This special issue of Optical Engineering contains 17 papers discussing various aspects of optical computing research. Papers are grouped in five functional areas: optical interconnects, materials and devices for optical computing, numerical optical computing, digital optical computing, and symbolic optical computing.

A simple technique for generating large (100 x 100+) arrays of uniform intensity spots of good contrast is proposed. One application of such spot arrays is as power supplies for optical logic devices in two-dimensional optical computing/switching architectures. This spot generation technique utilizes binary phase gratings both to produce small spot arrays (-20 x 20) and to multiply image them. Since the gratings need produce only small numbers of spots, the design computation and fabrication constraints are simplified. An experimental demonstration of this technique for an 81 x 81 array is presented along with a discussion of potential limitations.

Two classes of 0(N log(N)) network architectures known as one-dimensional trimmed inverse augmented data manipulator networks and two-dimensional trimmed inverse augmented data manipulator networks are described. These network architectures, which are derived from augmented data manipulator networks, may find potential applications as optical interconnection networks for multiprocessor computer systems. Comparisons between the network types are made based on hardware complexity and blocking probability. It is shown that pairs of extra stages (added to the input end and the output end of the networks) and the extra connectivity provided by two-dimensional optical interconnections can improve blocking probability if an increase in hardware cost is permissible. A potential optical implementation of the network, which uses computer-generated binary phase gratings, is described.

This paper discusses design of large-scale (1000x 1000) optical crossbar switching networks for use in parallel processing supercom-puters. Alternative design sketches for an optical crossbar switching network are presented using free-space optical transmission with either a beam spreading/masking model or a beam steering model for internodal communications. The performances of alternative multiple access channel communications protocol-unslotted and slotted ALOHA and carrier sense multiple access (CSMA)-are compared with the performance of the classic arbitrated bus crossbar of conventional electronic parallel computing. These comparisons indicate an almost inverse relationship between ease of implementation and speed of operation. Practical issues of optical system design are addressed, and an optically addressed, composite spatial light modulator design is presented for fabrication to arbitrarily large scale. The wide range of switch architecture, communications protocol, optical systems design, device fabrication, and system performance problems presented by these design sketches poses a serious challenge to practical exploitation of highly parallel optical interconnects in advanced computer designs.

This paper describes various nonlinear optical phenomena in photorefractive media and selected applications in optical computing. These phenomena include optical phase conjugation, two- and four-wave mixing, and real-time holography. The applications include image amplification and subtraction, logic and matrix operations, and optical interconnection.

The dependence of differential gain in GaAs bistable etalons on the incident angle of the switching beam is studied theoretically for the case of pulsed, single-wavelength operation. Both dispersive and absorptive aspects of the etalon are included. Simulations predict that differential-gain characteristics can be significantly improved over the normal incidence case by utilizing angular separation of the pump and switching beams. The limitations of the plane-wave approximation and the potential effect of beam walk-off are discussed.

Efficient light coupling into and out of nonlinear etalons is achieved by using direct fiber-etalon-fiber interfaces. This technique can be used with etalons operating in both transmission and reflection. The improved uniformity of the etalons having mirrors grown by molecular beam epitaxy allows this technique to be extended to interface fiber arrays with many optical logic gates. Some simple analysis and possible applications of optical fiber interconnects in a digital optical system are presented.

The accuracy of matrix computations performed on analog optical associative processors is limited by noise and spatial wavefront errors. Earlier studies show that the rate of convergence and accuracy of analog optical matrix data processing can be improved by lowering the condition number of the data matrix. In this paper, we describe a new preprocessing technique, the split-step polynomial preconditioning algorithm, that can reduce the condition number of a matrix efficiently. With a few additional steps, this algorithm can be used to calculate the inverse or to estimate the condition number of a matrix. A realization of this preprocessing algorithm on optical associative processors is considered, and its performance and complexity are analyzed. The results of numerical experiments on case studies with ill-conditioned matrices show that this new preprocessing algorithm is a practicable tool for improving the perfor-mance of analog optical processors. Preliminary analyses of the new preconditioning algorithm demonstrate its robustness with regard to the spatial errors and random noise present in most analog optical computing systems.

The modified-signed-digit (MSD) number system offers parallel addition and subtraction of any two numbers, with carry propagation constrained only between two adjacent digits. Based on MSD addition, parallel algorithms for multiplication and division are developed in this paper. The optical implementations of these MSD arithmetic algorithms are developed on the basis of symbolic substitution (SS). The space-invariant nature of SS matches well with the parallel nature of the MSD arithmetic algorithms presented. The potential advantages of using these algorithms for optical computing include the significant increase in speed, full exploitation of parallelism, and higher system throughput compared with existing electronic arithmetic processors. The performance of the proposed optical arithmetic system is analyzed and compared with that of state-of-the-art electronic counterparts.

The performances of optoelectronic (laser-diode-based) and electronic residue position-coded look-up tables are compared in terms of speed and power consumption. Experimental results for the optical and electronic look-up tables are also presented.

The binary symmetric logic function (BSLF), because of its invariance under the permutation of its input variables, is an important class of Boolean logic functions. The diversified BSLF applications include the synthesis of a full adder and subtractor, a text comparator, a median filter, a parity checker, and various threshold elements. The classic BSLF realization uses an array of triangularly interconnected slow-speed electric contact switches. Optical switches, because of their fast switching capability, are excellent candidates for an optical BSLF (OBSLF) implementation. In this paper, various OBSLF architectures are described, together with their applications to optical digital and symbolic computing, data communication, image processing, and neural networks.

Symbolic substitution is a method of performing parallel optical logic by recognition and substitution of structural elements. With spatial filtering it is possible to perform logic operations without an active logic gate. This paper describes how symbolic substitution can be implemented optically by use of spatial filtering. Earlier implementations used an additive logic, where shifted versions of the input pattern were added and then thresholded. Our new method is a multiplicative method that sequentially tests the pattern elements.

This paper introduces programmable arrays of optically inter-connected electronic processors and compares them with conventional symbolic substitution (SS) systems. The comparison is made on the basis of computational efficiency, speed, size, energy utilization, programmability, and fault tolerance. The small grain size and space-invariant connections of SS lead to poor computational efficiency, difficult programming, and difficult incorporation of fault tolerance. Reliance on optical gates as its fundamental building elements is shown to give poor energy utilization. Programmable optoelectronic multiprocessor (POEM) systems, on the other hand, provide the architectural flexibility for good computational efficiency, use an energy-efficient combination of technologies, and support traditional programming methodologies and fault tolerance. Although the inherent clock speed of POEM systems is slower than that of SS systems, for most problems they will provide greater computational throughput. This comparison does not take into account the recent addition of crossover interconnect and space-variant masks to the SS architecture.

This paper presents the architecture of an optical artificial intelligence system that uses mathematical resolution to reason from facts to conclusions. Data storage, logical operations, and interconnection are all accomplished using medium-scale optical components. The system performs parallel inference and search to achieve high performance. Alternative architectures are considered, and simulation results are presented that demonstrate the effect of variations in system architecture.

Many problems in artificial intelligence are intractable owing to the exponential growth of the solution space with problem size. Often these problems can benefit from heuristic search or forward-checking techniques, which attempt to prune the search space down to a manageable size before or during the actual search procedure. Many interesting search problems can be formulated as consistent labeling problems in which the initial problem information is given in the form of a set of binary constraints, for which Boolean matrices are a natural data representation. In this paper optical implementations of Boolean matrix operations are proposed for manipulating the constraint matrices to perform forward checking and thereby increase the search efficiency. The high degree of parallelism afforded by using optical techniques and the relatively low accuracy requirements of Boolean matrix operations suggest that optical techniques are well matched to this problem.

We propose an optical multifunctional processor that can perform logic, numeric, pattern recognition, morphological, and inference operations. The ability to perform such diverse functions on one optical processor architecture is unique. The processor uses the technique of symbolic substitution and is based on an optical correlator architecture. Several inputs can be operated on in parallel, and different functions can be performed at one time, making it a multiple-instruction multiple-data processor.

We examine the key issues in designing an optical expert system architecture. Our conclusions, however, are extendable to architectures for supporting traditional symbolic processing. To determine the basic operations necessary for constructing an expert system, we examine the underlying symbolic processing languages and their associated computational models. We show that traditional symbolic processing in optics would require efficient means of representing and manipulating complex structured data. This requirement necessitates a location-based addressable memory in optics. Based on the analyses of the computational models, we conclude that the architecture most feasible for optical implementation is that for a combinator graph reduction computational model. We briefly outline a proposed fine-grained optical architecture for this computational model.

A compact optical architecture capable of implementing a number of adaptive neural net models is described. Compact architectures do not involve traditional optical imaging systems and are potentially rugged, easily constructed, and scalable. The critical devices of the generic architecture include 1-D electro-optic modulators and detectors to implement the neural processing elements, along with the Pockels readout optical modulator (PROM) to encode the analog weights. The architectural advancements include an input/output compatible method of handing both positive and negative values for the elements of the neuron activation vectors and the synaptic weight matrices during learning and recall. These hybrid architectures are capable of implementing linear and nonlinear associators with adaptive learning algorithms.

We have constructed a small-scale laboratory demonstration of a laser-diode-based radar array for simultaneous coherent ranging and velocimetry of multiple target points. Signals are produced by an array of laser/detector packages in a self-detection geometry with common imaging optics for both the source and backscattered light. The radar has been used with a microcomputer to find the orientation and rotation speed of a spinning disk at an arbitrary position in the field of view.

Nova is the Lawrence Livermore National Laboratory's 10-beam Nd:glass laser, which is used for inertial confinement fusion research. It operates in the high power, high energy regime, where several interesting nonlinear optical phenomena can occur. These phenomena and their interactions limit the power and energy that can presently be delivered to targets for laser-target interaction experiments. Understanding and controlling these processes will allow us to increase the energy available for such experiments.

This work was supported by NASA grants NAG8-086 and NAG8-639 and NASA contract NAS8-37576. The grant numbers were erroneously reported in the February 1989 issue.

Even as I write this editorial, the Ides of March approach rapidly. This is unnerving and depressing because it signals that, in the United States, April Fool's Day is only a month away. I realize that some of you will quickly seize the opportunity to expose my error and point out that April 1st is only two weeks after March 15th-not a month. While I cannot disagree that April 1st occurs only two weeks after March 15th, I must nevertheless claim that April Fool's Day really falls on April 15,* the day we are called upon to account for our income-producing activities of the previous year. Yes, that is the day we are required by the IRS (Incentive Reduction System) to pay for our financial indiscretions of accum ulating wealth the old-fashioned way-by earning it. At least we can take comfort in knowing that the process of paying our taxes was made much simpler and more equitable when the 1986 Tax Reform Act l" went into effect.

Electro-optic and Photorefractive Materials is based on lectures and contributed papers presented at the Eleventh Course of the International School of Materials Science and Technology that was held in Erice, Sicily, Italy, in July of 1986. The book contains 30 papers grouped into six parts within 385 pages. Unfortunately, the book does not contain a subject index, which makes it somewhat difficult for the reader to find specific items.