Interference filters as nonlinear decision-making elementsfor three-spot pattern recognition andassociative memories

L. Wang, V. Esch, R. Feinleib, L. Zhang, R. Jin, H. M. Chou, Robert W. Sprague, H. Angus Macleod, G.

Khitrova, Hyatt M. Gibbs, Kelvin Wagner, and Demetri Psaltis

Simple patterns consisting of three spots (V and r) have been recognized by dividing, shifting, and recombin-ing beams onto bistable ZnS interference filters. This experiment demonstrates AND-gate operation,cascading, and a moderate amount of parallelism, but a laser power of several watts was required and theresponse times were several milliseconds. An associative memory for fingerprint identification has been

constructed using a VanderLugt correlator and an interference filter as a reflective thresholding device.

I. Introduction

The two all-optical systems described here demon-strate the use of nonlinear optical devices to makedecisions. The devices are demonstrated in two dif-ferent types of system. In the three-spot recognitionsystem multiple nonlinear elements are necessary for apattern recognition. Conventional optical compo-nents are employed to manipulate the orientation ofthe processing beams. In the associative memory sys-tem, conventional optical techniques play the key pro-cessing role through matched filtering of a partial in-put. The nonlinear optical decision-making elementutilizes the output of the matched filter, the cross-correlation beams, to decide closest match. The corre-sponding hologram is then read out with a counterpro-pagating beam.

II. Three-Spot Pattern Recognition

A. Goal and Motivation

The goal of the experiment was to identify the loca-tions of simple patterns consisting of three beams(spots), for example, the Vand F defined in Fig. 1, in aninput array. In this case a 2 X 9 beam array was used,

Demetri Psaltis is with California Institute of Technology, Pasa-dena, California 91125; the other authors are with University ofArizona, Optical Sciences Center, Tucson, Arizona 85721.

Received 28 January 1988.0003-6935/88/091715-06$02.00/0.© 1988 Optical Society of America.

with several randomly selected beams blocked. Sucha three-spot pattern could be recognized using a singleinterference filter as a three-input AND gate, but heretwo successive two-input AND-gate operations are per-formed to emphasize the capability of cascading thenonlinear interference filters.1 '2

One-bit addition by the technique of symbolic sub-stitution34 has been demonstrated previously usinginterference filters, showing that very simple patternscan be useful in digital optical computing.5 Thepresent experiment shows more parallelism and thepotential for nonlinear decision-making in optical pat-tern recognition. Furthermore it suggests that thebest use of nonlinear decision-making may not be fornumerical computing, already done so well by elec-tronics. Rather the best use may be to combine moretraditional optical techniques of image processing, forexample, real-time correlations, with a limited amountof nonlinear decision-making. Only if several correla-tion peaks or other events occur sufficiently simulta-neously will the system activate an appropriate re-sponse. The present experiment is admittedly slowand power hungry, but it illustrates the ability to rec-ognize the simultaneous occurrence of three brightspots with all-optical decision-making.

B. Experimental Apparatus

The apparatus is diagrammed in Fig. 1. A CoherentInnova-20 cw argon laser operating at 514 nm was thelight source. The beam was modulated by a rotatinghalfwave plate and polarization beam splitter, with amaximum transmission of 76% and minimum of 3%.Two binary phase gratings, that produce two and nineapproximately equal beams, respectively, were orient-

1 May 1988 / Vol. 27, No. 9 / APPLIED OPTICS 1715

lensSstem lens lens

X/2 /2 ZnS IF2 film

L 2 : , lens systemselfoc lens array ZnS IF

Il(PBS -.2PBS 62 3 path r [ ~~~shifter] (

Ar+ X/2 PG input PBS51454 Q 2x9 pattern film

Fig. 1. Experimental arrangement for digital pattern recognition.

ed orthogonally and used in tandem to divide the 2.3-W input beam into 2 X 9 beams. Patterns were thenencoded into the beam array by blocking selectedbeams. The power in each beam was 58 mW within10%, after reducing the two central order beams by-30%.

ZnS interference filters grown in the Thin FilmCoating Laboratory at the University of Arizona wereused as nonlinear decision-making devices. The peaklinear transmissions were 54% and 40% and the fullwidths were 17 and 13 A, respectively. With the ap-propriate scaling of the input intensities they requiretwo or more inputs to switch to the high transmissionstate, therefore these nonlinear devices can be used asbistable AND gates. The devices have millisecond re-covery times; they operate in the visible, facilitatingalignment; and they are relatively easy to grow orinexpensive to buy. These characteristics make themattractive for demonstrating optical computing con-cepts. However, their lack of uniformity and long-term stability make it necessary to search for goodregions repeatedly. The minimum switch-up powerswere 9 and 16 mW, respectively, in a 100-,um diam spot.In multiple-beam experiments the focusing was oftenimperfect, so that typical switch-up powers were 20-40mW on the filter and the nonlinear transmission wastypically 10-25%. However, the contrast was 3.5(ratio between the on and off state transmission), per-mitting fan-out and cascading. Other system losseslimited the number of AND-gate operations per watt to5 or 10, thereby limiting the parallelism achievable.The filters were grown for near-perpendicular opera-tion at 514.5 nm minimizing the complications of par-allel operation on a tilted device.

Patterns were tested by sequentially identifyingportions of the pattern. This operation was per-formed in conjunction with the shifters. The array ofbeams was first split into two arrays. One of the arrayswas then shifted and recombined with the unshiftedarray on the interference filter. In this way a portionof the pattern was tested. For example, a diagonalshift was needed to identify the left portion of a V.Either a Mach-Zehnder interferometer or triangular-interferometer setup could be used as a shifter.

Each lens system in Fig. 1 focuses each of the inputbeams so that the parallel logic operations could beperformed. The spots on the filters were -75 Atm indiameter and 1 mm apart. On IF1 the shifted inputpattern and original pattern were superimposed by the

Fig. 2. Recognition of V. Input pattern is in the upper left. Shift-ed pattern is in the upper right. The result is in the lower left,showing the occurrence of the right side of a V in only one location.

Fig. 3. Recognition of F. Input pattern is the upper two rows.The output of the two successive AND-gate operations used to lookfor s is shown underneath, clearly indicating the presence of

three rs.

shifter and focused by the lens system. On F2 thepattern, approximately shifted to search for the thirdspot, was focused on the reimaged output of IF1. Thelens systems consisted of two lenses, LI and L2, and aSelfoc lens array. The combination of L and theSelfoc lens array was used to provide enough intensityfor AND-gate operation in IFI. Lens L2 acted as arelay lens to pass signals to the next stage IF2. Tominimize aberrations in the system, the lens system inpath 2 was symmetrical to path 1, except that no logicoperation was needed in this path for recognizing thethird spot.

C. Experimental Results

The first step in recognizing a V is shown in Fig. 2.The upper left shows the input pattern, encoded in a 2X 4 format. The unshifted pattern and the patternshifted diagonally down and to the left are superim-posed in the upper right. The output of the AND-gateoperation, shown below the input, gives a bright spot atthe bottom of the V. Of course, this only shows thatthe right part of the V is present. A second ANDoperation, with the pattern shifted diagonally down tothe right, completes the V recognition.

Recognition of three s in a 2 X 9 input pattern isshown in Fig. 3. Clearly any three-spot pattern orsimultaneous occurrences could be used to trigger anoutput response from this all-optical coincidence cir-cuit.

1716 APPLIED OPTICS / Vol. 27, No. 9 / 1 May 1988

siter

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6, \'r,

Ill. Associative Memory

A. Motivation and Concept

The V and F experiments illustrate AND-gate opera-tion, cascading, and a moderate amount of parallelism.However they also illustrate the difficulties of dividinga beam into many beams so that each decision-makingpixel receives the same amount of power in approxi-mately the same cross-sectional area. These geomet-rical optics difficulties and the high power require-ments of large arrays of nonlinear decision-makingpixels are formidable hurdles to massively parallelnonlinear optical computing systems. This suggeststhe utilization of more conventional techniques of im-age processing such as correlation with a limitedamount of nonlinear decision-making.

Recent work has dealt with associative memories 6 7

based on various thresholding and feedback schemes,and several optical implementations have been dem-onstrated 8-1 1 (a good general reference for this work isthe 1 Dec. 1987 issue of Applied Optics on NeuralNetworks.) The optical associative memory discussedhere, similar to that presented by Soffer et al., 12 de-cides which stored object most closely matches a par-tial-object input. The associative memory employstwo elements. The first element, a VanderLugt corre-lator, gives an analog degree-of-match value, and thesecond, an optically bistable interference filter, gives abinary thresholding response.

The idealized system works by writing Fouriertransform phase holograms, sequentially multiplexedin reference beam angle, of the different objects. Thetest object is then correlated with the stored objectsgiving angularly separated cross-correlation beams.Each beam is focused onto an optically bistable inter-ference filter where the decision of closest match ismade at the central peak positions.

The interference filter was used in conjunction witha holding beam in this experiment. Power is supplied,in this case exactly counterpropagating with each cor-relation beam, to bias the device very close to theswitching threshold. Only the minimum switchingpower is then necessary to push the device into thetransmissive mode. This reduces the required corre-lation power, and thus the power through the holo-gram. The counterpropagating bias beam also facili-tates the recall of stored objects.

One of the beams, corresponding to the most closelymatched stored object, is sufficiently intense to pro-vide the minimum switching power, allowing the hold-ing beam to collinearly counterpropagate to the holo-gram. Because it is a plane wave at the properincident angle to the hologram it reads out the appro-priate object from the hologram, and the object ispropagated back through the optical system. Also,because the hologram is thick, only this one object isBragg matched; no other subjects are read out. This isthe autoassociative mode of operation, where a partialobject input recalls a reconstruction of the same object.

If the holding beam is propagated to another holo-gram or transparency, a heteroassociative recall can

II

: X/25xobj. f=200r

-it I t-N 1

25pmpinhole

Aulo-Associalive

Partial input /

Recalled oject ,!

J,

f to

tnm

object

Ar' 5t45A

-X/2 )

| DGhologrX/2

\C DG hologram

7X

He/ero-Associa/ivelecalled object DCG 2 0

/\DCG 1Partial inpt

' - 7nZ Fobj. t-obj\iris

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Fig. 4. Experimental arrangement for associative memory.

a

F

Fig. 5. Object fingerprints: (a) F2, (b) F3.

also be performed. In this case any output can beassociated with a matched partial input.

B. Experimental Apparatus

The experimental setup is shown in Fig. 4. In therecording stage, a collimated beam (object beam) illu-minates a transmissive object, a black-ink fingerprinton a slide. The object beam is transformed by a lensonto the Fourier plane where a holographic grating isformed by interfering with a collimated referencebeam in dichromated gelatin (DCG). Two differentobjects, labeled F2 and F3 [Figs. 5(a) and (b)], wereused in the experiment. F2 was interfered with areference beam angle of 470 at the Fourier plane, andF3 was interfered with a reference beam angle of 580.

1 May 1988 / Vol. 27, No. 9 / APPLIED OPTICS 1717

sI l; I I

BS BS

Fig. 6. Photograph of the Fourier transform plane for the objectfingerprints: (a) Fourier transform plane for F2, (b) Fourier trans-

form plane for fingerprint F3.

A considerable effort was made to optimize the DCGhologram.13 The system required optimal discrimina-tion to permit a minimal partial-object input. Theconstraint of necessary switching power for the opti-cally bistable interference filter dictated some mini-mum autocorrelation efficiency. These requirementsled to a trade-off between system efficiency and dis-crimination. The object fingerprints had a fairly lowmodulation depth, and thus only 20% of the power wasin the first order of the diffracted information ring ofthe Fourier transform [Figs. 6(a) and (b)]. In addi-tion, the Fourier transform information had a largedynamic range-from 1:15 to 1:500 compared to thezero order. It was important to determine the appro-priate reference beam intensity to give optimal gratingvisibility for the best efficiency while maintaining suf-ficient discrimination. It was also critical to ensurethat the zero order saturated the DCG, so that theholographic fringes were suppressed. This eliminatedthe contribution to cross correlation that was due tothe zero order. Even when the zero order saturates theDCG, some unwanted modulation occurs in the wingsof the feature. Large diffraction from the zero orderwould destroy the discrimination because all objectshave similar zero orders. It was found that an object-to-reference ratio of 20:1 in the Fourier transformplane (using the peak of the zero order as the objectintensity) and _190-mJ/cm 2 exposure gave 4% auto-correlation efficiency; this maximized the efficiency-discrimination trade-off in this experiment.

bFig. 7. Partially obstructed objects: (a) F2, (b) F3.

C. Results

When operating the system one of the objects waspartially obstructed and illuminated [Figs. 7(a) and(b)], causing autocorrelation beams to be diffractedfrom the hologram at the two reference angles. Theautocorrelation peaks can be seen for F2 and F3 inFigs. 8(a) and (b), respectively, for the unobstructedand partial cases. For the partial input case the dis-crimination ratios (autocorrelation intensity vs cross-correlation intensity, in the correlation plane) of thecorrelation peaks were 50:1 with F2 as test object and10:1 with F3. The reduced discrimination for partialF3 input was due to its smaller modulation depthwhich resulted in a larger zero-order content.

The autocorrelation peak for the partial-object in-put was of sufficient intensity (-3 mW in a 100-,um-diam spot) to switch the optically bistable interferencefilter into the transmissive mode (Fig. 9). The switch-ing of the optically bistable interference filter into thetransmissive state allowed the counterpropagatingholding beam to read out the hologram. The autoas-sociatively reconstructed image due to a single read-out beam [Fig. 10(a)] had a contrast ratio of 2:1 (theratio of the switched holding beam transmission to thepassive optically bistable interference filter transmis-sion of the beam, or equivalently, the switching con-trast of the optically bistable interference filter). Theheteroassociative reconstruction yielded similar re-sults, as seen in Fig. 10(b). Because the diffractionefficiency of the hologram was only 4% at least 75 mWof object input beam power was required, causing dy-namic thermal damage in the DCG. The relatively

1718 APPLIED OPTICS / Vol. 27, No. 9 / 1 May 1988

a

bFig. 8. Cross-correlation beams for partial and whole input objects.(a) Upper, partial F2 input; lower, whole F2 input. (b) Upper,

partial F3 input; lower, whole F3 input.

Fig. 9. Optically bistable interference filter response: Upper,switched on by the correlation input (vertically offset for clarity);lower, switched off. (Trace describes input holding beam intensity

-x vs transmitted holding beam intensity y).

poor quality of the reconstructed objects was due tothis thermal damage in the DCG.

Decision-making was demonstrated on only onecross-correlation beam at a time, having determinedthat sufficient discrimination was present to precludeswitching of both beams simultaneously. However, iftwo devices had been installed each would have pro-duced an off-state recall (from the off-state lineartransmission of the holding beam through the interfer-ence filter), further degrading the on-state recall dis-cernibility.

In a previous experiment one object was stored, theletters WX, a partial input was recognized, and asso-ciative recall was executed (Fig. 11). In this case dis-

bFig. 10. Recalled object F2. (a) Autoassociatively recalled: left,switched off; right, switched on. (b) Heteroassociatively recalled:

left, switched off; right, switched on.

Fig. 11. Recognition of partial input for stored WX. Top, partialinput; bottom left, recall switched off; bottom right, recall switched

on.

crimination was not necessary (only one object wasstored) so that increased cross-correlation efficiencycould be obtained through the use of the zero-order.High quality recall was facilitated because thermaldamage was not an issue.

IV. Discussion

The two systems described used nonlinear devices toprovide decision-making for optical processing. Al-though the spot-recognition system was more deci-sion-element intensive, both systems made obviousthe shortcomings of the interference filter devices (e.g.,power requirements, uniformity). Although a sub-stantial speed advantage can be gained by the use ofGaAs etalon devices, they would certainly not alleviatethe high power requirements of these systems. The

1 May 1988 / Vol. 27, No. 9 / APPLIED OPTICS 1719

speed advantage of the GaAs devices, however, may bethe decisive factor in certain applications.

In associative memory the DCG holographic Van-derLugt filter limited the performance of the system.Although the object employed was responsible for cer-tain aspects of the experimental difficulty, even inideal object conditions the diffraction efficiencyachievable will be a limiting factor. This is aggravatedas the number of stored objects is increased.14 Photo-refractive materials are a possibility to increase thenumber of stored objects due to large material thick-ness, but typically the diffraction efficiencies are evenmore limited than with DCG holograms. The powerthroughput requirements dictated by subsequent non-linear devices can also introduce serious complicationsdue to the storage and erasure dynamics of photore-fractive holograms. These dynamics can also intro-duce new flexibility to the holographic element.

V. Conclusion

Optical nonlinear devices were successfully em-ployed as decision-making elements in two all-opticalsystems. However, the limiting aspects of the nonlin-ear devices and the holographic element were felt evenin these comparatively simple systems.

Support from AFOSR, ARO, NSF, RADC/DARPA,SDIO, and the Optical Circuitry Cooperative is grate-fully acknowledged. Special thanks to J. McCann forthe phase gratings.

References

1. B. S. Wherrett, D. Hutchings, and D. Russell, "Optically Bi-

stable Interference Filters: Optimization Considerations," J.Opt. Soc. Am. B 3, 351 (1986).

2. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod,and F. Van Milligen, "Microsecond Room-Temperature OpticalBistability and Crosstalk Studies in ZnS and ZnSe InterferenceFilters with Visible Light and Milliwatt Powers," Appl. Phys.Lett. 45, 1031 (1984).

3. A. Huang, "Parallel Algorithms for Optical Digital Computers,"in Proceedings, IEEE Tenth International Optical ComputingConference (1983), p. 13.

4. K.-H. Brenner, A. Huang, and N. Streibl, "Digital Optical Com-puting with Symbolic Substitutions," Appl. Opt. 25, 3054(1986).

5. L. Wang et al., "Symbolic Substitution Using ZnS InterferenceFilters," Proc. Soc. Photo-Opt. Instrum. Eng. 752, 14 (1987).

6. J. J. Hopfield, "Neural Networks and Physical Systems withEmergent Collective Computational Abilities," Proc. Natl.Acad. Sci. U.S.A. 79, 2554 (1982).

7. T. Kohonen, Self-Organization and Associative Memory(Springer-Verlag, New York, 1984).

8. D. Psaltis and N. Farhat, "Optical Information ProcessingBased on an Associative-Memory Model of Neural Nets withThresholding and Feedback," Opt. Lett. 10, 98 (1985).

9. Y. S. Abu-Mostafa and D. Psaltis, "Optical Neural Computers,"Sci. Am. 256(3), 88 (1987).

10. E. G. Paek and D. Psaltis, "Optical Associative Memory UsingFourier Transform Holograms," Opt. Eng. 26, 428 (1987).

11. D. Anderson and M. C. Erie, "Resonator Memories and OpticalNovelty Filters," Opt. Eng. 26, 434 (1987).

12. Y. Owechko, G. J. Dunning, E. Marom, and B. H. Soffer, "Holo-graphic Associative Memory with Nonlinearities in the Correla-tion Domain," Appl. Opt. 26, 1900 (1987).

13. T. G. Georgekutty and H.-K. Liu, "Simplified DichromatedGelatin Hologram Recording Process," Appl. Opt. 26, 372(1987).

14. J. Hong and D. Psaltis, "Storage Capacity of Holographic Asso-ciative Memories," Opt. Lett. 11, 812 (1986).

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1720 APPLIED OPTICS / Vol. 27, No. 9 / 1 May 1988