7. Study density effects by testing plants with high density (e.g., some tree branches are very dense) and other plants with low density (e.g., Coleus leaves). 8. Develop a general model for the dielectric properties of plant materials that incorporates all their physical parameters. Special attention should be given to the temperature effects in general and to the freezing point discontinuity in particular. Freezing point discontinuity is a transitional 308

state and the measured data showed a hysteresis behavior that has been attributed to supercooling behavior. Also, the properties of bound water at low temperatures should be considered. 309

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APPENDIX A Dielectric Data at Room Temperature This appendix contains the dielectric data for some vegetation materials at room temperature. The set consists of eight parts: 1. Sucrose solutions (A.1 - A.8) Seven sucrose solutions, with different concentrations, are reported. Some of them were already given in Chapters 5 and 6, but the whole set is presented here for the sake of completeness. 2. Comparison between corn leaves and soybean leaves (A.9 - A.13) at 1, 2, 4, 8, and 17 GHz. 3. Comparison between corn leaves and corn stalks (A.14 - A.20) The measurements were taken on the inside part of the stalk (not on the sheath) at.7, 1, 2, 4, 8, 17, and 20 GHz. 4. Comparison between the model developed in Sec. 6.3.2 (solid line) with PDv =.52 and the Measured data for corn stalks at.7, 1, 2, 4, 8, 12, and 20 GHz (A.21- A.27). 5. Measured dielectric spectra for Aspen leaves with M9 as parameter for M9 =.28,.57, and.86 (A.28- A.29). 6. Measured dielectric spectra for Black Spruce tree trunk with M, as parameter for M, = 0,.136,.257,.38, and.52 ( A.30 - A.31). Also, for the same samples, measured dielectric data versus M, for f = 1, 2, 4, and 8 GHz (A.32 - A.35). 7. Measured dielectric spectra for Balsam Fir trees (branches, trunk, and leaves). Since the leaves are needle-like, a single needle was measured against two different backgrounds (teflon and metal). (A.36 - A.45) 8. Comparison of measured dielectric data for corn stalks and corn leaves between those reported in (Ulaby and Jedlicka, 1984) and those reported in this work at different frequencies (A.46 - A.50). Differences are mainly attributed to samples variability. A.0

0.1 41 "4NGP HF SUCROSE*A 0.250"NGP VLF 12/17/1985GH 80 VS=0.239 YB=O. 120 70 O YF'0.641 60 so EPSILON 40 30 20 10 0 2 4 6 8 10 12 14 FREQUENCY IN GHZ Figure A.1

.141" NGP 12/17/85 G,H.250' NGP 70.250" NGP 7 0I SUCROSE s B D 60:I. 50 + -. VS=.385.:.:* VB=. 194 4 4 VF=.421 D 40 EPSILON (EP*) 30 - 20 — i —-I-II-IiIl-I ILU \* 10 LIP Li 0 5 10 15 20 25 FREQUENCY (GHZ) Figure A.2

.141"NGP SUCROSE #C 12/17/85 GH.250" NGP 60 ID 55 i.i 50 D 45 to VS.485 VB=.244 40- - VF=.271 35 EPSILON (EP*).. 30 25 - 20 - 15 ltiLIEu. m1_ 5 O 5 10 J5 20 25 FREQUENCY (GHZ) Figure A.3

SuCROSE*D V 4i"NGP lif 1 2 /I7i 985G,#" 0.250"0 L so vswo.~~~yc0559 vFvO.1 62 40 35 30 EPSILON p ~~25 1 5 20 5 I 0 o 5 ~~~~~~~FREQUENCY IN GHZ Figure A.4

oSE *E ~~12/ i 715 G, sUCRO X.1 41 "NGP.250" NGP 0 35 VS=.6\3V8=.~~~~B..306 50 b ~~~~~~~VF=.8 25 EPSILON (EP*) 20 15i'8" 61 E I~ ~ " ~c 0 6 a 106 1 2 0 2 4 ~~~~FREQUGICY(HZ Figure A.5

'I 41 "NGP SUCROSE #F 12/17/85 6*1.250" NOP 35T 30 t 30\ VS.655 eo V=8=.327 25 VF=.O 8 20' EPSILON (EP*) 15 5 0 2 4 6 8 1 0 12 1 4 1 6 18 2 FREQUENCY (GtZ) Figure A.6

SLICROSE*G; 0. 1 41"NGP HF 0.250"NGP VLF 12/17/19856,H 35 V ynO.667 VB=0.?333 YFOO-000 30 25 20 ]EPSI LON 15 00 0 2 4 6 8 10 12 14 1 8 2 FREQUENCY IN GHZ Figure A.7

0.141 "NGP HF YS-0.559 SUCROSE*D 0.250"NGP VIF VB-0.279 YflO. 162 ~~~~~12/17/1985G H YFn0. 1'62 14.5 14.0 IMAGINARY PARTS 13.5 / 13.0 EPSILON 12.5 12.0 1 1.5 11.0 10.5 10.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 FREQUENCY IN GHZ Figure A.8

Appendix A.cl+sb(l.O hz) 062486 17 45. + CorrLeaves Real) CornLeaves Ima. ) 40- Soybeans L Imag.) 35. f = 1 GHz z 30. O 25. 20.:) 15. 10. 5. 0. 0.0 0.2 0.4 0.6 0.8 Gravixnetric moisture Figure A.9 A.9

Appendix A.cl+sb(2.0 hz) 062486 17 45. CornLaves eal) CornLeaves lma.) 40.: SOLR) 40 - L-*- Soybeans LImag) 35..~ 30. 1 f = 2 GHz t 30. O 25. 20. cu 15. 10. 5.0.0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure A.10 A.10

Appendix A.cl+sb(4.0 hz) 062486 17 45. -- CorrLeaves Real) Corncavesma?.) 40. - Sobeans L(Iag) 35. c: 30.< > f = 4 GHz 0 25.'-.. 20. (U 15. 10. 5. 0. ~.o 0.2 0.4 0.6 0.8 Gravirnetric moisture Figure A.11 A.11

Appendix A.cl+sb(8.O hz) 062486 17 45. CrLaves Real)' CornLeaves ) 40. LL ma) 35. f = 8 GHz (c 30. 0 25. 20. 4j 0 10. 5. 0.0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure A.12 A.12

Appendix A.cl+sb(17.Oghz) 062486 17 45 Cornyeavs(Real) — CornavesIa) ~~40.~ LImag. 40. -e- Soybeans L Real) 35. ct 30. f = 17 GHz 0 25. Q 20. ) 15. 10. 5. 0. 0.0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure A.13 A.13

Appendix A CL+CSIN(0.7GHZ) 062486 17 45.i - ComrLeaves ) -.- CornmStaLks Rea) 40. -- CorrStalks mag.) 35. v I 30. ~ ~ f =.7 GHz 0 25. Q 20. ~. 15. 10. 5, 0. 0.0 0.2 0.4 0.6 0.8 Gravirnmetric mnoisture Figure A.14 A.14

Appendix A.cl+csin(l.Oghz) 062486 17 -- ConJeavs (Real) -' CornLeaves Ima. ) 40. -0- CornStalks RABaI) CornStalks mag.) 35. 4-1: 30=f: 1 GHz 30. 0 25. 20.10 5. 0. 0.0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure A.15 A.15

Appendix A.cl+csin(2.Oghz) 062486 17 --- co.n ravy (Real) CorinLeavesa ) @ CornstalkseaI) 40. -- CornStalks iaIg.) 35. 03 30.0 f = 2 GHz 0 25. 20. Qa) 15. 10. 5. 0. 0.0 0.2 0.4 0.6 0 Gravimetric moisture Figure A.16 A.16

Appendix A.cl+csirn4.Oghz) 062486 17 4. 40. -0e- CornStalks ReaI) CornStalks Imag.) 35. -~ |f = 4 GHz 30. o 25. C.) 20. QC) X) 15. 10. 5. 0.0 0.2 0.4 0.6 0 8 Gravirnetric nnoisture Figure A.17 A.17

Appendix A.cl+csinr8.Oghz) 062486 17 --- ConLaves Real) - CornLeaves ma. ) 40. -0 —- CornStalksaI) 35. 4. 30. f = 8 GHz _l 25. - Q 15. 20. 10. 5. 0. 0.0 0.2 0.4 0.6 0.8 Gravimetric mnoisture Figure A.18 A.18

Appendix A.cl+cs(17. hz) 062486 17 45. -- CornLeaves Real) ConLeaves ) -e- CornStalksea) 40. -- CornStalks (Irag.) 35. 30. l) |f = 17 GHz 0 25. 20. Q) C) 15. 10. 5. 0.o 0.2 0.4 0.6 0.8 Gravirnetric moisture Figure A.19 A.19

Appendix A.cl+csin20.ghz) 062486 17 - CornLeaves Real) CorLeaves(Ima. ) --- CornStalks I~gI! 40. - CornStalks ) 35. f = 20 GHz 30. 0 25. * ao 20. 1( 15. 10. 5. - 0.0 0.2 0.4 0.6 0.8 Gravimetric moisture Figure A.20 A.20

Appendix A CORNSTALKS(IN)0.7G 40 + EPM REAL STALKS' EM IMAG STALKS -- EPC REAL LEAVES - EDC IMAG LEAVESCAL 35 f =.7 GHz + 4 30 25 < 20 o 15 + * - * 5 + Volumetric moisture Figure A.21 A.21

Appendix A CORNSTALKS(IN) 1. OG 45 EPM REAL STAUCS EAS EM IMA SALKXS 40 - EPC REAL LEAVES CALA 4 0 ~x EDC IMAG LEAVES CALC) f = 1 GHz Q + - 30- 4 C 25 20 o I1 510 0 0.0 0.1 0.2 0.3 0.4 0.5 Volumetric moisture Figure A.22 A.22

Appendix A CORNSTALKS(IN)2.OG 45 EPM REAL SALKS * Ed IMAG STALKS 40 e —o EPC REAL LEAVES 40 - EDC IMAt LEAVES 35 f = 2 GHz 30!7 25 20 o 15 7 5 +++ r 10 4/ 0.0 0.1 0.2 0.3 0.4 0.5 Volumetric moisture Figure A.23 A.23

Appendix A CORNSTALKS(IN)4.0G EPM REAL SEXS(EAS EIM IMAGE STJXRE ASJ --- EPC REAL LEAVESCL) 40 - EDC IMAG LEAVES CALC 35 f =4 GHz ~ /30 25 20 Z + 15 1 0 0 I 0.0 0.1 0.2 0.3 0.4 0.5 Volurnetric moisture Figure A.24 A.24

Appendix A CORNSTALKS(IN)8.OG 35 EPM REAL SIAXSTL ASl' EDM IMAG SlTEA S) -e- EPC REAL LEAVES CAL=) --- EDC IMAG LEAVES CALC) 30 25 f= 8 GHz 15 1 I 0 0.0 0.1 0.2 0.3 0.4 0.5 Volumetric moisture Figure A.25 A.25

Appendix A CORNSTALKS( IN)12. O 35 + EPM REAL SAKS MEAS)' EEM IMAG STAIXSM --- EPC REAL LEAVES CALk -- EDC IM/G LEAVES CAC) 30 25 f =12 GHz 20 15 z 4 o;) 10 X -' O. I 1 I l 0.0 0.1 0.2 0.3 0.4 0.5 Volurnmetric moisture Figure A.26 A.26

Appendix A CORNSTALKS(IN)20.0 25 EPM REAL STLXS(EAS['EM IM, SrALXSMEAS --- EPC REAL LEAVES -x- EDC IMEX LEAVES 20 f = 20 GHz d ~15 10 O I + 0.0 0.1 0.2 0.3 0.4 0.5 Volumetric moisture Figure A.27 A.27

T=22 C Aspen Leaves (Real Parts) M9= D 40 T 35 ee..__ev.86 30 25 Dielectric 2057 Constant 15 10 5.....- ~ ~.28 1 2 3 4 5 6 7 8 9 Frequency in (GHz) Figure A.28

T=22 C Aspen Leaves x (Imag. Parts) 12~ 12 * Mg= 8 10~~~~~~~~~~~~~~~~~~ Dielectric 6 In Constant O~-o —. — 28 1 2 3 4 5 6 7 8 9 Frequency in (GHz) Figure A.29

12/15/1986 X Black Spruce Tree Trun o.250" (Real Parts) 11 T 13~ ~ ~ ~~~~~~D-~ —D 1'1 9 t a —~a —-uo u —u ~ —-a~-a —-u- a- a.521 Dielectric 6!0=A _H. 0.3 9 ~Constant 5l Ad * - F.7 ~O-O O4~o - NO ^O cO-~OO 3 4 i — ~~~~~~~~ILLCIL ~ 0W.000g0 002 7 o 5 I o_._^~~~~~5 1 ~~~~3 4 in(z) 2 Frequency Figure A,30

0.250" Black Spruce Tree Trunk12/15/1986 (Imaginary Parts) Mg 3.5 A A~AA 0.521 3.0 2.5 2.0 l Dielectric 2. 1 9 Constant 105 1.5 ~ 0.380 By > 0.257 1.0v =1-.0.5 136 1 2 3 4 5 6 7 8 9 Frequency in (GHz) Figure A.31

0.250 12/15/1986 Black Spruce Tree Trunck f=1.0 GHz 12 Real 10 8- o Dielectric 0 Constant 6 0 Nc Imaginary 2 O 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Gravimetric Moisture Figure A.32

0.250" 12/15/ Black Spruce Tree Trunck f = 2.0 GHz 1 0 TReal 0 9 8 7 6 0 ~~~~~~00 Dielectric Constant 4 0 0 Imaginary 3 2 00 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.0 0.1 0.2 0.3 0.4 0.5. Gravimetric Moisture Figure A.33

0.250" 12/15/1986 Black Spruce Tree Trunck f = 4.0 GHz 9T Real O 8 7 6' 0 Dielectric 0 t3 Constant 4 Imaginary 0 3 2 L 1 ~ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Gravimetric Moisture Figure A.34

0.250" 12/15/1986 Black Spruce Tree Trunck f = 8.0 GHz Real 4.5 4.0 0 0 3.5 3.0 2.5 Dielectric Constant Imaginary Constant 20 2.0 1.5 1.0 0.5 0.0 I I I l, l l, 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Gravimetric Moisture Figure A.35

11/5/85 -i BALSAM FIR m.141" NOP TRUNK (BARK) T 1 22 DEO C 20 18 | e e REAL 16 14 12 EPSILON (EP') Mg = 0.268.. 10 8 6 IMAGINARY o 4 — ~"c~ o o o o o o ~ 4 0 0 0 2 4 6 8 10 12 14 16 18 20 FREQUENCY (0HZ) Figure A.36

11/5/85 > BALSAM FIR 141" NOP BRANCH(DRY) T = 22 DE0C 5.5 5.0 4.5- e~ REAL 4.0 3.5 + ~ EPSILON(EP') 3.0 2.5 Mg= 0.375 2.0 1.5 - IMAGINARY 1.0 lC o0 ~ o o o o o 0.5 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ)

11/5/85 BALSAM FIR.141" I N BRANCH (DRY) T a22 DEOC 6 5 4 REAL EPSILON(EP) 3 Mg = 0.375 co 2 IMAGINARY o< > 0 1 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 FREQUENCY (0HZ) Figure A.38

11/5/85 BALSAM FIR.141"' OP BRANCH (DRY) 1-a 22 DEG C 1.4 1.2 1.0 IMAGINARY 0.8 EPSILON (El") Mg = 0.375 0.6 0.4 0.2 0.0 0.5 1,0 1.5 2.0 2.5 3.0 3.5 4.0 FREQUENCY (0HZ) Figure A.39

11/5/85.141" NOP BALSAM FI R 1. 22 DEOG C TRUNK (DOWN) 7. 6 - REAL 5 441 EPSILON(EP') 4 - v ~ -~ 2Mg = 0.277 3 2 Scot., IMAOINARY 2 —' ~ oo. o o o o o o 0 0 0 0 0 1. o o o o o 0 2 4 6 8 10 12 14 16 1t 20 22 FREQUENCY (GHZ) Figure A.40

1 1/5/85 rD BALSAM FIR BRANCH.141" NOP B T - 22 DEOC (WET) 14~e, 12 REAL 10 e EPSILON(EP') 8 6 Mg = 0.413 o IlMAOGINARY 4 to% 0 ~0 0 o 0 0. 2: 0 2 4 6 8 10 12 14 16 181 20 22 FREQUENCY (OHZ) Figure A.41

BALSAM FIR. 141" NOP BRANCH T 22 DEOC (WET) (WET) 5.0 4.5 4.0- ~ REAL 3.5 3.0?> EPSILON (EP") 2.5 2.0 - Mg =.413 1.5 1.0. IMAOINARY 0.5 0.0 I I I 0.5 1.0 1.5 2.0 2.5 3.0 3.5 40 FREQUENCY (0HZ) Figure A.42

I 1/5/85 _.1 41 " NOP BALSAM FIR T = 22 DEG C LEAF/TEFLON 7 Al REAL 6 5 *, 5 EPSILON (EP') 4 Mg = 0.502 2 - 4:0m, 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (0HZ) Figure A.43

11/585 14 1.40 1.35 1.30 1.25 D PSILON(EP") ~ 10 NP1.20 1.15 IMAGINARY 1.10 1.05 Mg = 0.502 1.00. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 FREQUENCY (0HZ) Figure A.44

11 /5/85 T14 22 DE BALSAM FIR ~T = -~22 D0~EOC ~LEAF/METAL 16 14 t t REAL 12 10 EPSILON (EP') * 8 0 6 IMAOINARY Mg = 0.502 4 0 2 0 o o. o o. 0 2 4 6 8 10 12 14 FREQUENCY (0HZ) Figure A.45

10/31/85 -.1412NOP 3C0 CORN STALKS (IN) T -22 DEGC c1.4 25 solid ine RUSc(1.50HZ) ME ASURED ON 10 / 14/853 00 20. ~ D EPSILON (EP) 15 + of o o o 10: ~5~~~' o 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 VOLUMETRIC MOISTURE (MV) Figure A.46

0D CL -J. X 10/31/85.141 NGP 25 CORN STALKS (IN) T - 22 DEG C f -9.0GHZ 20 SOLD LIHE RUSS (18.0.0HZ) ME ASURED ON 10/14 /8500 1 5 EPSILON (EP) \r O~~~~~~ 10 0~ O~~~~~ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 VOLUMETRIC MOISTURE (MV) Figure A.47

10/24/1985 0. 141"N<P ~' r. 22.DEO.C. FRESH CORN LEAVES RUSS W.0. MEAS. AT 1.5 0HZ 30 t RECENT MEAS. ARE AT 1.4 0HZ 25 20 EPSILON (EP') 15- 10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 VOLUMETRIC MOISTURE (MYV) Figure A.48

10/30/85 FRESH CORN LEAVES.141" NOP 25 T = 22 DE C I * RUSS W.O. MIEAS. AT 5.0 0HZ /: RECENT MEASURES AT 5.0 0HZ 20 + re, D 15. * D EPSILON(EP*) 10 0 0.00 0.05 0. 10 0. 15 0.20 0.25 0.30 0.35 0.40 0.45 VOLUMETRIC MOISTURE (MYV) Figure A.49

10/30/85 FRESH CORN LEAVES.141" NOP 25 T = 22 DEO C RUSS W.0 MEAS. AT 8.0 0HZ RECENT MEASURES AT 8.0 GHZ 20 t0 15- o EPSILON (EP*) D0 I 0 o ~ ~ 0.00 0.05 0.10 00. 15 0.20 0.25 0.30 0.35 0.40 0.45 VOLUMETRIC MOISTURE (MY) Figure A.50

APPENDIX B Dielectric Data as a Function of Temperature This appendix contains the temperature data collected during the course of this work. The set consists of four parts: 1. Fatshedera temperature measurement (experiment # 1 in Section 5.6). (B.1- B.17) 2. Banana-like tropical tree temperature measurement (experiment # 2 in Section 5.6) (B.18 - B.23) 3. Fatshedera temperature measurement (experiment # 3 in Section 5.6). (B.24 - B.34) 4. Fresh corn leaves temperature measurement (experiment # 4 in Section 5.6). (B.35 - B.42) B.O

11/8/1985 F.1,O OHZ 0. 141 "NOP THICK SAMPLE/METAL 35 30. 25 Mg (before) = 0.745 20 EPSILO2 Mg (after) = 0.711 EP$ LON 15 10 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure B.1

11/8/1985 C0 FZ1x 0.1 41 "NO F4.0OIHZ THICK SNIPLE/MCTFA 25 Mg (before) = 0.745 ELON 15 Mg (after) = 0.711 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DE0. C. Figure B.2

FZ*l THICK SAMPLE/MTAL 25Q Mg (before) 0.745 15 co EPSLON Mg (after)= 0.711 CA) 5 -40 -130 -20 -10 0 10 20 30 TEMPERATURE I DEO. C. Figure B.3

11/8/198 FZ#I O.141"KNOP Fm20.O OHZ THICK SAPLE/METAL 16 14 EPSLON Mg (before) = 0.745 Mg (after) = 0.711 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure B.4

0.141'NOP 11/8/1985 FZ l (T+:o. DEO.C / ~~~~~~~~~~~~~~~~~~~~~~30~~~~~~ Mg (before) = 0.745 x Mg (after) = 0.711 ~~~+25 * ~ ~ 20' EPSLON 15 c) c, 10, - (> CCC, 0 0 0 |C o 0 ~ 0 2 4 6 8 10 12 14 16. 18 20 FREQUENCY IN (OHZ) Figure B.5

0.141 "NOP Ft 1 (T,+20. DEO.C) 118 ~3 T + Mg (before) = 0.745 r25 ~C v Mg (after) = 0.711 20 9 + EPSLON 15 10 o o 0 0 0 0o 0 5 i i i i I I I I I 0 2 4 6 8 10 12 14' 16 18 20 FREQUENCY IN (0HZ) Figure B.6

0.141 "NOP FZ 1 (T"+ 10. DEO.C.) -a 35 Mg (before) = 0.745 30 Adz Mg (after) = 0.711 25 tPSLON2 20 15 o O jo *?' o ~~10'2 ~0 0 5, I I I i... I O 2 4 6 8 10 12 14 16 18 20 FREQUENCY BI (MHZ) Figure B.7

O.14"1 "NP F1 (TO. DEO.C.) 1819 350 Mg (before) = 0.745 30 4 Mg (after) = 0.711 SO 4. ft* 25 EPSLON 20 o I.. 00 0 15 t o o o ao ~. o C) 9 c. 5 I.Ic,,,, 0 2 4 6 8 10 12 14 16 18 20 FREQUENCY IN (OHZ) Figure B.8

0.141 "NOP -~ FZI1 (To-SDEO.C.) 18 5 35 Mg (before) = 0.745 30 Mg (after) = 0.711 25 CPLON 20'.0~~~~~~~~~~~.. 0 /% 0~~~~~~~ 10 (Occo 0 2 4 8 10 12 14 16 18 20 FREQUENCY IN (GHZ) Figure B.9

0.141 1OP FZ 1 (T"-10.DEO.C.) / 1 9 10 Mg (before) = 0.745 9 a Mg (after) = 0.711 6 v+ + + o 4 0,, I I 0 2 4 6 8 10 12 14 l.18 20 FREQUENCY IN (HZ) Figure B.10

0.141 N FZ (T-1 5 DO.C.) 98?. 7 TMg (before) = 0.745 6 Mg (after) = 0.711 5 - + 40 4' EPSILON 3 2 0,~0 0 0 0 0 0 0 0 2 4 6 8 10 12 14' 16 18 20 FREQUENCY (OHZ) Figure B.11

0.1 41'NO FZtl (TI-20 DEO.C.) CI I 5 4, Mg (before) = 0.745 co: EPSLON 3 Nr) |Mg (after) = 0.711 2 C " ~0.......If~' 0 2 4 6 8 10 12 14 16 1e 20 FREQUENCY IN (0HZ) Figure B.12

0.141 "'NOP FZt1 (T —25.DEO.C.) 11/8/19 5.0 * * * * * 3.5 Mg (before) = 0.745 3.0 EPSLON 2.5 Mg (after) = 0.711 2.0 1.5 1.0 0.5 0 o 000 00 0 0 0.0 00 0o.0 ^. I ^.. 0 2 4 6 8 10 12 14 16 18 20 FREQUENCY I (0HZ) Figure B.13

0.141 "NOP 11/8/1985: FZ 1 (T.-40.EO.C.) 4.5 C?0 C o, s.5 <, Xo o Mg (before) = 0.745 3.0 2.5. EPSLON Mg (after) = 0.711 2.0 1.5 1.0 0.0 0 2 4 6 8 10 12 14 16. 8 20 FREQUENCY IN (OHZ) Figure B.14

0.1141 NOP FZl1 REAL PARTS.. 35 - Mg (before) = 0.745 30 * FZ ~ VS.FQREAL)T-+30 Mg (after) = 0.711 o FZ VS.FQ(REAL)T-+20 25 A FZ1iVS.FXREAL)T,+10 L0 o * 0 FZIVSSFQ(REAL)TO.0 20 L. OEEo o E* L E IL FZ1 VS.FQREAL)T,-5 w hPSILON A L 0 * FZ o oV.FQ Ln 15- A, 15 o L x FZ 1 YVS.FQ(RAL)T.-1 A 1 n h; | x FZ IIVS.FQ(REAL)T-20 10 " A rrh A - FZ'1VS.FOQ(REAL)T,-25 -2 l -: ~- VSF(REA)T-40.00 2 4 6 S 10 12 14 16 18 20 FREQUENCY IN (0HZ) Figure B.15

0.141'NOP FRl 611/8/1985 IMAO. PARTS Mg (before) = 0.745 15 - 1 ABOVE FREEZINO I Mg (after) = 0.711 14. 13 12 1 FZ 1VS.F(IAO.)T.+30 12 | FZ'1V8S(FXI.)T+20 J ~EPSnON 11 t FZV I (lS IMAO.)TO10 Y 10-F - FZ # iVS.FOitAO.T =.. 7 0 2 4 6 0 10 12 14 16 18 20 FRJ'ENCY IN (OHZ) Figure B.16

0.141 "NOP 1 1 /8/1985 D FZ1 -J IMSA. PARTS 3.0'BELO FREEZI I Mg (before) = 0.745 2.5 +ljr Mg (after) = 0.711 2.0 t 4 - FZ1 VSOQ(IMO.)T.-10. FZ*I V.FX(MAO.)T-1 5 EP8LON 1.5 FZ 1 VS.F1(IMA.)T,-20 s' I \'g' FZ1 VSF.FX (IAO.)T'-25 1.0 -. - FZ*IVS.F Q(IA.)T,,40 0.5 0.0 0 2 4 6 8 10 12 14 16 18 20 FREQUNCY I (OHZ) Figure B.17

0.1 41"NGP 11/11/1985G FZ*2VS.T( 1.0GHZ) 60 4+.50 -" 6- - 40 Mg (before) = 0.839 Mg (after) = 0.818.:' EPSILON 30 O0+~20. 0__O-_ oso I,...... 20 0 ~-9-O-O~-"E~ "_____ 10 0I-,0" -50 -40 -30 -20 -10 0 10 20 30 40 50 TEMPERATURE IN DEG.C. Figure B.18

0.1 41 "NOP iFZi 2S.T(4.00HZ) 50 r40 t Mg (before)= 0.839 30L Mg (after) = 0.818 25 EPSILON 20 10 -0 -40 0 1-30 -20 10 10 20 350 TEMPERATURE IN DEO.C. Figure B.19

O. 1 41 "NOP FZ2YS.T( 8.00OHZ) 50,40H Mg (before) = 0.839 35 30 - Mg (after) = 0.818 EPSILON I 25 15 10 5 -50 -40 -30 -20 -10 0 10 20 30 40 50 TEMPERATURE IN DEO.C. Figure B.20

+15 DEOC 11/11850.141 NOP Mg (before) = 0.839 55 Mg (after) = 0.818 s50 - REAL 45..... 40 35 EPSILON (EP) 30 25 ~ 20 - S A co O I MAOI NARY 15 - o~, ~~10~ ~0 0 2 4 6 8 10 12 14 16 FREQUENCY (GHZ) Figure B.21

-15 DEGC.141"NP DEC 10 9 8 t @t*r+ REAL 7 * 6 v *+ + + * * EPSILON (EP) 5 Mg (before) = 0.839 xr~~~~~~~~~~~j~~~~ tMg (after) =0.818 3, 2 IMAGINARY O'O~~ C I 0 ~ 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ) Figure B.22

141 NOP -30 DEOC 7 6 REAL ~ + 5- $ + 5 * ~ Mg (before) = 0.839 4 wo EPSILON (EP) 3 - Mg (after) = 0.818 2 1.5 IMAGINARY 0 2 4 6 8 10 12 14 16 18 20 22 FREQUENCY (GHZ) Figure B.23

0. 141"NOP cD 11 /14/19850 FZQ4VS.T( 1.00HZ) ~~~~~EPSILON~~ 1~ ~20 tMg (after) = 0.718 10 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO.C. Figure B.24

0. 141 "NOP F Z#V 4VS.T( 4. OOHZ) 30 25 Mg (before) = 0.736 20 Mg (after) = 0.718 E PSI LON 1 5 IMAG. PART 00 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG.C. Figure B.25

0. 141 "NOP 1 / 1 4/19850 FZ#4VS.T( 8.00GHZ) Mg (before) = 0.736 25 Mg (after) = 0.718 20 EPSI LON -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO.C. Figure B.26

0.1 41',NOP 11/14/19850 FZ#4VS.T 35' 1.0 0HZ Mg (before)= 0.736 8.0 0HZ Mg (after)= 0.718 20 EPSI LON 15 REAL PARTS 10 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO.C. Figure B.27

O. 141"N0P -p 11/14/19850 FZ#14VS.T 14 1 2 Mg (before) = 0.736 10 1.00OHZ Mg (after) = 0.718 8.00(HZ co gEPSILON I'3 (4.00HZ IMAG. PARTS 2 -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO.C. Figure B.28

0.1 41 "NOP 11 1 /14/19850 - FZ#4VS.T 1.0 0HZ 35 - FREEZINO )*304-" -- THAWI N 25 Mg (before) = 0.736 20 EPSI LON Mg (after) = 0.7185 - REAL PARTS -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEO.C. Figure B.29

0. 1 41 "NGP 0.1 1/14/19850 FZ#4VS.T 1.0 0HZ 1" 0 - asFREEZING 9 Mg (before) = 0.736 8 THAWINO Mg (after) = 0.718 E PSI LON' CDC dX ~3 IMAG. PARTS -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEO.C. Figure B.30

0. 1 41 "NV11/14/19850 C FZ#4VS.T 4.0 GHZ 30 FREEZING 25 THAWING3 Mg (before) = 0.736 Mg (after) = 0.718 EPSI LON 1 5 1 0 REAL PARTS -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEG. C. Figure B.31

0. 141 "NP 11/14/19850 FZ#4YS.T 4.0 0HZ 10.9 Mg (before) = 0.736 8 7 FREEZINO Mg (after) = 0.718 6 EPSI ION S T 4 IMAX. PARTS 2 -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEG. C. Figure B.32

0. 141 NOP 11/14/1985 FZ#4VS.T 8.0 0HZ FREEZINO 25 Mg (before) = 0.736 20T HAWINO Mg (after) = 0.718 15 EPSILON REAL PARTS 10 e-%~~~~~C I ~~ 1, I -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEG.C. Figure B.33

0.141 91NGP 11/14/19850 FZ#4VS.T 8.0 0HZ 1 4r HAhWING Mg (before) = 0.736 10 Mg (after) = 0.718 8 E PSI LON 6z~ FREEZING p 6~~~~~~~~~~~~~~~ IMAG. PARTS -40 -30 -20 -10 0 10 20 30 40 TEMPERATURE IN DEG.C. Figure B.34

0. 141"NOP FZ# 1 V.S.T REAL PARTS FRESH CORN LEAVES 12/06/1985 55 Mg (before) = 0.835 Mg (after) = 0.781 451.0HZ FREEZING CYCLE 4.0 0HZ g~~35 <~ b8.00HZ EPSI LON 20 15 -40 -^30 -20 -0 0 0 20 30-40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure B.35

0. 141"NOP FZ#1 1YS.T IMHAG. PARTS FRESH CORN LEAVES 12/06/19850 Mg (before) = 0.835 25 Mg (after) = 0.781 FREEZING CYCLE "";.. X,.,,.0GHZ EPSI LON' 8.0HZ 10 4.0 OHZ -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO. C. Figure B.36

FZ~ 11 V$.T( 1.0 GHZ)P.EAL 0. 141 "NGP FRESH ORiN LEAVES 12/06/19850 Mg (before) = 0.835 Mg (after) = 0.781 ~_FREEZING REFREEZINO EPSILON T HAWI NO.....:......I..0- I -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO. C. Figure B.37

rD. 1 41"NP FZN 1 $l S.T( 1.0 GHZ)IMA. FRESH CORN LEAVES 12/06/19850 20 Mg (before) = 0.835 Mg (after) = 0.781 REFREEZINO T HAW I NG?J CTEPSILON -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO. C. Figure B.38

0. 1 41 I$t'.P FZ4r11 TS.T(4.0 GHZ)FiREAL F P.ES H OOR N L EA- Evc1206195 60 Mg (before) = 0. 835 Mg (after) 0.781 40,..AN EFSI Lr~~~~~~J r R~~~~fC7EREFEEI NO~ 2 ij T HA01 I NO 0-40 -30 -20 -10 0 10 20 3 TEMPERAtTURE IN DEO. C. Figure B.39

0. 1 41 9 "ISP FkP 1lY$3.Ti 40 jilSo'0 FRESHI.IO CO~RN LEA'YE$ 12/06/19850 20 Mg (before) = 0.835 Mg (after) = 0.781 |REFREEZI I FREEZNI 14 w t~EPSILON o I H.~-:W I H N -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEO. C. Figure B.40

0.141"NiP FZ 1 I1V$S.T(..O O )REAL FRESH CORN LEAVE 1S2106/1985, 40 X FREEZING O, Mg (before) = 0.835 REFREEZI NO Mg (after) = 0.781 EPSILON 1 20t X THA,.WING -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure B.41

0. 1 41 1NOP FZ#1 "VS.T (8.0 OHZ)I MAO. FRESH OORN L EAVES 12/06/19850 25 Mg (before) = 0.835 Mg (after) = 0.781 REFREEZINGF EPSI LON 10 THAWING -40 -30 -20 -10 0 10 20 30 TEMPERATURE IN DEG. C. Figure B.42

APPENDIX C Probe Modeling Program Listing C.O

Appendix C C C PROGRAM TO CALIBRATE PROBE SYSTEM C O.C, S.C, S11,D o W. METHo, AND UNKNOWN MATERIAL C REFLECTION COEFFICIENTS ARE KNOWN C ON 5/23/1984 BY M.A.EL-RAYES C COMPLEX Z,RS,RO,RW,RM, S11,ROP,RSP,ROSP,EM, Z1, Z2,ECW COMPLEX S22, RCW, RCM, S121, ROA, S121P, ZOC, ZW, ZM, EMM, EMW COMPLEX ECB, RB, RCB, ZB, EMB, RCO, ZWC, RWA, S11l, Sllll PI=4.*ATAN (1.) Z=(0.0,1.0) ZO=50.0 T=22.0 S=0.0 C O P E N T H E I/P A N D O/P F I L E S OPEN(1,ERR=99,FILE=' *PLEASE ENTER INPUT FILE NAME: OPEN(2,ERR=99,FILE='*PLEASE ENTER OUTPUT FILE NAME: 1 READ(01, *,END=99)F,AO,PO,AS,PS,AW,PW, AB, PB READ (O 1, *, END-599) XS11, YS11, AM, PM IF (S.LE.O.0)CALL WATER(F,T,ECW) IF(S.GT..0)CALL SWAT(F,T,S,ECW) IF(S.GT.20.0)CALL SWATH(F,T,S,ECW) CALL METH (F, T, ECB) PRINT *,'D.W. CALC. =',ECW PRINT *,'METH. CALC.=',ECB WRITE (02,111) ECW WRITE (02, 112) ECB 111 FORMAT(lX,'D.W. CALC. =',2(1X,F9.3)) 112 FORMAT(1X,'METH. CALC. =',2(1X,F9.3)) CF1=0. 006E-12 C01=0. 028E-12 B1=0.0 A10. 5E-12 W-2. E9 *P I *F WA2. *PI*F AS=10. ** (- (25.-AS)/20.) AO=10.** (- (25.-AO)/20.) AW-10.** (- (25.-AW)/20.) AB=10 ** (-(25.-AB)/20.) AM=10. ** (- (25.-AM)/20. ) PS5PS*PI/180. PO=PO*PI/180. PW=PW*PI/180. PB=PB*PI/180.0 PM=PM*PI/180. RS=AS*CEXP (Z*PS) RO=AO*CEXP (Z*PO) RW=AW*CEXP (Z *PW) RB=AB*CEXP (Z*PB) RM=AM*CEXP (Z*PM) Sll=CMPLX (XS11, YSll) ROP=RO-S ll RSP=RS -S 11 ROSP=ROP/RSP PRINT *,t FREQUENCY IN (GHZ) = r F WRITE (02,73) F 73 FORMAT(1X,' FREQUENCY IN (GHZ) =',F7.3) C.1

Appendix C PRINT *,' ----------- WRITE(02, 74) 74 FORMAT (X,' ---------------------—' ) II=0 2 CONTINUE II=II+1 CF=CF1 CO=CO 1 B=B1 A=A1 ZOC=1./(A* (WA**4)+Z*W* (CF+CO+B* (WA**2))) ROA= (ZOC-ZO) / (ZOC+Z0) S22= (ROSP+ROA) / (ROA* (ROSP-1.)) S121=ROP* (1.-S22*ROA)/ROA S121P=-RSP* (1.+S22) PRINT *,S121,S121P WRITE (02,75) S121, S121P 75 FORMAT(lX,'S121,S121P=',4(lX,F12.5)) C C CORRECTIONS C RCW= (RW-Sll)/ (S121+(RW-Sll) *S22) ZW=Z0*(1.+RCW)/( 1.-RCW) RCB- (RB-Sll) / (S121+ (RB-Sll) *S22) ZB=Z0*(1.+RCB)/(1.-RCB) RCM=(RM-Sll)/ (S121+(RM-Sll) *S22) ZM=ZO* (1.+RCM)/ (1.-RCM) C C EVALUATION OF EQUIVALENT CIRCUIT PARAMETERS C CALL FEQUIV(RCW,RCB,ECW,ECB,CF1,C01,B1,Al,W,WA,ZO) IF(II.GT.20)GO TO 9 IF (ABS (CF1-CF).GE. 1.E-15.OR.ABS(COl-CO).GE. 1.E-15. + OR.ABS(B1-B).GE.1.E-20.OR.ABS(A1-A).GE.1.E-15)GO TO 2 9 CALL ITER(ZM, CF,CO, B,A,W,WA,EM,DM) CALL ITER(ZW,CF,CO,B,A,W,WA,EMW,DW) CALL ITER(ZB,CF,CO,B,A,W,WA,EMB,DB) PRINT *,' CALIBRATION USING O.C.,S.C.,AND Sll:' WRITE (02,76) 76 FORMAT(1X,' CALIBRATION USING O.C.,S.C.,AND Sll:') PRINT *,~'...... —-------—.-.' WRITE (02, 77) 77 FORMAT(lX,' —----------------------------— ~) PRINT *,' # OF ITERATION =',II WRITE(02,78)II 78 FORMAT(1X,' # OF ITERATION =',I3) II=0 PRINT *,f'DW. =',EMW WRITE(02,79)EMW 79 FORMAT(1X,' D.W. =',2(1X,F12.3)) PRINT *,'METH.=',EMB WRITE (02, 80) EMB 80 FORMAT(1X,' METH. =',2'(lX,F12.3)) PRINT *,'MATERIAL EPS =',EM,DM WRITE (02, 81) EM, DM 81 FORMAT(1X,' MATERIAL EPS =',3(1X,F12.3)) EMR=REAL (EM) EMI=-AIMAG (EM) PRINT *,'CF,C0,B,AND A = C.2

Appendix C WRITE(02, 82) 82 FORMAT (X,' CF,C0,B,AND A =') PRINT *,CF,CO,B,A WRITE(02,83)CF,CO,B,A 83 FORMAT(4 (1X, E12o 5)) PRINT *,' —-------------------------------------------- WRITE(02,84) 84 FORMAT(lX,' —----------------------------------------- 700 CONTINUE GO TO 1 99 PRINT *,'ERROR IN WRITING TO OR READING FROM A FILE WRITE(02, 91) 91 FORMAT(1X,' ERROR IN READING FROM OR WRITING TO A FILE' ) STOP END C C SUBROUTINE TO SOLVE THE INVERSE PROBLEM (GIVEN c REFLECTION COEFFICIENT CALCULATE THE UNKNOWN DIELECTRIC c CONSTANT OF THE MEDIUM) USING AN ITERATION ALGORITHM AS C OPPOSED TO SOLVING A 5TH ORDER EQUATION (ACCURACY IN c THIS CASE IS XX.XX). C SUBROUTINE ITER(ZM,CF,CO,B,A,W,WA,EMM,D1 ) C C THIS PROGRAM SOLVE THE EQUATION IN ZM C TO GET EM BY ITERATION C BY M.A.EL-RAYES ON 5/25/1984 C COMPLEX ZM, EM, Z, EM1, EMM Z=(0.0, 1.0) C C C FIRST ITERATION C N=11 M-11 EPI=1.0 EDI-0.0 IF(EPI.LE.1.0)EPI=1.0 IF(EDI.LE.0.0)EDI=0.0 Dl=-.E9 DO 100 I-1,N EP=EPI+ (I-1.) *10. DO 100 J-1,M ED=EDI+ (J-1.) *10. EM1=CMPLX (EP, -ED) D=CABS (ZM-(1./(Z*W* (CF+C0*EMI+B* (WA**2) * + (EM1**2))+A*(WA**4)*(EM1**2.5)))) IF (D. LE.D1) EM=EM1 IF (D.LE.D1)D1=D 100 CONTINUE C SECOND ITERATION EP=REAL (EM) ED-AIMAG (-EM) N=22 M-22 C.3

Appendix C EP I=EP-10. EDI-ED-10. IF(EPI.LE.1.0)EPI=1.0 IF (EDI.LE. 0.0) EDI-0.0 Dl-1.E9 DO 201 I-1,N EPEP I+I DO 201 J=1,M ED=ED I+J EM1=CMPLX (EP, -ED) D=CABS (ZM- (1. / (Z*W* (CF+C0*EM1+B* (WA**2) * + (EM1**2))+A*(WA**4)*(EM1**2.5)))) IF (D.LE. D1) EM=EM1 IF (D. LE.D1)Dl=D 201 CONTINUE C C THIRD ITERATION C EP=REAL (EM) ED=AIMAG (-EM) N=22 M=22 EPI=EP-1.0 EDI=ED-1.0 IF(EPI.LE.1.0)EPI=1.0 IF(EDI.LE. 0.0)EDI=0.0 Dl=1.E5 DO 200 I=1,N EP=EPI+I*0.1 DO 200 J=1,M ED=EDI+J*0.1 EM1-CMPLX (EP, -ED) D=CABS (ZM- (1. / (Z*W* (CF+C0*EM1+B* (WA**2) * + (EM1**2))+A* (WA**4)*(EM1**2.5)))) IF (D. LE. D1)EM-EM1 IF(D.LE.D1)Dl=D 200 CONTINUE C C FOURTH ITERATION C EP=REAL (EM) ED=AIMAG (-EM) N=22 M=22 EPI=EP-0.1 EDI=ED-0.1 IF(EPI.LE.1.0)EPI=1.0 IF(EDI.LE.0.0)EDI=0.0 Dl=l1.E5 DO 300 I=1,N EP=EPI+I*0.01 DO 300 J=1,M ED=EDI+J*0.01 EM1=CMPLX (EP, -ED) D=CABS (ZM-(1./(Z*W* (CF+C0*EM1+B* (WA**2) * + (EM1**2))+A*(WA**4)*(EM1**2.5)))) IF(D.LE.D1)EM=EM1 IF (D.LE.D1)Dl=D 300 CONTINUE Co4

Appendix C EMM=EM RETURN END C C SUBROUTINE TO SOLVE 4 EQUATIONS IN 4 UNKNOWNS, C FOR THE COMPLETE EQUIVALENT CIRCUIT (CF, CO, B, AND A). C SUBROUTINE FEQUIV(RCW,RCB,ECW,ECB,CF1,C01,B1, Al, W,WA,Z0O ) C C SUB. TO ESTIMATE EQUIVALENT CIRCUIT PARAMETERS C COMPLEX Z,RCW,RCB,ECW,ECB, RHW, RHB DIMENSION A(4,5),B(4,5) Z=(0.0, 1.0) RHW=(1.-RCW)/(1.+RCW)/ZO RHB=(1.-RCB)/(1.+RCB)/ZO A(1, 5)=AIMAG (RHW) A (2,5) =AIMAG (RHB) A(3,5) REAL (RHW) A(4, 5) =REAL (RHB) A(1,1)=WA A(2, 1)=WA A(3, 1)=0. O A(4, 1)=0.0 A(1, 2) =WA*REAL (ECW) A(2,2)=WA*REAL(ECB) A(3,2) =WA*AIMAG (-ECW) A(4,2) =WA*AIMAG (-ECB) A(1, 3)=(WA**3) *REAL(ECW**2) A(2,3) = (WA**3) *REAL (ECB**2) A(3,3)- (WA**3) *AIMAG (- (ECW**2)) A(4,3)=(WA**3) *AIMAG(-(ECB**2)) A(1,4)=(WA**4) *AIMAG(ECW**2.5) A(2, 4) = (WA**4) *AIMAG (ECB**2.5) A (3, 4) = (WA**4) *REAL (ECW**2.5) A(4,4)=(WA**4) *REAL(ECB**2.5) C C PROCESS THE MATRIX USING DIAGONAL METHOD C DO 111 I=1,4 DO 111 J=1,5 B (I,J) =A(I, J) 111 CONTINUE C C PROCESS THE MATRIX USING DIAGONAL METHOD C DO 10 I=1,4 IF(ABS(A(I,I)).LE.1.E-37)GO TO 20 10 CONTINUE C C CHANGE DIAGONAL ELEMENTS TO UNITY C DO 100 J=1,4 X-=A(J,J) DO 200 L=1,5 A(J,L)=A(J, L)/X 200 CONTINUE DO 100 I-1,4 IF(I.EQ.J)GO TO 100 C.5

Appendix C X=A (I, J) DO 300 K=1,5 A(I,K)=A (I, K) -X*A (J, K) 300 CONTINUE 100 CONTINUE CF1=A(1, 5) *1.E-9 CO1=A (2,5) *1.E-9 B1=A(3,5) *l.E-9 A1=A(4, 5) DO 700 I=1,4 D=B(I,5) DO 701 J=1,4 D=D-B(I,J) *A(J,5) 701 CONTINUE 700 CONTINUE GO TO 30 20 PRINT *,'DIAGONAL ELEMENT/S WITH ZERO!!!!' WRITE(02, 87) 87 FORMAT(1X,'DIGONAL ELEMENT/S WITH ZERO!!!!!') 30 RETURN END C C SUBROUTINE TO SOLVE 2 EQUATIONS IN 2 UNKNOWNS, FOR THE SIMPLE EQUIVALENT CIRCUIT (ONLY CO AND A). C SUBROUTINE EQ(RC,EC,AK,CO, A,W, WA, ZO) C COMPLEX Z,RC,EC,Y C Z=(0.0,1.0) Y=(1.-RC)/(1.+RC)/ZO CF=AK*CO XK1-REAL (Y) XK2=AIMAG (Y) Al l=-W*AIMAG (EC) A12= (WA**4) *REAL (EC**2.5) A2 1W*AK+W*REAL (EC) A22= (WA**4) *AIMAG (EC**2.5) CO= (XK1/A12-XK2/A22) / (All11/A12-A21/A22) A (XK1-All*C0)/A12 AP- (XK2-A21*C0) /A22 RETURN END C C DIELECTRIC CONSTANT OF DISTILLED WATER ( S = 0.0 PPT). C SUBROUTINE WATER(F,T,EDW) C THIS IS A PROGRAM TO CALCULATE THE COMPLEX DIELECTRIC C CONSTANT OF FRESH WATER. C BY M.A. EL-RAYES C OCT.15,1981 COMPLEX EDW PI=4.*ATAN(1.0) EPSWI=4.9 TAW-(1.1109E-10-3. 824E-12*T+6.938E-14*(T**2) + -5.096E-16*(T**3)) TAW=TAW/ (2*PI) EPSWZ = 88.045-0.4147*T + 6.295E-4*(T**2) + +1.0735E-5 *(T**3) C.6

Appendix C EPSWP=EPSWI+ ( (EPSWZ-EPSWI) / (1+( (2*PI*F*1E9*TAW) **2) ) ) EPSWD= (2*PI*F*1E9*TAW* (EPSWZ-EPSWI) + / (1+( (2*PI*F*1E9*TAW) **2) ) ) EDW=CMPLX (EP SWP, -EP SWD) PRINT *,'EPS.D.W. -',FEDW RETURN END C C DIELECTRIC CONSTANT OF SALINE WATER WITH LOW SALINITIES C ( S < 20 PPT ). C SUBROUTINE SWAT(F,T,S,ESW) C A PROGRAM TO CALCULATE SALINE WATER DIELECTRIC C CONSTANT AS A FUNCTION OF FREQUENCY, TEMPERATURE, C AND SALINITY. C ON 4/22/1982 C BY M.A.EL-RAYES C COMPLEX ESW PI=4. *ATAN(1.0) ESWI=4.9 ESWO-87.134-1. 949E-1*T-1.276E-2* (T**2) +2. 491E-4* (T**3) A=1. 0+1. 613E-5*T*S-3. 656E-3*S+3.21E-5* (S**2) -4.232E + -7*(S**3) ESWOS=ESWO*A TAWO= (1. / (2.*PI)) * (1. 1109E-10-3. 824E-12*T+6. 938E + -14*(T**2)-5.016*(T**3)) B=1.0+2.282E-5*T*S-7.638E-4*S-7.76E-6 (S**2) + +1.105E-8*(S**3) TAWS=TAWO*B DELT=25. 0-T PHI=DELT*(2.033E-2+1.266E-4*DELT+2.464E-6*(DELT**2)+ S*(1.849E-5-2.551E-7*DELT+2.551E-8*(DELT**2))) SIG25=S*(0.18252-1.4619E-3*S+2. 093E- 5*(S**2)-1282E + -7*(S**3)) SIGSIG25*EXP (-PHI) EPS0=(1.E-9) / (36.*PI) ESWP=ESWI+ ((ESWOS-ESWI) / (1.+( (2.*PI*F*1.E9*TAWS) **2))) ESWD=2. *PI*F*1. E9*TAWS* (ESWOS-ESWI) + /(1.+((2.*PI*F*1.E9*TAWS) + **2))+SIG/(2.*PI*EPSO*F*1.E9) ESW=CMPLX(ESWP, -ESWD) PRINT *,'EPS.S.W. -',F,ESW RETURN END C C DIELECTRIC CONSTANT OF SALINE WATER WITH HIGH SALINITIES C ( S > 20 PPT ). C SUBROUTINE SWATH(F,T,S,ESW) C A PROGRAM TO CALCULATE SALINE WATER DIELECTRIC C CONSTANT AS A FUNCTION OF FREQUENCY, TEMPERATURE, C AND SALINITY. C ON 4/22/1982. C BY M.A.EL-RAYES C COMPLEX ESW REAL N AA=1.0 C.7

Appendix C PI=4. *ATAN(1.0) N=AA* (1. 707E-2+1.205E-5*S+4. 058E-9*S**2) *S D=25.-T C1=1.-1.96E-2*D+8.08E-5*D**2-N*D*(3.02E-5+3.92E-5*D + +N*(1.72E-5-6.58E-6*D)) SB-N*(10.39-2.378*N+0.683*N**2-0.135*N**3+1.01E-2*N**4) B1=-1.+0.146E-2*T*N-4.89E-2*N-2.97E-2*N**2+5.64E-3*N**3 TB=1.1109E-10-3.824E-12*T+6.938E-14*T**2-5.096E-16*T**3 TB=TB/(2.*PI) A1=1.-0.255*N+5.15E-2*N**2-6.89E-3*N**3 EW0=88.045-0.4147*T+6.295E-4*T**2+1.075E-5*T**3 SB=SB*C1 TB=TB*B1 EWO=EWO*A1 EWI=4.9 E0= (1.E-9) / (36.*PI) EFP=EWI+(EW0-EWI)/(1.+(2.*PI*F*1.E9*TB)**2) EFD=(2.*PI*F*1.E9*TB)*(EW0-EWI)/(1.+(2.*PI*F*1.E9*TB)**2) EFD=EFD+SB/(2.*PI*EO*F*1.E9) ESW=CMPLX (EFP, -EFD) PRINT *,'EPS.S.W. =',FESW RETURN END C C DIELECTRIC CONSTANT OF METHANOL. C C SUBROUTINE METH (F, T, EMETH) C COMPLEX Z, EMETH C PI=4. *ATAN(1.0) Z=(0.0, 1.0) W=2.E9*PI*F IF(T.LT.10..OR.T.GT.40.)GO TO 111 ES=39.2-0.22*T IF(T.LE.20..AND.T.GE.10.)EI=4.9-0.02*T IF(T.LE.30..AND.T.GE.20.) EI=4.7-0.01*T IF (T.LE.40..AND.T.GE.30.)EI=5.6-0.04*T IF (T.LE.20..AND.T.GE.10.) TAU=84.-1.4*T IF(T.LE.30..AND.T.GE.20.) TAU-80.-1.2*T IF(T.LE.40..AND.T.GE.30.)TAU=71.-0.9*T TAU-TAU*1.E-12 IF (T.LE.20..AND.T.GE.10. )ALP=0.026+0.0009*T IF(T.LE.30..AND.T.GE.20.)ALP=0.052-0.0004*T IF(T.LE.40..AND.T.GE.30. )ALP=0.082-0.0014*T EMETH=EI+(ES-EI)/(1.+(Z*W*TAU)** (1.-ALP) ) PRINT *,'F, TEPS =',F,TEMETH RETURN 111 PRINT *,f'TEMP. SELECTED BEYOND LIMITS!!!!!! WRITE (02, 89) 89 FORMAT(1X,' TEMP. SELECTED BEYOND LIMITS!!!!') RETURN END C.8

UNIVERSITY OF MICHIGAN 91111111111111111 011111 1111 1 111111 3 9015 02827 6593