TERRAIN CLASSIFICATION IN TERMS OF RADAR REFLECTION PROPERTIES by Ro Fo Goodrich Final Report under COntract with Fairchild Guided Missiles Division 2802-1-F October 1958 The University of "Michigan Research Institute Radiation Laboratory Ann Arbors Michigan

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2802-1-F STUDIES IN RADAR CROSS SECTIONS I "Scattering by a Prolate Spheroid", Fo VO Schultz (UMM-42, March 1950), W-33(038)-ac-14222o UNCLASSIFIED, II "The Zeros of the Associated Legendre Functions pm(/&') of Non-Integral Degree", Ko M. Siegel, Do M. Brown, H. E. HunteryH, A. Alperin and Co Wo Quillen (UMM-82, April 1951), W-33(038)-ac-14222o UNCLASSIFIED. III "Scattering by a Cone"t Ko M. Siegel and H. A. Alperin (UMM-87, January 1952), AF-30(602)-9. UNCLASSIFIED. IV "Comparison Between Theory and Experiment of the Cross Section of a Cone", K, Mo Siegel, H. AO Alperin, Jo W. Crispin, Jro. H. E. Hunter, R. E. Kleinman, W, Co Orthwein and Co E. Schensted (UMM-92, February 1953), AF-30(602)-9. UNCLASSIFIEDo V "An Examination of Bistatic Early Warning Radars", K. M. Siegel (UMM-98, August 1952), W-33(038)-ac-14222o SECRETo VI "Cross Sections of Corner Reflectors and Other Multiple Scatterers at Microwave Frequencies", Ro R. Bonkowski, Co Re Lubitz and C. E. Schensted (UMM-1069 October 1953), AF-30(602)-9o SECRET - Unclassified when Appendix is removedo VII "Summary of Radar Cross Section Studies Under Project Wizard"t K. Mo Siegel, Jo Wo Crispin, Jr.o and Ro Eo Kleinman (UMM-108 November 1952), W-33 (038)-ac-14222. SECRET. VIII "Theoretical Cross Section as a Function of Separation Angle Between Transmitter and Receiver at Small Wavelengthst" Ko Mo Siegelp H. Ao Alperin, Ro Ro Bonkowski, Jo Wo Crisping Jro, A. Lo Maffett, Co Eo Schensted and Io Vo Schensted (UMM-115 October 1953), W-33(038)-ac-14222o UNCLASSIFIED. IX "Electromagnetic Scattering by an Oblate Spheroid", L. M. Ranch (UMM-1169 October 1953), AF-30(602)-9o UNCLASSIFIEDo X "Scattering of Electromagnetic Waves by Spheres"t Ho Weil, Mo Lo Barasch and To Ao Kaplan (2255-20-T, July 1956), AF-30(602)-1070. UNCLASSIFIED. XI "The Numerical Determination of the Radar Cross Section of a Prolate Spheroid", Ko Mo Siegel, B. H. Gere, Io Marx and F. B. Sleator (UMM-126, December 1953) AF-30(602)-9o UNCLASSIFIEDO ii

2802-1-F XII "Summary of Radar Cross Section Studies Under Project MIRO"t Ko M. Siegel, Mo E. Andersons R. Ro Bonkowski and W. Co Orthwein (UMM-127p December 1953), AF-30(602)-9. SECRET. XIII "Description of a Dynamic Measurement Program"9 K, Mo Siegel and J. Mo Wolf, (tMM-128s May 1954), W-33(038)-ac-14222o CONFIDENTIAL. XIV "Radar Cross Section of a Ballistic Missile", Ko Mo Siegel, Mo Lo Barasch, J. Wo Crispin, Jr., Wo C. Orthwein, Io V. Schensted and Ho Weil (UMM-134, September 1954), W-33(038)-ac-14222. SECRETo XV'tRadar Cross Sections of B-47 and B-52 Aircraft"o Co Ee Schensted, Jo W. Crispin, Jro. and K, M. Siegel (2260-1-To August 1954), AF-33(616)-2531. CONFIDENTIAL XVI "Microwave Reflection Characteristics of Buildings", Ho Weil, Ro Ro Bonkowski, T. Ao Kaplan and M. Leichter (2255-12-TS May 1955), AF-30(602)1070o SECRET XVII "Complete Scattering Matrices and Circular Polarization Cross Sections for the B-47 Aircraft at S-band", Ao Lo Maffett, Mo Lo Barasch9 W. E. Burdick, R. Fo Goodrich, Wo Co Orthweins C. E, Schensted and K. M'Siegel (2260-6-Ts June 1955), AF-33(616)-2531. CONFIDENTIAL. XVIII "Airborne Passive Measures and Countermeasures", Ko Mo Siegel, Mo Lo Baraschg Jo Wo Crispin, Jro. Ro Fo Goodrich, Ao Ho Halpin, Ao Lo Maffett, Wo Co Orthwein, Co Eo Schensted and Co J. Titus (2260-29-Fp January 1956), AF-33 (616)-2531o SECRET. XIX "Radar Cross Section of a Ballistic Missile II"t Ko M. Siegelg M. Lo Barasch, Ho Biyskq Jo Wo Crispin, Jro, To B. Curtz and To Ao Kaplan (2428-3-Tp January 1956) AF-04(645)-33o SECRET~ XX "Radar Cross Section of Aircraft' and Missiles"' Ko Mo Siegels WO Eo Burdicks Jo W. Crispins Jr, and S. Chapman (WR-31-J, ONR-ACR-10 March 1956)0 SECRETO XXI "Radar Cross Section of a Ballistic Missile III"1 Ke Mo Siegel, H. Brysk, Jo Wo Crispin, Jr.o and Ro Eo Kleinman (2428-19-T October 1956), AF-04(645)-33 SECRET o XXII "Elementary Slot Radiators " Ro Fo Goodrich, Ao Lo Maffett, N. Eo Reitlinger, Co E. Schensted and K. M. Siegel (2472-13-T, November 1956), AF-33(038)-28634, HAC PO L-265165-F47o UNCLASSIFIEDO iii

2802-1-F XXIII "A Variational Solution to the Problem of Scalar Scattering by a Prolate Spheroidt' F. B. Sleator (2591-l-T, March 1957), AFCRC-TN-57-586, ASTIA Document No. 133631, AF-19(604)-1949. UNCLASSIFIED. XXIV "Radar Cross Section of a Ballistic Missile IV", to be published. SECRET* XXV "Diffraction by an Imperfectly Conducting Wedge", T. B. A. Senior (2591-2-T, October 1957), AFCRC-TN-57-791, ASTIA Document No. AD 133746, AF-19(604)1949. UNCLASSIFIED. XXVI "Fock Theory", R. F. Goodrich, Scientific Report No. 3 (2591-3-T), AFCRC TN 58-350, AD 160790, AF 19(604)-1949 (July 1958). UNCLASSIFIED. XXVII "Calculating Far Field Patterns from Slotted Arrays On Conical Shapest" R. E. Doll, R. F. Goodrich, R. E. Kleinman, A. L. Maffett, CO E. Schensted, and K. M. Siegel, (2713-1-F) AF 33(038)-28634 and AF-33(600)-36192 (February 1958). UNCLASSIFIED. XXVIII "The Physics of Radio Communications Via the Moon", M. L. Barasch, H. Brysk, B. A. Harrison, T B. A. Senior, K. M. Siegel and H Weil, (2673-I-F), AF 30(602)-1725 (March 1958). UNCLASSIFIED. XXIX "The Determination of Spin, Tumbling Rates, Sizes of Satellites and Missiles", K. Mo Siegel, M. L. Barasch, W. E. Burdick, JO Wo Crispin, Jr., B A. Harrison R. E. Kleinman, R. Jo Leite, Do M. Raybin and H. Well (2758-1-T), AF 33(600)-36793. To be published. CONFIDENTIAL. XXX "The Theory of Scalar Diffraction With Application to the Prolate Spheroid", R, K. Ritt (Appendix by N D. Kazarinoff) Scientific Report No. 4 (2591-4-T) AF 19(604)-1949, AFCRC TN-58351, AD 160791 (August 1958)o UNCLASSIFIED. iv

28021-F PREFACE For several years The University of Michigan has been conducting a major study of radar cross sections (i.e.s radar reflection characteristics of specific shapes), antenna and radiation problems, and radar propagation phenomena. The primary alms of the program in the study of radar cross sections are: (1) To show that radar cross sections can be determined analytically. (2) To develop means for computing cross sections of objects of military interests (3) To demonstrate that these theoretical cross sections are in agreement with experimentally determined values. Intermediate objectives are: (1) To compute the exact theoretical cross sections of various simple bodies by solution of the appropriate boundary-value problems arising from Maxwellts equations. (2) To examine the various approximations possible in this problem, and determine the limits of their validity and utility. (3) To find means of combining the simple body solutions in order to determine the cross sections of composite bodies. (4) To tabulate various formulas and functions necessary to enable such computations to be done quickly for arbitrary objects. V

2802-1-F (5) To collect, sunmarize, and evaluate existing experimental data. This work has resulted in a series of Studies in Radar Cross Sections summarizing the results obtained for many problems of a relatively broad nature. Titles of the papers already published or presently in process of publication are listed on the preceding pages. Since the material contained in this report will be of general interest to all individuals concerned with radar cross section problems, it is intended that the results reported here will be presented in a future paper in the Studies in Radar Cross Sections series. vi

2802-1-F TERRAIN CLASSIFICATION IN TERMS OF RADAR REFLECTION PROPERTIES We wish to classify various types of terrain in terms of their properties as radar reflectors. This we do in terms pertinent to a range finding application which makes use of the correlation between signals received directly through the atmosphere and signals received by way of reflection from the grounds Certain simplifications will be made in order to facilitate the terrain classifications' We have a transmitter T and a receiver R located at altitudes H and h above the earth and a distance L apart as in Figure lo T Figure lo The transmitter output is taken to be a continuous'wave X-band carrier modulated by band-limited white noise We consider the signal reaching the receiver as being made up of that transmitted directly, along path Ls and that reflected by the grounds along path t.If now the earth were a smooth plane, so that the reflection path l-I

2802-1-F (path - ) would be primarily specular, the cross-correlation between the direct and ground return would give a measure of (!-L), the path differences which along with a knowledge of h and the elevation angle OC would be sufficient to give information as to the range L. We write x(t) for the transmitter output and yd(t) or Yg(t) for the direct and reflected received signals respectively. We wish to examine the effect of various ground configurations on the cross-correlation of the functions yd and ygo In particular we wish to characterize the various types of terrain in terms of the effect of the departure from the ideal case - flat smooth earth - on the crosscorrelation function. To this end we make the inessential simplifying assumptions that the transmitter and receiver are at the same altitude and that the earth is plane. The first assumption is justified since it will not essentially alter our description of the terrain in the above terms. The second assumption is justified since the ranges considered (L v 50 mi) are sufficiently small that the curvature of the earth is a negligible effect. We take the ground to be in the X-Y plane, the Z-axis upward and place the origin at the midpoint between the transmitter and receiver as in Figure 2. z T _____L R T- I' ~; -y P(Xoy) X Figure 2. -2

2802-1-F We designate the specular path length as -o, the general path length ast where -t=A +, (1) and ~1 and 12 are the distances TP and PR respectively. To find the ground return we note that the signal scattered from the point P and received at a time t had its origin at the transmitter at an earlier time t - 1 t. Hence, we write the return from a small areaA S about P as c ik6 e k A(P) x (t - l )S (2) 1 2 1 where the exponential gives the correct phases the denominator -~~ accounts 2 for the geometric attenuation, and for a field incident in the direction TP we write A(P) L S as the field scattered in the direction PR from the area S about the point P. We choose to give a scalar treatment of the problem for reasons of simplification which we justify below. The total field from the ground is then this expression integrated over the X-Y plane, i.e., ik 1 yg(t) dS A(P) x (t )o (3) We neglect the effects of atmospheric noise again, because we are primarily interested in characterizing the types of grounds -3

2802-1-F The direct signal at a time t also will have its origin at an earlier time t - and will be of the form c eikL 1 Yd(t) L x (t- I L). (4) Hence, the cross-correlation function will be -iklJ ik R (z) L ~ j dS A(P) R ('' ) (5) Ydyg 1 2) i Because of the form of the integrand in Equation (3) we find it useful to express the integration in terms of the path length/ and a polar angle 0 as the variables of integration. To do this we need the locus of constant tin the X-Y plane. The coordinates of the points T, R9 and P are L; 3L T: (09 - - h), R: (09 L h), P: (x Y, ). (6) 2 2 Hence 2 2 L2 2 TP (xy+, + yLL —- see ) 2i 4 2= PR = (x2 - y L t- se ) - (7) 4

2802-1-F Then, from Equation (1) we find the locus to be the ellipse x~^ ~~~ y2^~ ~ ^ ~ = I o ~(8) 22 z2_,;2,2,2 R2 2 110 0 s _ 4 4( e222 C082 e 4(,^ os1S o We now need to o e te Jae ttion and te dnoi After a sin straightforward (9) ~1 ~2 ~1 2 112 j 1 2 ~R~~~. (. )- =.... (. ()*Substituting for the integrand in Equation (5) oeig'i2r ei 2 7d7g L ) d~J- " 2 c o2 0 0o ~^^ (II) 0

2802-1-F We now recapitulate our description of the process. The signal received by way of the ground reflection at a given time t will have arisen in the transmitter at some earlier time t -1 as we have pointed out above. The least time delay C will correspond to the path length ~ detenmined by the specular reflection point which in our case is the midpoint between the receiver and transmittero Signals corresponding to a greater delay times say t - lwhere. i >e will arrive at 0 0 the receiver after having been scattered from the region of the ground given by -- =- - 2 ~ This is just the equation for the ellipse which we have finally put in parametric form in Equation (9)0 The center of the ellipse corresponds to & = ^, hences we can conceive of elliptical zones about the specular refleetion points each zone giving a contribution to the received signal0 This is just the physical content of Equation (11)o For a fixediwe have that the $-integration gives us the contribution from the,tth elliptic zone as in Figure 3o Myth zone T R Figure 3 -6

2812-1-F Writing this explicitlyp we find the eontribution to the ground return from the Zth zone to be /\ y (t) -A4 ~ x(t _ )o ( do A( 0) o (lla) 2 2 2 V ao or for the cross-correlation function -ikL eit L 2 L z R ('Z7) = R (Z ) ( d A(g) (mb) yg L I2~ os ) W ev^ -/ t~Cto^0 0 We now turn to a detailed..onsideration of the ianlitude function A(i 0)o We first note the extremes of the behavior of A( s l).o If the ground behaves like a perfectly refleeting smooth plane A is essentially the delta function 8 ( -= ~o)O This is a case given very appiroxtately by a quiet seao On the other handD if A is independent of the variables' and OD ioeo, diffuse reflee tion, we have a case given appro3ximately by say a green uniformly forested areao In terms of the cross-eorrelation function we give a qualitative description of the various forms of the amplitude funetiono In the smooth plane case the cross-correlation function dll be sharply peaked at the value 0 = C For rough but plane ground there ill be two effects on the cross-correlation function the magnitude of the peak will be less and the peak ill be broadened aswe have pictured qualitatively in Figure 4< -"I

2802-1-F smooth plane X /\ __rough plane / I ". 0 o Figure 4o The rough plane presents no essential problem since9 as we show below9 the cross-correlation function will still be a maximum at h =-o$ however9 the amxplitude may be so low as to make the peak undetectableo It is this case that should concern us and we shall propose a simple method for classifying various terrain in terms of the size of the cross-correlation peak. The behavior of A( & ~ ) is most efficiently determined experimentally. HoweverP we Will give an example of how we might arrive at a given A from a local analysis of the ground. Suppose we have a grassy area with a distribution of rocks which are large with respect to the wavelengtho The grassy patches will scatter diffusely giving some average return per unit area9 say ago The rocks will scatter according to geometric optics9 the scattered field being ~8~

2802-1-F proportional to some average value of the characteristic dimension of the rocks, say <r> o This will then be multiplied by the distributionp the number per unit areao This then gives us a function A = a <r) p where we have assumed that the phase correlation between scatterers is random, ioeo all phases are equally likely9 and we have neglected interactions between the scattererso This gives a constructive but not very useful method of determining the amplitude function. We say this since what would be involved in such an analysis would be first a determination of the individual behavior of the various ground seatterersp ioeo the return from individual rockss grassy patches, etco and then an averaging over some collection of these scatterers; however, this averaging is just hlat is done in performing an experimental determination of the ground returns We claim it is much better to make use of the large body of experimental data or ground returns using X-band radaro It is now useful to make an assumption as to the functional behavior of A( a 0)0 We assume that near the specular reflection direction A(e & 0) is describable as a function of the angle the line PR makes with the specular directiono This is illustrated in Figure 5$ A ray from T to P, characterized by the vector 6L will be specularly reflected in the direction e o We now take A( t, 0) to be a function of 9 alone as long as the angle 9 is smallo There is much to be criticized in this assumption. However, we again insist that for our purposes this is a sufficiently good characterization of the ground -9

2802-1-F return, since, as we will see below the particular form of our characterizations of the ground, i.e., in terms of the cross-correlation functions we need only consider small values of the aglee e T R t o/ ^ SP Figure 5o Under our assumption we write A(t ) = -z(e), (12) where 9 is the angle between PR and the specular directiono If we define 1 and as the vectors from T to P and P to R respectively we have the vector in the specular direction given by p, -lO - (13) sp"^^^~^>- Y

202-I-F Hence, cos e --- --- (u14) 1 f2 sp After some straightforward manipulations, we have cos 0 1 - (15) 21 2 We now examine the cross-correlation function in more detailo The integrand in ikt Equation (5) is made up of three factors: The geometric factor e-. ig 2 -g2 cos2g the amplitude factor 2(o) where 9 = 9e(, 0) and the autocorrelation function c The geometric factor has its maximum at ~ =-t0 in fact g(^) ~ ~ 1I sin8 The amplitude factor also is a maximum at =. s ioeo at e = 09 except o for certain extraordinary events* These extraordinary events could arise from say a single large reflector which could dominate the return at a given instant or say from the rare case that a number of obstacles be so distributed that they scatter coherentlyo That is to say in Equation (llb) the amplitude from theeth zone -Il

2802-1-F 21r d A(,s I) 0 as a function of could-have a maximum for some d- ut due to coherent 0 scattering from the elements in this zone or due to the specular return of some large smooth obstacle which lies at some position (i, 0), 1t4 1 o We propose not to consider such cases since in the application envisaged the number of trials will be large enough to make their consideration of no importancee The autocorrelation function for white noise taking the frequency band to be (O, c) and the power spectral density to be Wo is given by 2Wo R( T ) = ~ sin A. This has its maximum value at Z= 1; in fact | (et) | S 2W,R (O)= 2W c. Hence, because of the behavior of the other factors in the integrand, we have that the cross-correlation will be a maxomumn, excluding the extraordinary events, at the values ~o -L tr=o0o c

2802-1-F What we now do is to examine the cross-correlation at T = and 0 1-L estimate the relative size for various types of terrain. Now R ( A l-) c is half-maximum for C,0(' - — ) |( 2, (16) 0 e C or rewriting, for Fat 2c - - t + -. (17) 0 Taking the upper limit of the modulation frequency to be 1 Me and measuring P in meters, Equation (17) becomes 0 e-1~ 102 ~(18) The corresponding value for 9 we get from Equation (18) lO2 102 cos e = + O ( ). (19) 0 Hence, for any reasonable value of the range or j we are justified in writing 00 2d0 ike Ryd(o) < Ia,(O) I ( do.,e R(.-..R). (20) yv0 do0 dyg I I I2 ) 2 -1K ~O O O~~~~Co

2802-1-F We see then that we can compare the various types of terrain in terms of the magnitude of the return in the specular directiono It only remains now to experimentally determine the amplitude for specular reflection from various types of terrain. Unfortunately the large body of experimental data is for monostatic ground returno We can, however, make the reasonable assumption that the bistatic specular returns which we need are scaled in the same way as the monostatic specular return from the same types of terrain. This we propose to do classifying the various ground returns in terms of power in decibels below the return from a calm sea. This is done in Table 1 using the data of Grant and Yaplee (Reference l)o Finally we note that only a relatively small region of the ground about the specular reflection is of importance in determining the cross-correlationo This fact.then, is a justification of our scalar treatment of the problem since the angle the polarization vector makes with the ground will change very little over this small region about the specular reflection direction, Since polarization effects will be of little importance for our purposes the vector treatment will be only a complicating encumbrance adding little to the solutiono The effect of rolling or sloping terrain will introduce a bias error independent of the type of terrain; hence, for the purposes of terrain classifications we need not consider this effect. -14

2802-1-F Type Power Shape of A(e) calm sea 0 sharply peaked rough sea -9 db peaked marsh 0 peaked grass and sand 0 peaked green grass -10 db peaked short dry grass -25 isotropic green forest -25 isotropic Table 1 In conclusion we can say that the usefulness of this approach is limited primarily by the discrimination of the receivers If the cross-correlation is detectable in the difficult cases of diffuse reflection the device will be successful0 We suggests therefore, that the most useful experimental check need be made over heavily forested areas~ If the cross-correlation is there detectable we are assured that the results of a run will not be negative, although the bias error introduced by sloping ground will need be considered in any ~aseo We now make more precise what we mean by sloping groundo We use the term to describe very large obstacles as for examples a large hillo In this case the departure of the ground from flat occurs over much larger areas than previously consideredo The effect on the cross-correlation function will be to introduce a bias error as we indicate quatlitatively in Figure 6 -15

282-1-F YdYg(Z) flat plane minimum time delay I\ /i \ biased return from \ / I \ sloping ground,, to 1 - ^ measured delay time Figure 6. This bias error will be partially corrected in application since the transmitter and receiver will be in motion andp hence~ the specular reflecetion point will be also in motion~ The effect of this is to cause the crosscorrelation function to jitter back and forth in time so that the problem becomes that of determining the minimum time delays presumably too 0 The simplest means of correcting for this bias error is then to take a large enough sample in time that many nhillst have been passed overo Thenp on the average the return will appear isotropic and the above analysis is applicable. To characterize sloping ground we need count the number of hills per unit areao We then decide on the number of samples necessary to establish the minimum time delays and finally, we take a large enough sample in time so that the agreed number of hills have been passed over0 -l6~

2802-1-F The limitations imposed by sloping ground would seem to be on the rapidity with which a range determination can be made. For single slopes of many miles the system fails. For uniformly hilly regions in which there are a sufficiently large mmber of peaks per unit area so that the return is isotropic on the average for a reasonable duration of the sample the systems can be expected to -ork. Inhabited areas will behave much like the sea in terms of the crosscorrelation functiono This obtains since there will be a large number of flat, level specular reflectors such as flat roofs, paved areas, and graded areaso The only important departure would arise in the case of a large number of pitched roofs, eogo a heavily built-up subdivision. In this latter cases depending upon whether or not there is preferred orientation of the pitched roofs, there will or will not be a bias error introducedo This bias error'would be of the same form as that cited above for single slopes. As in that case, the system fails if the array of oriented pitched roofs is of many miles extento We have considered various types of terrain in terms of their radar reflection propertieso These considerations have been somewhat qualitative because of the lack of experimental data necessary for this particular applicationo We haves howeverp pointed out the type of experiments which would most usefully be performed for this application. We repeat our suggestions for experiments. You need tw classes of information to check-the se results~ 1o The relative magnitude of the cross-correlation for the types of terrain as, for example, those presented in Table 1o 2o The duration of a sample in order to get a tgood" reading over sloping or hilly groundo -17

2802-1-F Reference Grant, CO R. and Yaplee, B. S., tBack Scattering from Water and Land at Centimeter and Millimeter Wavelengths", Proceedings of the IRE, Vol. 45, No. 7, pp. 976 - 982, July 1957. -18~