Compact Phase-Conjugating Correlator: Simulation and Experimental Analysis

Compact phase-conjugating correlator:simulation and experimental analysis

James H. Sharp, David M. Budgett, Tim G. Slack, and Brian F. Scott

A simulation and experimental investigation of a recently proposed, compact, phase-conjugating corre-lator is undertaken. The effects of noise and other distortions in the input image and in the correlatorfilter plane are considered. As with other phase-only designs, the phase-conjugating correlator issensitive to distortion of the input image while being robust in the presence of filter-plane distortions; thisrobustness is enhanced by the phase-conjugating property of the design. © 1998 Optical Society ofAmerica

OCIS codes: 070.0550, 070.5040, 070.5010.

1. Introduction

Optical correlation promises high-speed object recog-nition and identification for applications as diverse astarget acquisition, fingerprint verification, and pro-cess and quality control. The approach proposed byYoung et al.1 of using a hybrid digital–optical corre-lator system has been adopted in this study to cir-cumvent the performance limitations commonlyimposed on correlator systems by spatial light mod-ulator ~SLM! frame rates in the input plane. How-ever, the optical system of this proposed designemployed the conventional 4f VanderLugt correlator,which is difficult to implement because of the need tomatch the phase spectra of the optically derived Fou-rier transform ~FT! and the digitally calculated fastFourier transform ~FFT! displayed on the filter plane.This is not a trivial problem since most of the widelyused SLM’s, e.g., those derived from the Seiko-Epsonliquid-crystal television ~LCTV! projector, have anonunity aspect ratio. Imperfections of SLM’s, suchas phase distortion owing to nonflatness, nonlinearphase response, residual amplitude coupling, and so

on, also have implications for ultimate performance.The compact phase-conjugating correlator ~PCC! de-vised by Duelli et al.2 has been adopted to obviatesome of these problems, while retaining the hybrid,high-speed concept.

A simulation of this correlator was undertakenprior to its construction to identify critical designissues and predict the effect on performance of noiseand distortions. The correlator was built and tested,and its robustness to these distortions was observedexperimentally.

2. Correlator Design

Figure 1 illustrates the digital and optical sub-systems that constitute the correlator. Phase im-ages of the reference data are calculated by the digitalFFT system and recorded in the optical memory.This FFT system employs a Sharp Model LH9124FFT digital signal processor chip set and can calcu-late a 512 3 512 FFT in less than 40 ms. Phaseinformation is extracted from the fully complex FFTresult by a GEC Plessey Pythagoras chip. Phaseimages are displayed at 25 Hz by use of a SLM de-rived from a Seiko-Epson LCTV and stored as angle-multiplexed volume holograms in crystals of Fe:LiNbO3.3 The phase conjugates of the stored imagesare reconstructed by use of a beam counterpropagat-ing with respect to the reference beam, compensatingfor the nonunity aspect ratio and phase distortionspresent in the object-beam optical path. Angulartranslation of the reconstruction beam is achieved byuse of an Isomet Model LS-110 acousto-optic deflectorthat provides random access to any template in theoptical memory within 15 ms.4

The inverse transform is produced behind the SLM

When this study was performed, the authors were with theLaser and Optical Systems Engineering Centre, Department ofMechanical Engineering, James Watt Building, University of Glas-gow, Glasgow G12 8QQ, UK. D. M. Budgett is now with theDepartment of Engineering Science, University of Auckland, Pri-vate Bag 92019, Auckland, New Zealand. T. G. Slack is now withSowerby Research Centre, Department of Optics and Laser Tech-nology, FPC 267, P.O. Box 5, Bristol BS12 7QW, UK.

Received 5 January 1998; revised manuscript received 10 April1998.

0003-6935y98y204380-09$15.00y0© 1998 Optical Society of America

4380 APPLIED OPTICS y Vol. 37, No. 20 y 10 July 1998

and is extracted and scaled by use of a beam-splitterand lens system, with images of the correlation planebeing captured and digitized to analyze correlation-peak characteristics. A high-speed, area-scan CCDcamera captures the correlation-plane data andpasses them to a specially built imaging board, whichimplements a parallel pixel-processing architectureto characterize the correlation-plane image and thequality of any peak detected.5 This subsystem iscapable of operating at frame rates of up to 3000framesys, which ultimately limits the obtainable cor-relator speed. The system was tested with images ofa camshaft bearing cap supplied by Rover, UK. Animage of the object at 0° in-plane rotation is shown inFig. 2.

3. Correlator Analysis

The aim is to understand the effects of any imperfec-tions in correlator components and their impact onsystem performance. The effects of imperfections inthe input image and in the behavior of the phase-modulating filter-plane SLM were analysed: theeffects of distortions and noise, first in the inputspace-domain image ~prior to its transformation andstorage! and second in the frequency-domain phaseimage ~as displayed on the SLM! were evaluated.

A. Input Image

1. Intensity NoiseIntensity noise present in the input image and passedto the FFT subsystem was assumed to be additive.A series of simulations was run under the assump-tion of a Gaussian noise distribution normalized tothe maximum available gray level ~255! in the inputimage. Values exceeding this maximum or less thanthe minimum gray level were set to 255 or 0, respec-tively. Images with increasing levels of noise deg-radation were derived from a reference image of thetest object oriented at a 0° in-plane rotation. Thesimulation numerically cross-correlated these imageswith the original reference. The noisy image set wasthen applied to the PCC, and the correlation planeoutput was examined experimentally.

Figure 3 illustrates the quality of the autocorrela-tion peak, as derived from the experiment. Figure 4shows the results of the simulation and the experi-ment. The same functional trend is present in bothsets of data. A large reduction in the correlation-peak height ~CPH! is caused by relatively smallamounts of intensity noise. Because the frequency

Fig. 1. Correlator design: SF, spatial filter and point stop; L, lens; BS, beam splitter.

Fig. 2. Image of the test component in the reference position of a0° in-plane rotation angle.

10 July 1998 y Vol. 37, No. 20 y APPLIED OPTICS 4381

spectrum of the noise signal is inherently biased to-ward higher frequencies, minor additions of noise inthe space-domain images shift a disproportionateamount of energy from the lower to the higher spatialfrequencies. The pure-phase nature of the correla-tion exacerbates this tendency and results in thesharp drop-off observed in CPH. The performanceof the PCC falls off more quickly than is predicted bythe simulation. At noise levels with a standard de-viation of s . 0.25, signal levels become indistin-guishable from the background-noise level in thecorrelation plane. To account for the experimentalbehavior it should be borne in mind that other im-perfections, including phase errors, occur in the phys-ical correlator, whereas the simulation examines thecontribution of intensity noise in isolation.

2. Scale and RotationPure-phase correlators are sensitive to variances inscale and rotation. The results of a simulation of thescale sensitivity of the PCC are presented in Fig. 5.Here the height of the correlation peak is plotted as afunction of the percent scale error. The curve isasymmetric about the zero point because negativelyscaled images result in a reduction of the total energyavailable to form the correlation-signal plane. How-

ever, it was found that the experimental sensitivity toscale error is more pronounced. As can be seen fromFig. 6, a 15% scale error causes a reduction of theCPH to approximately 10% of the originalautocorrelation-peak height compared with the 50%reduction predicted by simulation, while a 25% scaleerror causes the peak to drop to 6% of its originalvalue. This higher sensitivity is likely to be due tothe spatial nonuniformity of the phase response overthe aperture of the SLM area. It has been demon-strated that the application of a given gray level ~i.e.,a given voltage! to the SLM produces a varying phasemodulation, depending on the pixel location.

Fig. 3. Isometric plot of the experimental autocorrelation.

Fig. 4. Variation of the CPH with the intensity noise in the inputscene.

Fig. 5. Dependence of the calculated CPH on the scaling error.

Fig. 6. Isometric plot of the experimental ~a! autocorrelation and~b! cross correlation with a 5% scale increase ~103 scale!.


An experimental cross correlation of the compo-nent rotated by 1° in plane had a similarly markedeffect: As can be seen from Fig. 7, experimentallythe CPH dropped to approximately 25% of the auto-correlation value, whereas a 5° rotation resulted inthe CPH being reduced to 5%, just above the exper-imental noise background. This high degree of sen-sitivity to rotation might be a consequence of scalingdifferences in the x and y directions that results fromthe nonunity aspect ratio of the SLM. For thesereasons, experimental verification of the simulatedresults below were restricted to examining the behav-ior of the autocorrelation function.

3. TranslationThe reference image of the test component was sub-jected to a series of diagonal translations ~e.g., 5 pix-els both horizontally and vertically!, and theresulting images were used to simulate the effects oftranslations of the object in the input plane. Thesimulations showed a small linear drop in the CPHcaused by translations of the object. Cross correla-tion of the translated image set with the original wasthen performed by use of the PCC; the results areshown in Fig. 8. Within the experimental error, thechange in the CPH with translation is linear, al-though it is worth noting that the rate of change islarger than that predicted by simulation. This couldalso be accounted for by the nonuniformity in theSLM phase response because object translationshould result in a linear phase shift in the filter-planeimage.

B. Fourier Plane

1. Lateral MisalignmentInitial alignment of the correlator optics is automaticbecause we are using a phase-conjugating configura-tion for the correlator. However, mechanical creepin the optical mounts can cause a gradual misalign-ment of the reconstructed phase-conjugate imagewith respect to the digitally calculated image dis-played on the filter-plane SLM. Numerical simula-tions of the correlator sensitivity to misalignment arerepresented in Fig. 9 for the autocorrelation function.These are illustrative results, as the horizontal, ver-tical, and diagonal dependencies are image specific~except for the special case of circularly symmetricFT’s!. Step sizes of less than one pixel could be re-alized because the digital representation of the phaseimage was expanded to include three zero-amplitudepixels surrounding each image pixel. In this waythe effect of the dead space surrounding pixels couldbe modeled, and a misalignment step size of one quar-ter of a pixel could be simulated.

Fig. 7. Isometric plot of the experimental ~a! autocorrelation and~b! cross correlation for a 1° rotation of the test component ~43scale!.

Fig. 8. Dependence of the CPH on the translation of the image inthe input plane.

Fig. 9. Calculated dependence of the CPH on the misalignment ofthe reconstructed FT and SLM.


It is evident from Fig. 9 that a displacement of onepixel horizontally is sufficient to reduce theautocorrelation-peak height by 21%. Similar dis-placements vertically and diagonally produce reduc-tions in the peak height of 71% and 51%, respectively.Experimentally it was found that a horizontal dis-placement of 80 mm ~approximately a one-pixel pitch!reduced the autocorrelation-peak height by 64%,whereas a vertical translation of only 50 mm wasenough to reduce the signal by 72%. It is apparentthat lateral alignment of the phase images duringreconstruction should be maintained to better thanone quarter of a pixel ~approximately 20 mm! to main-tain the optimum correlator performance.

2. Pixel Amplitude NoiseA perfect phase-modulating SLM would have unitytransmission for every pixel over the full range of thephase modulation, i.e., from 0–2p. In real deviceswhen displaying phase images, amplitude modula-tion of the light can occur accompanying the phasemodulation.6 This can be regarded as coupled am-plitude noise: noise affecting the magnitude of thepixel phasor in the Fourier plane but leaving thephase angle unchanged. As there is no informationavailable on the strength of this coupling prior to thesimulation, the initial model employed a stochasticrelation. The results of this modeling are shown inFig. 10. Amplitude noise causes a linear decrease inthe CPH. At the maximum noise value, the peaksfor each object have fallen to approximately 85% oftheir original values. Note that also shown in Fig. 9are the simulated results for cross correlation withthe images of the test object subjected to 5°, 10°, and85° in-plane rotations.

The simulation was repeated with the addition ofconstant phase noise ~see below! that had a standarddeviation s of 0.79 rad. The purpose of this addednoise was to discover whether the correlation outputwould be affected by the coupling of phase and am-plitude noise. It was concluded that the addition ofpixel phase noise acts to lower the absolute height of

the CPH but, from analysis of the correlation-planeimages, does not add significantly to the noise back-ground in the correlation plane.

This simulation could not be validated in the phys-ical correlator because fully complex modulationwould be required in the filter plane. If the pixelamplitude-coupling response is uniform over theSLM, this effect will be compensated by the phase-conjugating property of the correlator. A nonuni-form response might be expected in a real SLM.However, even with the most severe noise-degradation level simulated, a relatively small de-crease in the CPH of 15% occurs. Previousresearchers have shown that only weak couplingmight be expected in real devices.7

3. Phase NoiseThe conversion of the intrinsically digital represen-tation of the data output from the FFT system to ananalog signal resampled by the SLM driver includesseveral opportunities for the introduction of noise.Thus the phase modulation produced in a given pixelcan depart from that in the FFT phase image. Thephase response is also assumed to be linear, withincreasing gray levels in the filter image. This char-acteristic is only approximated in real devices.8 Aseries of simulations was therefore undertaken tostudy the ways in which phase noise might affect theperformance of the correlator and the implications ofcompounding phase noise with additional effects.

Figure 11 demonstrates the simulation of purephase noise in affecting the autocorrelation functionand some cross correlations. The correlation signalsfall relatively slowly at first, but the rate of fall in-creases for noise levels above s 5 0.39 rad. Thesignals for the 0°, 5°, and 10° objects fall to 26%–29%of their original, noise-free values. This implies thatthe capacity of the correlation process to discriminatethese objects is unaffected by the noise. However,the CPH for the 85° object falls to 57% of its originalvalue. Thus the discrimination ratio for this objectis more than halved. This difference in behavior for

Fig. 10. Calculated dependence of the CPH on the pixel ampli-tude noise.

Fig. 11. Calculated dependence of the CPH on the SLM phasenoise.


the 85° object is explained by the closeness of thepeak height compared with the noise floor of the cor-relation plane. As the phase noise increases, thispeak collapses into the noise floor. Analysis of thecorrelation plane confirmed this to be the case: thelocation of the detected peak moved to positions re-mote from the original peak for tests with noise levelsof s 5 1.18 rad and s 5 1.57 rad. The peaks for the0°, 5°, and 10° objects remained in the same place forall levels of phase noise.

All four correlation peaks fell to within 92% of theirnoise-free values when the phase noise was 0.39 rad.At this noise level, the correlation continues to dis-criminate between the 0° object and any of the otherobjects.

For the purpose of experimental validation phasenoise was added artificially to the filter-plane images.Results for the autocorrelation function are shown inFig. 12. The functional form of the response is sim-ilar to that predicted, but, with a slightly slower fall-off in the CPH with increasing noise, the totalreduction in the CPH is approximately 50% at themaximum noise level. This result implies that thePCC is more robust than the simulation predicts.No increase in background noise was observed thatwas large enough to account for this signal level.Images captured in the correlation plane displayed aconsistent level of background noise that was equiv-alent to 610 gray levels. It can be speculated thatthe nonlinear, nonuniform response of the SLM de-vice reduces the amount of phase noise applied at thefilter plane.

Simulations of phase noise were repeated with afixed level of pixel amplitude noise ~SLM amplitudecoupling!. The results were similar to those pro-duced with pure-phase noise, although the correla-tion peaks were reduced in height by the additionalamplitude noise. The peaks for the 0° and the 5°cases fell to 26% of their starting values; the peakproduced by the 85° object fell to 54% of its initialvalue. However, the peak for the 10° object fell to33%, which in turn reduced its discrimination ratio

compared with the other two objects. At a phasenoise level of s 5 1.57 rad together with a pixelamplitude noise of s 5 0.2, the 10° and the 5° objectsproduced the same CPH and could not be discrimi-nated. However, at this noise level the output peaksof the 5° and the 10° objects shifted their locations,suggesting that correlation peaks were hidden in thenoise floor. The correlation peak for the 85° objectrandomly changed its location at a phase noise levelof s 5 0.39 rad.

The effect of phase noise in the presence of phasequantization was then considered. It was assumedthat the SLM was able to display only four levels ofphase ~see below! with additional phase noise addedas before. Figure 13 demonstrates the simulation.

Again, these results ~Fig. 13! are similar to thoseproduced for pure-phase noise, except that the peakfor the 85° object does not fall as far. At the highestnoise level, the signals from the 5° and the 10° objectsfall below that of the 85° object. This would meanthat the correlator, although able to separate the 0°object from any of the others, would not, by use oftheir cross-correlation values, be able to discriminateamong the 5°, the 10°, or the 85° objects. This out-come was due to the presence of noise spikes in thecorrelation plane that become higher in the case ofthe 85° image than either the noise or the signals inthe other correlation planes.

Experimental results are presented in Fig. 14.The functional behavior of the curve is seen to beconsistent with predictions from the simulation withthe reduction in the CPH for the autocorrelation func-tion to approximately 60% of its original value.Compared with the case for phase noise only, a muchlarger effect is seen because the starting height of thecurve is dropped owing to the additional phase quan-tization, whereas values at higher noise levels seemto be affected to a lesser degree. Once again, betterperformance is found from the experiment thanmight be predicted, with the correlation peak at alltimes clearly distinguishable from the background.

The effects of phase noise with the addition of a

Fig. 12. Experimental dependence of the CPH on the SLM phasenoise.

Fig. 13. Calculated dependence of the CPH on the SLM phasenoise with phase quantization added.


constant intensity noise in the input image with anormalized standard deviation of s 5 0.03 was thenconsidered. Results of the simulation were verysimilar to those found with pure-phase noise, withthe effect of the intensity noise being to reduce theoverall CPH across the phase noise range. As can beseen from the experimental results of Fig. 15, theautocorrelation function falls to approximately 40%of its starting value at the most extreme level ofphase noise, compared with the case of phase noisealone, which produces a reduction to approximately55% of the autocorrelation CPH ~Fig. 9!.

4. QuantizationIn the attempt to increase correlator speed, binaryphase-modulating SLM’s have gained some accep-tance, and we decided to examine the effects on cor-relator performance of differing levels of phasequantization. Beginning with a standard 8-bit im-age of 256 gray levels, we found that the number ofavailable gray levels was reduced for the phase imageand for simulations made of the comparative corre-

lator performance. Figure 16 shows the correlationresults when phase quantization was applied to theSLM in the absence of any other effects.

From the simulations it was found that going fromno phase quantization ~32 bits of phase modulationcorresponding to 232 levels of phase! to a representa-tion of the FT with just four phase levels caused onlya slight reduction in the CPH. The signals for the0°, 5°, 10°, and 85° objects fell to 89%, 89%, 87%, and93%, respectively, of their initial values. Hence theability of the PCC to discriminate among all threeobjects remained roughly constant to this level ofquantization. In going to a binary phase-only filter~BPOF! representation, however, there were furtherdramatic falls in the peak heights for the 0°, 5°, and10° objects of 41%, 51%, and 55%, respectively. Thepeak height for the 85° object remained unchanged inheight but jumped to a new location, suggesting thatthe correlation plane consists mainly of noise spikes.A second effect seen is a relatively large variation inthe CPH as the object is translated in the input im-age. Both these effects arise because the BPOF con-tains representations of both the original object and asecond version rotated by 180°.9 Both these storedobjects have the same amplitude, but their phasesare opposite ~2py2 and 1py2, respectively!. Forsome positions of the input object, the cross correla-tion from the stored, rotated object cancels some ofthe main correlation peak, reducing its height.

Experimentally, the results shown in Fig. 17 wereobtained. For the autocorrelation function it can beseen that an approximate decrease of 75% in the CPHis found when moving from 256 gray levels to the caseof a BPOF. This result is worse than the simulationpredicts when considering phase quantization in iso-lation from other noise and distortions, but one mustrecall that other sources of SLM noise are alwayspresent within this experiment.

The phase-quantization experiments were re-peated in the presence of fixed levels of phase noise.The results, in terms of the percent changes in thePCH’s, were almost identical to those produced by

Fig. 14. Experimental dependence of the CPH on the SLM phasenoise with phase quantization added.

Fig. 15. Experimental dependence of the CPH on the SLM phasenoise with intensity noise in the input image added.

Fig. 16. Calculated dependence of the CPH on the SLM phasequantization.


quantization alone. The most significant effect wasa small decrease in the initial value of the CPH forthe autocorrelation function.

4. Conclusions

For noise or distortion in the input image the CPH ismost sensitive to scale and rotation variance ~as maybe expected! and intensity noise. These effects se-verely degraded the peak in the correlation planeeven when present in only small amounts. Gener-ally, simulation predicted the correlator to be moretolerant than it was found to be experimentally, par-ticularly with respect to object rotation.

Translation of the object in the image plane showeda weak linear dependence on position during opera-tion of the PCC. This effect has been accounted forby the nonuniformity of the SLM phase response.

In the case of errors in the correlator filter plane,the most striking impact on correlator performancecomes from misalignment of the phase image recon-structed from optical memory and the phase image asdisplayed on the SLM. From simulation and exper-iment it is concluded that a tolerance of 620 mmshould apply to maintain a reasonable level of corre-lation output. This has clear implications for theoptomechanical design of the working correlator.

Virtually no noise was observed in the correlationplane when pixel amplitude noise on the SLM wasconsidered, even when noise levels became excessive.The intensities of the correlation peaks fall in a linearfashion as the standard deviation of the Gaussiannoise increases. No changes in the discrimination ofthe correlation process are observed; hence the abilityof the correlator to distinguish between the referenceobject and rotated versions of the object is unim-paired. This is an encouraging result, as the noiselevels used in the simulation were higher than thoseexpected in real devices. A repeat of the pixelamplitude-noise experiments in the presence of afixed level of pixel phase noise yielded identical re-sults. It is not anticipated that SLM pixel ampli-tude noise will pose a problem for the correlator.

Pixel phase noise was investigated by simulationand experiment in which phase noise was added ar-tificially to test correlator tolerance. Phase noisewas seen to have two main effects on the correlationprocess: first reduction in the PCH’s and second re-distribution of the light from these peaks into noisebackground in the correlation plane. As noise levelsincrease, the correlation peaks subside into an in-creasing noise floor. Eventually a point is reachedat which the highest peak in the correlation plane isa noise spike. The result was that relatively lowcorrelation peaks from objects quite dissimilar fromthe reference object quickly reached this noise floor,after which no further reduction occurred.

The effects of varying the phase noise were alsoinvestigated in the presence of fixed levels of pixelamplitude noise, phase quantization, and input-intensity noise. In these cases, the effects of phasenoise were found to be nearly identical in form tothose experienced from phase noise on its own, indi-cating little or no coupling between these effects.

The worst noise level used was s 5 1.57 rad, whichcan reasonably be regarded as excessive, since therange of phase values in the FT was only 2p–p rad.In this case, with the 0° object as the reference, the 0°object could always be discriminated from the otherthree objects. However, when other fixed distor-tions were also present, cross correlation with theother objects could produce ambiguous results.

Phase-quantization modeling and experimentsdemonstrated that virtually no degradation in corre-lation performance was observed even if only fourlevels of phase were used to represent the FT. Com-pared with a continuous phase representation, a dropof approximately 10% was observed in the CPH’s forthe four-level case. With only two levels of phase,corresponding to a BPOF, there was a drop in thepeak heights of ;50%, and variation in the CPH asthe object was moved around in the input imageplane is produced. The results for varying the levelsof phase quantization in the presence of fixed levels ofphase noise were virtually identical to the case inwhich only quantization was included. There wasno apparent interaction between the distortions. Itwas concluded that only a limited set of phase valuesneeds to be displayed on the SLM for high-qualitycorrelations to be obtained.

In light of these simulations and experiments andgiven the levels of noise known to be present in typ-ical SLM’s, it is apparent that, although mechanicaltolerances can be maintained, hybrid PCC’s willmake excellent high-speed correlation systems.Current performance is limited by the speed of pro-cessing the data from the correlation plane and thespeed and modulation characteristics of currentlyavailable SLM’s. As this technology advances, it isto be anticipated that yet higher performance can beobtained.

This study was funded by the European Commis-sion under the Brite–EuRam research program.The authors gratefully acknowledge valuable discus-

Fig. 17. Experimental dependence of the CPH on the SLM phasequantization.


sions with M. Duelli, now at the Electro-Optics Re-search Institute, and Neil Collings of the Universityof Neuchatel. Thanks are due to C. Buckberry of theApplied Optics Group, Rover, UK, who supplied testcomponents.

References1. R. C. D. Young, C. R. Chatwin, and B. F. Scott, “High-speed

hybrid optical digital correlator system,” Opt. Eng. 32, 2608–2615 ~1993!.

2. M. Duelli, A. R. Pourzand, N. Collings, and R. Dandliker, “Purephase correlator with photorefractive filter memory,” Opt. Lett.22, 87–89 ~1997!.

3. J. H. Sharp, D. M. Budgett, P. C. Tang, and C. R. Chatwin, “Anautomated recording system for page oriented volume holo-graphic memories,” Rev. Sci. Instrum. 66, 1–4 ~1995!.

4. J. H. Sharp, D. M. Budgett, C. R. Chatwin, and B. F. Scott,“High-speed, acousto-optically addressed optical memory,”Appl. Opt. 35, 2399–2402 ~1996!.

5. D. M. Budgett, P. E. Tang, J. H. Sharp, C. R. Chatwin, R. C. D.Young, R. K. Wang, and B. F. Scott, “Parallel pixel processingusing programmable gate arrays,” Electron. Lett. 32, 1557–1559 ~1996!.

6. A. R. Pourzand, M. Duelli, and N. Collings, “Frequency planefilter performance assessment II,” BRITE-EURAM project RY1,Tech. Rep. T222, Doc. ref. RY1yTRyNCHyNC&AR&MDP961205~European Commission, Brussels, Belgium, 1996!, pp. 1–6.

7. A. R. Pourzand and N. Collings, “Detailed experiments on phasemodulating SLM characteristics,” BRITE-EURAM Project RY1,Tech. Rep. T213-1, Doc. ref. RY1yTRyNCHyNC&ARP950523~European Commission, Brussels, Belgium, 1996!, pp. 1–14.

8. R. D. Juday, “Correlation with a spatial light modulator havingphase and amplitude cross coupling,” Appl. Opt. 28, 4865–4869~1989!.

9. T. G. Slack, “Simulation of SLM degradation,” BRITE-EURAM Project RY1, Tech. Rep. T341, Doc. ref. RY1yTRyBAEyTS951020 ~European Commission, Brussels, Belgium,1995!, pp. 1–60.


Documents

Compact Phase-Conjugating Correlator: Simulation and Experimental Analysis