I i 1 ENGN3 4 TV UNIVERSITY Of, F UMR0034! I' I UM NM 73-1 - ENGINEERING LILBLR,&.I" | Coded Aperture Gamma-Ray Imaging 11 with Stochastic Apertures A. Z. AKCASU* R. S. MAY* G. F. KNOLL* W. L. ROGERS** K. F. KORAL** L. W. JONES*** November 1973 Text of talk delivered at Society of Photo-Optical Instrumentation Engineers Seminar on Application of Optical Instrumentation in Medicine. November 29, 30, 1973, Chicago, Illinois. *Department of Nuclear Engineering \1Y AO **Division of Nuclear Medicine.^%,, ****Department of Physics 1 7811

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tional approach, but the additional So far nothing has been said degree of freedom introduced by the about the aperture functions TV. The time modulation will be seen to have philosophy behind the approach is most important consequences. easily defined by describing the stochastic aperture. ONE-DIMENSIONAL CODED APERTURE A. Stochastic Aperture Suppose that we generate the M aperture representations by choosing member functions of some prespecified stationary random process T, whose mean and autocovariance. function are $OUNCE denoted by: m m (T (y)) I |\ ~ and A (y-y') = ((T(y) -m) (T(y')-m). (l) Each aperture can be considered to be APERTURE a sample or a "realization" of the stochastic process T. We can further i~// ^ rF identify time fluctuations in trans/ / mittance by: //B t(v) =T -m.(2) / / j The autocovariance function $ of, l i I I DtTECTOR the generating process is a measure of C.~~~-^ -the extent of interdependence between ~]~~~~1 ~transmission values at various positions. $ is a peaked function whose igure 1. Geometric arrangement for half width and tail properties detera 1-dimensional coded aperture. mine respectively the resolution and side lobe properties of the point response function. Unlike fixed coded aperture techniques, the integral One now records a sequence of M properties of any particular aperture coded images using the M aperture function are unimportant; only collecplates. Assuming that each coded tive aspects are of interest. The image and aperture function are digi- crucial point is that time dependent tized and represented respectively by transmittances are uncorrelated for Nd and Nf numbers, the recorded data different locations on the aperture consists of: plane. i) Cji = number of counts In practice the generating process recorded by the jth detector T often consists of a class of pieceelement during the vth time wise constant binary functions which interval. (v=1,...,M; assume only the values of 0 and 1 j=i,.. Nd.) ii) TiV = transmittance (proba- Equation (1) can be reexpressed ii) Ti = transmittance (proba- discrete form as: bility of photon transmission) of the ith aperture element= ((T.-m)(T.-m) (3) during the vth time interval. i,i') (v=1,...., M; i=l,...,Nf.) The smallest interval, designated a The o t is to s w ue filter increment, 6, directly deterThe object is to somehow use mines the width of the function 9. these recorded data to estimate the these recorded data to estimate the As well as facilitating aperture conspatial source distribution, which i s a inar transissio - represented in discrete form by: I1,..., Ik,. *... Ie

tion generally provides statistical is not a factor, the image resolution, properties superior to classes which R, becomes: allow continuous values between 0 and 1 r-.0 A+B 1. R B 6 (6) B. Cross Correlation where A and B are the source-to-aperUsing the data described above, ture and aperture-to-detector diswe can compute and store the following tances respectively and 6 is the "Temporal" cross correlations between width of the smallest filter interval. observed counts and aperture transmittance fluctuations: Of more practical interest is the M mean response encountered for finite V M excluding the photon statistics. ij EMu C. (Ti -m) (4) Figure 2 shows the point response cal1 culated for 500 realizations of a one dimensional stochastic aperture and infinite photon statistics. where i=l,...Nf j=l,. Nd POINT SOURCE RESPONSE FOR STOCHASTIC APERTURE (M-500) These numbers constitute an Nf by Nd matrix. Q contains all the available information from the above measurement. / \ It has been shown (Ref. 9,10,11) - x that an estimate of the source strength 2k can be specified by a linear combination of the elements Qij; that is, there exist coefficients ckij dependent only on the experimental geometry such that: IN FOCUS I/ \ ~A. Nk X k Nd Nf M -\ X aijk M C j(TiY -m) (5) j=l i=l v=1 A-7'he a's are non-zero only for those aperture elements, T i, which X lie between the kth source element and the jth detector. Examination of Figure 1 further shows that the a's Figure 2. Point source response for select a unique collection of aperture 500 realizations of a stochastic elements for every resolvable image aperture. point. This is true even though only a single detector element is used. Some small sidelobes are in evidence (However, both statistical accuracy whose average amplitude decreases and depth information is gained by roughly as V/M. The peak width is using many detector elements.) As M found to be relatively insensitive to become infinite these unique collec- M. The peak is defocused smoothly tions of aperture elements become but assymetrically in depth. More orthogonal as determined from Equation rapid defocusing occurs for planes 3 and the assumed randomness of the closer to the aperture since the subprocess T. If detector resolution tended angle changes more rapidly.

It is of paramount importance to counting statistics, but the wings are understand the effect of photon statis- reduced indicating that neighboring tics in a coded aperture imaging scheme sources contribute significantly less if it is to be applied in Nuclear to the local error. This dependence Medicine. The quantity of interest is of the error on mean transmission is the variance of the mean response func- explicitly illustrated in Figure 4 tion defined as for the case of a point source. Since f mi o 2 _ ( (x) 2 the mean transmission is readily varied, ( i(x) 2M _. ()2~a method is available for optimizing the aperture for a given source distriThis will give rise to a standard bution. deviation equal to ~Var f7(x) where fM(x) is the mean response. The variance at any position may be expressed as the J..j convolution of the source distribution )m=.04 with an error kernel, EM(x - x'). The shape of the error kernel is strongly dependent upon the mean transmission of the aperture, m. Error.. kernels calculated for uniform distri-... butions and several values of m are illustrated in Figure 3. KmI H HF b)m=.50 ized to mean response s sa function of - - for 3 different mean transmissions. I-' I lIl I' t lr~~~~ "i~ ~ \ I c)m=.96.7 Figure 3. Plot of error kernel normalized to mean response as a function of igie l lation displacement for several values of Figure 4 Illustration of the error teaing trhat all soure locations con- hadistribution about a point source tribte eal to th rrorfor 3 different mean transmissionsFor m large the error is locally small The mean transmission need not be reflecting good counting statistics. spatially uniform, but the effect of The large wings show that distant varying this parameter has not yet sources will strongly affect the local been determined. error. For m = 0.5, the error distribution is approximately uniform indi- A digital Monte Carlo simulation cating that all source locations con- has been made to compare a pinhole and tribute equally to the error and that a stochastic aperture of mean transthe error is proportional to the inte- mission, m = 0.5 for the case of a grated signal strength. As the mean pair of adrenal glands. They were transmission is further reduced, approach-represented by point sources in a coning the pinhole as a limit, the error tinuous background distribution having is locally increased reflecting poor both width and depth as shown in Figure 5.

SIMULATED ADRENALS IN CONTINUOUS BACKGROUND SIMULATED ADRENAL SOURCE DISTRIBUTION 9 * PINHOLE APERTURE RELATIVE SOURCE INTENSITY 8.3200 Histories 9 - 110 photons detected 7- * * is. % ^~ I- 0. *@ *. 25.6 7 - 5/i *ego**- * *.8 - 3 ~ ~. 1 5 g * Ld 4 3 3 U I 0~ ~~ ~ ~OO ~ ~ 3g,, 3 - * Through Adrenals i (0-,~ 5248~~~5 4 8 2 14036 20 24 2 0 1 128 20 1 dimensional si STOCHASTIC APERTURE L-_glands. The dtc FILTER 10 w 1nd lo d2 4 5s b w te7 89 ft0er PLANE. Rd i o 20 wh mst be a d or 3 detect I- 12 - - w5 order to achiee comographic Slice a c. ~ the pinhole exposure time wod n hrgh Ahoughdrenals "~~~~ ~ ~~~~~~Furth~~~2 25 filter increments mization of the men t.3200 Histories SOURCE COORDINATE X 1300 photons detected 0 t 8 12 16 20 24' 28 32 36 40 44 48 52 Figure 5 Source distribution used for SOURCE COORDINATE 1 dimensional simulation of adrenal glands. The detector is 10 units wide and located 4 units below the filter Figure 6. Reconstructed images of the or aperture plane. adrenal using the pinhole aperture (Top) and stochastic aperture (Bottom). The background increases to the right to simulate the liver, and the projected source distribution is typical Note that an estimate based solely on of that observed about 8 days post- the increased solid angle of the stochinjection. The source distribution astic aperture would predict a factor was viewed for equal time and at equal of 12 difference in exposure times. resolution by the two apertures. The The smooth appearance of the stochastic pinhole image is shown at the top of aperture image not only results from Figure 6 and that from the stochastic increased statistical accuracy but is aperture at the bottom. The calculated a reflection of the fact that the error in this image is uniformly dis- statistical fluctuations have a correltributed (see Figure 3) and equal to ation length equal to the spatial 1.5 relative intensity units. This resolution. Such smoothing is optimal gives an error in the left adrenal in the sense that it engenders no loss peak height of 13.9/%. The pinhole data in spatial resolution. which must be averaged over 3 detector elements shows an error of 23.5%. In C. Pseudo-Random Strings order to achieve comparable accuracy the pinhole exposure time would need Although it is possible to reduce to be increased a factor of 2.9. the sidelobes on the point response Further improvement would follow opti- function to an arbitrarily small value mization of the mean transmission.

by increasing the number of random realizations, it is reasonable to expect POINT SOURCE RESPONSE FOR CYCLICLY that for a finite number of realizations PERMUTED PSEUDO-RANDOM STRING there will be a "best set" of realizations which will exhibit the orthogonal property obtained from the infinite set of random realizations. This is indeed A.2 true, and such sets have been widely x employed in neutron and molecular beam time-of-flight spectroscopy (Ref. 13, 14). These sets may be generated by cyclic permutation of pseudo-random strings of l's and O's, such as Barker codes, which exhibit a peaked auto-covariance function with zero sidelobes. For a IN FOCUS string length M, the collection of M A. 4 cyclic permutations forms a complete, orthogonal basis set. Numerous such strings of varying length and mean transmission have been tabulated (Ref. 13, x 14). Despite the fact that these strings are one dimensional, they may be dis- A.n tributed over a two dimensional aper- ture plate. This follows from the method's dependence on the time integral rather than the spatial integral. It is important however that no two Figure 7. Point response obtained points on the plate simultaneously using a cyclically permuted 40 element describe identical non-zero sequences. pseudo-random string. Three focal This would destroy the orthogonality depths are illustrated. condition between points on the aperture. A section through the center of a two-dimensional point response function obtained with a 40 element string distributed in a 6 x 6 matrix D. Relation to Fixed Aperture is shown in Figure 7 both in and out of focus. The 40 realizations were gener- It is perhaps of interest to ated by permuting the string, one explore in a qualitative way the relaelement at a time, through its full tionship of the time modulated aperlenqth. (The fact that 4 elements ture to a fixed aperture. To do this were left over makes no difference.) reconsider the expression (Eq. 5) for The result is similar to that obtained the strength of the kth source element, with 500 random realizations mentioned Ik, and reverse the order of temporal earlier except that in the present case and spatial summation: there are no sidelobes. The slight M negative bias can be eliminated by 1 k V V correction for the finite string Ik ( aij C (Tim) (7) length. v= i,j From the geometric relations in Figure 1, i is given by: (8) B A i = 8k +J' = A+B' A+B

with suitable allowance made for handling the discrete quantities. The sum over i and j reduces to a single sum: single sum: POINT RESPONSE FOR SPATIAL M d CORRELATION OF A PSEUDO- RANDOM STRING k= (k+j ( 3 kT -)c -m). (9) v=1 j The image is now expressed in terms of a coherent summation of M scaled spatial cross correlations between the \ IN OCUS coded image and fluctuations in the A -4 mean transmission. The question which comes immediately to mind is, "Why not choose a transmission function x which has a peaked spatial autocorrelation like a zone plate and just let M = 1?" Part of the answer lies in the manner in which the reconstructed image goes out of focus. Examples / \ are shown in Figures 8 and 9. Figure 8 illustrates the case for one of the\ pseudo-random strings which, as we / / previously indicated, does have a peaked auto correlation. The point response which is sharply'peaked with- - A1 out sidelobes for the in-focus case deteriorates seriously as it goes out of focus. When M such correlations are summed for the permuted string, J however,the spurious oscillations add to zero and the result shown previously in Figure 7 is obtained. Figure 8. Point response obtained usThe second example, Figure 9, is ing spatial correlation of a pseudofor an on-axis zone plate. The letters random string. Three focal depths are K and R were in planes separated by illustrated. 3 cm. With the R in focus the K has degenerated into 4 individual K's. Off-axis zone plates do not demonstrate quite such a dramatic effect, but do, never-the-less cause problems for out of focus sources. imaging with stationary codes and by temporal modulation differ fundamentally from each other in the operations and conditions necessary for their success. The stationary code relies upon a spatial integration to provide the completeness relationship which guarantees a peaked response function free of spurious structure; this relationship breaks down when the scale of a code is varied (as for sources at different depths) or when the integration cannot be completed Figure 9. Illustration of out-of-focus (such as when a portion of the aper- behavior of on-axis zone plate. The ture shadow falls beyond the detector defocussed letter breaks into 4 compoboundary). nents correspondalng to the 4 orders of the half-tone screen.

In contrast, a time modulated Data is acquired using a Medical aperture requires only that the time Data Systems computer system based on fluctuations in transmittance are a Data General NOVA computer with dual uncorrelated for any two points in the disks. The 121 short exposures are aperture plane separated by more than sequentially recorded on one of the a filter increment. A point-by-point disks for reconstruction after the reconstruction is thus obtained which study. allows us to produce a good response function based upon even a single At the present time reconstruction detector element. Depth information is accomplished in two steps: and improved statistical accuracy may be gained by combining results from First, a complete set of correlamany elements, but the important tion coefficients is calculated and point is that no spatial integration stored: is necessary so that questions of scale and integration limits do not 121 even arise. Qi y C (Tk -m) (10) ij~kt ( T k ~ III. Experimental Implementation v=1 We have constructed a time modu- Second, the desired slice through lated aperture plate based on a 121 the image is constructed; the image is constructedelement pseudo-random string. The string has 40 open elements for a mean transmission of 33/o%. The filter incre- I xyz (11) ment of 3 mm was selected for use on xyz Lijk4 an Anger camera. A photograph of the ijk ij aperture is shown in Figure 10. The code is arranged on the plate so that This approach has the advantage that advancing the plate by one filter once the Q's are calculated any tomoincrement permutes the string cyclically graphic slice through the image may by one step for each of the 121 filter gh e by one step for each of the 121 filter be rapidly constructed. However, if elements being viewed by the detector. one or two pre-selected slices are to The detector view is limited by a be reconstructed it is more rapid to 3.3 cm square aperture beneath the 3.3 cm square aperture beneath the calculate the appropriate spatial integrals first and sum them over the realizations. A. Preliminary Results E a, S 1,.Preliminary results have been obtained using computer generated data for a point source at A=B=4 cm. The data simulates the case for the aperture code shown on the lead plate in Figure 10 and described above. The first four realizations are pictured in Figure 11. Figure 12 shows reconstructions of the point source i n 3 differe nt Figure 10. Photograph of coded leadin 3 different aperture. The code is based on a 121 planes: 12-a: in-focus element pseudorandom string Each A=2, B=4, and 12-c: A=8, B=4. Both a central profile and an intensity aperture realization is r accomplished modulated plan view of the reconstructed by moving the plate one filter incresource distribution are shown. The ment. The 11 x 11 aperture area is defned by a 3 3 u aperture aintensity is scaled in each case such befineathy t cod pa sthat the peak counts in the image are beneath the code plate~ displayed at maximum intensity. (The small black regions result from an error in the display program.) The

low-level pattern evident in the outof-focus reconstructions is most probably a round-off error in the,,} b) Figure 13. Plan views of same point source reconstructions pictured in Figure 12 with Figure 11. Simulated data for a point source located 4 cm from aperture plate shown in Figure 10. The first r rlizions a s n. The same 3 images are shown in Figure 13 with the intensity scaled to the peak of the in-focus source in order to indicate the contribution one would actually observe from an out-of-focus point source. B. Limitations There are two difficulties encountered in the actual application of time modulated apertures to n) - b) Nuclear Medicine. The first is that the method can be applied to fast dynamic studies only with difficulty since the framing rate will have to be,121times faster than with a stationary aperture. Data storage problems might well be encountered as a dynamic study can easily require over a hundred images. Short codes C) could be employed with a reduction in efficiency, or perhaps codes can be employed which will combine some Figure 12. Profile and intensity of the required temporal and spatial modulated plan views of reconstructed characteristics with the aim of point source for 3 different planes: reducing the number of realizations a) in-focus A=4, B=4, b) A=2, B=4, needed. c) A=8, B=4.

angle efficiency than a pinhole for information from each point in the equal spatial resolution. The zone source over a large region of the plate, for instance, has 50% open area detector, non-uniformities in the and can yield two-to-three orders of detector do not as seriously degrade magnitude greater collection efficiency the image as in the case of direct than a pinhole of equal resolution. imaging. Since coded apertures subtend a finite angle at a source point, This gain in solid angle provides the scale of the coded images contains a gain over detector noise proportional information about the longitudinal to the square root of the solid angle source distribution, and the images increase. This fact has made it possible may be reconstructed in tomographic to use x-ray film as a low cost detector slices corresponding to various depths despite the fog level and the small in the source distribution. These number of grains developed per inter- properties of coded apertures provide acting 7-ray (Ref. 7). The lower inter- significant motivation for their study action efficiency of the film detector and application to Nuclear Medicine. may be compensated in part by using large area multiple detectors for simul- The zone plate aperture has met taneously recording several views. One with considerable success in both can also, as a consequence of the large phantom imaging and clinical imaging collection efficiency, consider large and has yielded high quality, high diameter, efficient photocathode devices resolution images (Ref. 12). There with correspondingly high thermal noise are, nevertheless, several reasons components as a means for increasing to explore alternative techniques: the spatial resolution of 7-ray detectors. In order to eliminate the conjugate and higher order images enIt was hoped that similar gains countered with on-axis zone plates might also be made with respect to an off-axis zone plate must be photon noise, but it turns out than employed (Ref. 1, 4). This change when the noise arises from statistical requires a threefold increase in the fluctuations in signal, the actual gain detector resolution required for a in image signal-to-noise depends expli- given image resolution and also requires citly on the source distribution. A that the source be spatially modulated detailed analysis has been performed by by a half-tone screen with a corresBarrett (Ref. 8) in the case of the zone ponding 50% loss in efficiency. plate and by Akcasu, May and Knoll (Ref. 9, 10, 11) in the case of the The point response function for stochastic aperture. This dependence a finite zone plate contains residual upon source distribution may be broadly side-lobes which can contribute articharacterized thus: Sizeable gains can facts to the images. Furthermore, be realized for small isolated sources sources out of the focal plane do not and for strong sources at the expense blur smoothly, but instead contribute of increased noise in the less intense false structure to the image. Such regions of the image. There are a artifacts cannot be tolerated in clinnumber of Nuclear Medicine imaging situa- ical images. Source regions which do tions in which the detector area is not project the entire zone plate onto poorly utilized resulting in low average the detector are imaged with a frecount rates over the field of view. quency response which depends upon These situations should benefit markedly position. These difficulties can all from coded apertures. Among these are be resolved by employing time moduthe imaging of small organs such as the lated apertures. thyroid, adrenals, pancreas, kidneys and eye. Skeletal imaging, in which the II. Time Modulated Apertures sources are essentially line sources separated by empty areas, should also Consider the geometry illustrated benefit. Some blood flow studies may in Figure 1. Suppose that the measurealso show improved signal to noise. In ment time is partitioned into M segaddition, it is possible to optimize the ments, and during each such interval, aperture for a given source distribution =1...M, a different aperture plate and this aspect will be discussed later. is inserted between the source and detector. Such a procedure is apparSince coded apertures spread the ently a generalization of the tradi

CODED APERTURE GAMMA-RAY IMAGING WITH STOCHASTIC APERTURES A.Z. Akcasu,, R.S. May,*G.F. Knoll, W.L. Rogers, K.F. Koral, L.W. Jones The University of Michigan I. Introduction detection efficiency places severe requirements on the detector as well A. Nuclear Medicine Imaging as the aperture. Most detectors used in Nuclear Medicine use i" to 1i" Tracer doses of 7-emitting, thick sodium iodide scintillator as radio-labeled pharmaceuticals have the detecting medium. A variety of been used for a number of years for schemes exist to obtain position infortumor localization and to provide the mation from these detectors with clinician with regional information accuracy ranging between five and ten concerning organ function and blood millimeters. flow. An image of the radio-pharmaceutical distribution is formed by B. Coded Apertures means of the emitted 7-rays. Elevated or depressed concentration of the In an attempt to relieve some of tracer agent as reflected by hot or the restrictions placed upon both apercold spots in the image is indicative ture and detector a number of investiof abnormalities. The 7-rays, which gators (Ref. 1-6) have been exploring must be of sufficient energy to pene- the use of stationary coded apertures trate tissue with minimum scattering for 7-ray imaging. In this paper we and absorption, cannot be refracted shall discuss the concept and applicaor reflected so the image must be tion of time varying apertures to formed by aperture limitation; (i.e. 7-ray imaging and make some comparisons a pinhole in lead or multi-channel to fixed apertures, in particular the collimators). Such an aperture is zone plate, which has received the extremely inefficient with solid angle most attention to date. In the zone efficiencies on the order of 10-4; plate scheme a large scale zone plate efficiency may be increased but only made of a high atomic number material at the sacrifice of resolution or such as lead or gold is interposed field of view. This, coupled with the between the source distribution and need to minimize the radiation dose to detector in place of the pinhole. A the patient and to maintain reasonably point source casts a geometric shadow short imaging times, results in low of the zone plate onto the detector resolution images corrupted by noise rather than being directly imaged as arising from the statistical fluctua- with a pinhole. The image of the tion of the y-photon emission. A source may be readily reconstructed typical 25 cm diameter image field optically from a reduced transparency seldom contains more than 1000 resolved of the zone plate shadow; alternatively image elements and the information is if the data is available in digital often carried by fewer than 100,000 form, a computer using fast transform photons. techniques may be employed. The penetrating nature of 7-rays There are a number of reasons combined with the need for maximum for investigating coded apertures and their applications in Nuclear Medicine. tDepartment of Nuclear Engineering The intense initial interest was stimu* lated by the fact that a coded aperDivision of Nuclear Medicine ture may have a much greater solid Department of Physics

The second limitation is that of 6. Walton PW: An Aperture Imaging computing time. To generate the full System with Instant Decoding and set of correlation coefficients for a Tomographic Capabilities. 46 element by 46 element detector ma- J. Nuc. Med. 14: 861, 1973. trix and a 121 element code requires 2 hrs. and 17 min. on a NOVA-800 con- 7. Barrett HH, DeMeester GD, Wilson puter using programmed multiply-divide DT, Farmelant MH: Recent Advances and 24k of core storage. Reconstruc- in Fresnel Zone Plate Imaging, tion cfa31 x 31 image slice requires Medical Radioisotope Scintigraphv, about 10 minutes. Use cf hard wired 1972, Vol. I. 282-283. IAEA, multiply-divide is expected to Vienna (1973). reduce these times by a factor of 5 or 10. This limitation is expected 8. Barrett HH, DeMeester GD: to further yield to improved recon- "Quantum Noise in Fresnel Zone struction algorithims and is not at Plate Imaging. Raytheon Technical present viewed as a basic limitation. Report T-972, 1973. IV. Summary 9. May RS, Akcasu AZ, Knoll GF: 7-Ray Imaging With Stochastic Time modulated coded apertures Apertures. (Submitted to Applied yield good 3 dimensional response func- Optics.) tions, do not require half tone screens or excessive detector resolution. 10. May RS: Stochastic Aperture There are many codes available which Techniques in Gamma Ray Image should permit aperture optimization for Formation. Ph.D. Thesis, The Univmany imaging situations encountered ersity of Michigan, (1974). in Nuclear Medicine. 11. May RS, Knoll GF, Akcasu AZ: Acknowledgements A Cross-Correlative Technique for Gamma-Ray Imaging. (Submitted to This work was supported by the J. Nuc. Med., Nov. 1973). National Institutes of Health Grant No. GM 16188-04 and a grant No. 474 12. Farmelant MH: Improved Anatomfrom the Michigan Memorial-Phoenix ical Definition by a Fresnel Zone Project. We also wish to acknowledge Plate Imager. (Abstract) J. Nuc. the computing facilities and assistance Med. 14: 393, (1973). provided by Medical Data Systems for processing the coded images. 13. Hossfeld F, Amadori R: On Pseudorandom and Markov Sequences References Optimizing Correlation Time-OfFlight Spectrometry. Kern1. Barrett HH: Fresnel Zone Plate forschungsanlage Julich Report, Imaging in Nuclear Medicine. Jul-684-FF: (1970). J. Nuc. Med. 13: 382, 1972. 14. Rydin RA, Hooper RJ: Numerical 2. Rogers WL, Han KS, Jones LW, Evaluation of Spatially Dependent Beierwaltes WH: Application of a Dynamic Reactor Systems Using Fresnel Zone Plate to Gamma-Ray Pseudorandom Signals. Nuc. Sci. Imaging. J. Nuc. Med. 13: 612, 1972. Enq. 38: 216-228, (1969). 3. Dicke RH: Scatter-Hole Cameras for X-rays and Gamma-Rays. Astrophysical J. 153: L101, 1968. 4. Rogers WL, Jones LW, Beierwaltes WH: Imaging in Nuclear Medicine with Incoherent Holography. Optical Enqineering 12: 13, 1973. 5. Barrett HH, Wilson DT, DeMeester GD: "The Use of Half-tone Screens in Fresnel Zone Plate Imaging of Incoherent Sources." Opt. Comm. 5: 398, 1972.

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