Optical implementation of content addressable associative memory based on the Hopfield model for neural networks and on the addition of nonlinear iterative feedback to a vector-matrix multiplier is described. Numerical and experimental results presented show that the approach is capable of introducing accuracy and robustness to optical processing while maintaining the traditional advantages of optics, namely, parallelism and massive interconnection capability. Moreover a potentially useful link between neural processing and optics that can be of interest in pattern recognition and machine vision is established.

The remarkable collective computational properties of the Hopfield model for neural networks [Proc. Nat. Acad. Sci. USA 79, 2554(1982] are reviewed. These include recognition from partial input, robustness, and error-correction capability. Features of the model that make its optical implementation attractive are discussed, and specific optical implementation schemes are given.Optical information-processing systems can have high processing power because of the large degree of parallelism as well as the interconnection capability that is achievable. Typically, more than 106 parallel processing channels are available in the optical system, and furthermore each of these channels can be optically interconnected (broadcasted) to 106 other channels. The majority of optical processors are analog systems, designed to perform linear operations. The accuracy of an analog processor is limited by the linear dynamic range of the devices used (detectors, light modulators).In principle, the accuracy and the repertoire of achievable operations can be improved with systems that perform nonlinear operations on binary encoded data using bistable optical devices. Optical bistability is a subject that has received considerable attention recently as a means of achieving efficient high-speed logic, and it has been demonstrated with several nonlinear optical materials and devices. If we are to use such bistable devices to realize powerful, nonlinear optical computers, it is important to find algorithms that are well matched to the characteristics of the optical processor and utilize effectively its parallelism and interconnection capability. In this Letter we examine a method for synthesizing optical processing systems, based on optical associative memory and threshold logic, that appears to meet these requirements well.Associative (or content-addressable) memories are of interest in computer science, and it is theorized that information is stored in the human brain in this manner.Holographic associative memories have been described by Gabor,' who also commented on the similarity of the holographic memory to the way information may be stored in the human brain. More recently, Hopfield 2 introduced an associative-memory model to describe the collective behavior of neural networks. Hopfield's model consists basically of an associative memory similar to the holographic, with the addition of threshold and feedback. The incorporation of nonlinear feedback enhances dramatically the error-correcting capability of the holographic memory. Let where the last term accounts for Tij = 0 and No is the number of l's in vUi(O). We assume that for m # mo the binary words vi (m) are statistically described in the following simple manner:where vim) are independent for all i and m. Then If N is sufficiently larger than M, then with high prob-

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