Optical information processing continues to prosper despite the competition from purely digital computer techniques. This conference attests to this fact but so does the current literature and particularly the recent books, including the two volumes in the series Topics in Applied Physics; Volume 23, edited by Casasent." (1978) and Volume 48, edited by Lee² (1981). These two volumes contain a very good summary by many of the leading contributors to the field (Abramson,." Balasubramanian,' Casasent,¹92 Caulfield,' Considine,' Gonsalves,' Goodman,² Knight,² Lee,² Leith,' Rhodes,² Sawchuk,² Thompson."). The even more recent book edited by Stark3 (1982) has contributions by nineteen authors. Textbooks have not been ignored either, with Gaskill's4 book in 1978 on Linear Systems and just a few weeks ago a new and much revised edition of Yu's book on Optical Information Processing5 (1983). The content of these volumes, particularly the first three, gives some overview of current trends in this field; each of the books deals of course with basic concepts (Lee,² Casasent and Caulfield,' Stark³). Specific topics include chapters on biomedical applications (Caulfield1); radar (Leith,." King3); crystallography (Thompson ¹); nondestructive testing (Abramson ¹); photogrammetry (Balasubramanian ¹); particle measurement (Anderson3); photographic image measurement (Shannon and Cheatham3). Techniques and methodology are also dealt with in some detail in each of these treatises, including complex spatial filtering (Almeida and Indebetouw3); hybrid systems (Leger and Lee,³ Casasent²); nonlinear processing (Sawchuk and Strand3); interface devices (Knight²); space-variant methods (Goodman,² Rhodes³); incoherent techniques (Bartelt et al³; Rhodes and Sawchuk²).

The performance of achromatic optical processors is reviewed and described. Both in-line and off-axis configurations are compared. Matched filtering experiments using a white light source of low spatial coherence are reported. Plots of correlation intensities are presented for the spatially coherent and non-coherent cases.

A polychromatic correlation detection technique by complex spatial filtering is presented. This technique utilizes a diffraction grating and three co-lineared (red, green and blue) coherent sources. The techniuue of complex spatial filter synthesis for the polychromatic correlation detection is demonstrated. This technique offers true color correlation detection which is very suitable for color signal recognition and identification. The correlation diffraction efficiency with this technique is generally higher than that of the wavelength-multiplexed technique. Several interesting experimental demonstrations if this color signal correlation detection scheme are provided. Finally we note that this color signal detection is a simple and versatile processing technique which has broad range of applications of complex color signal detection, recognition and identification.

An optical system is designed to perform two-dimensional space-variant processing for the case of a separable point spread function. The design makes use of the wavelength dimension of light by color-encoding the input to provide the necessary third dimension required in performing the operation. An analysis of the system provides theoretical results which are compared with the results obtained in an experiment using real, positive functions for the input and point spread function. Finally, the inherent limitations of the system are discussed, noting both the advantages and disadvantages of the technique.

Diffraction Gratings permit many and diverse optical processing techniques to be carried out with light of greatly reduced coherence, either spatial or temporal. Several such techniques are described, including phase-amplitude imaging, fringe projection and tomography.

A first order analytical model which describes the imaging performance of the total internal reflection (TIR) linear array spatial light modulator is presented. Two modulator configurations are identified, each with a distinct imaging response. The modulator crystal orientation defines which image response model applies. Several optical readout techniques for converting the optical phase modulation into an intensity modulation are described.

This electrically alterable magneto-optic device can be used as a two-dimensional spatial light modulator (SLM) in an optical image processor or a display system. A thin magnetic garnet film is epitaxially desposited on a transparent nonmagnetic garnet substrate, in the manner of magnetic bubble memory films. Semiconductor photolithographic techniques are used to etch the film into a two-dimensional array of mesas and to deposit X-Y drive lines for matrix-addressed current switching of the mesa magnetization. Electromagnetic switching provides higher speed switching than previously reported thermal switching methods. The axis of polarization of polarized light transmitted through the film is rotated by the Faraday effect in opposite directions where opposite magnetic states have been written, and a polarization analyzer converts this effect into image brightness modulation. The resulting high speed random access light modulator is applicable to all three planes of the classic coherent three-plane correlator. Although the basic effect is binary, there are at least four possible configurations which achieve gray scale rendition. This reusable transparency has non-volatile image storage and a relatively modest projected cost expected to be comparable to that of integrated circuits of the same size. Evaluation of prototype units has shown the material to be well behaved, exhibiting excellent uniformity and readily engineered into devices suitable for numerous applications.

The Deformable Mirror Device (DMD) is an X-Y array of deformable mirror elements addressed by an underlying array of MOS transistors. A comparison of the modeled and experimentally measured optical processing parameters of a 128 x 128 DMD are presented.

The structure, operation and performance of the silicon-based liquid crystal light valves: the photoactivated, CCD-addressed and visible-to-IR converter are described. The performance limitations of the readout structure, in particular, those affecting resolution, sensitivity, contrast ratio and speed, are discussed.

The physical principles of operation of the Variable Grating Mode Liquid Crystal Device are described. The VGM device is capable of performing a two-dimensional intensity-to-spatial frequency conversion, which in turn allows the implementation of a wide range of nonlinear optical processing and computing functions. The device utilizes certain nematic liquid crystal mixtures that are observed to form variable frequency diffraction gratings under the influence of an applied bias voltage. Both fundamental and technological limitations to device performance characteristics are discussed.

The fundamental operating characteristics and materials limitations of the optically addressed microchannel spatial light modulator (MSLM) are discussed. The role of secondary electron emission in the operation of the device is stressed and some of the write, cycling and readout modes and their limitations are described. In addition, the limitations of the inherent space-domain image-processing operations of the device are discussed.

Optical image processing using four-wave mixing is described. The relevant properties of photorefractive materials for these applications are discussed.

The charge transport model of photorefractivity is used to evaluate four figures of merit that can be used to characterize the performance of photorefractive materials. The figures of merit are the steady-state index change, the response time, the energy per area to write a grating with one percent diffraction efficiency, and the index change per absorbed energy per unit volume (photorefractive sensitivity). These indices are evaluated as a function of grating period and applied external electric field for Bi₁₂Si0₂₀, a fast material with a relatively small electro-optic coefficient and BaTiO₃, a slower material with a much larger electro-optic coefficient. Methods for optimizing the materials are discussed.

Computer programs were written to simulate the performance of an adaptive optical filtering system that is implemented in the frequency domain. Since this system uses Bragg cells as both the delay line and the accumulator, the primary interest is on the effects of finite integration times within the accumulator. By tapering the contributions to the accumulator so that the values that leave the accumulator do not cause as much misadjustment to the weights, the performance of the system is significantly improved while maintaining the ability to respond to changing signal statistics. Several examples of the performance of the system in the presence of multiple jammers as a function of the number of taps, the length of the accumulator, the degree of accumulator tapering and the feedback gain are given.

Two-Dimensional (2-D) inputs can be reduced to a set of 1-D functions by projection coding. Two-dimensional (2-D) operations can be implemented by the appropriate processing of these 1-D distributions. This paper discusses two possible projection coding methods and describes the operations and hardware necessary to measure the 1-D functions, process them, and reconstruct the desired 2-D distribution.

Several sophisticated imaging methods are based on measurements that lead to accessing a finite volume of the 3-D Fourier domain of an interrogated object and subsequent retrieval of 3-D image detail by 3-D Fourier inversion. Examples are found in inverse scattering, integral holography, x-ray and radio emission imaging, crystalography, and electron microscopy.This paper examines a unified approach to all these methods, namely through reduction of dimensionality based on the pprojection-slice property of the multidimensional Fourier transform. We describe two hybrid (opto-digital) computing schemes, one employing coherent light and the other incoherent light, that can be used with these techniques to reconstruct and display true 3-D image detail tomographically. Reduction of dimensionality is shown to provide flexibility in hybrid (opto-electronic) computing by permitting trade-off between the degree of parallel and serial processing employed. It leads to new architectures capable of enhanced throughput and dynamic range and extends the domain of optical computing beyond one and two dimensional signals.

The structure and operation of the two silicon liquid crystal light valves - the photoactivated and the charge-coupled device - addressed - are described. Applications of these devices for image processing, and electronic signal processing, including systolic array operation, are given.

The application of a newly developed transmission-mode magneto-optic spatial light modulator to optical image processors is being examined. This high speed, reusable, electrically addressable spatial light modulator can provide a non-volatile random access interface for optical processor input and output. The light modulator employs a magnetic irongarnet thin film on a transparent nonmagnetic substrate. The magnetic film is divided into an array of separate magnetically bistable mesas. Plane polarized light transmitted through the array of mesas and the polarization analyzer is spatially modulated by the Faraday effect. This paper describes the operation of the new magneto-optic spatial light modulator in simple tests in the input plane, transform plane and output plane of optical image processors. Test patterns written into the object input plane produce Fourier transforms having most of their energy. lying near the X and Y axes. Operation of the spatial light modulator in the Fourier plane was demonstrated by reproducing the classic Abbe-Porter mesh component deletion experiment, and by obtaining edge-enhancement images. The spatial light modulator. was also tested as a compact output image scanner in the output plane. Image addressing is particularly straightforward in applications requiring only binary light modulation.

In optical implementation of statistical image recognition, new optical transforms on large images for real-time recognition are of special interest. Several important linear transformations frequently used in statistical pattern recognition have now been optically implemented, including the Karhunen-Loeve transform (KLT), the Fukunaga-Koontz transform (FKT) and the least-squares linear mapping technique (LSLMT).^1-3 The KLT performs principle components analysis on one class of patterns for feature extraction. The FKT performs feature extraction for separating two classes of patterns. The LSLMT separates multiple classes of patterns by maximizing the interclass differences and minimizing the intraclass variations.

In recent years, we and others have developed a type of reflective tomography based on coherent processing of Doppler frequency-shifted echoes from rotating objects. The objects are placed in the Fraunhofer region and irradiated with microwaves as they rotate. The returning signals are sampled and stored in digital form. These are later processed using an optical computer, and highly-resolved, two-dimensional images (tomograms) can be reconstructed. Holographic character is apparent in the processed data. To produce an image, we first make a data film strip and then irradiate it with light from a He-Ne laser in our coherent optical processor. The available resolution predicts images comparable to those produced with digital computation. A coherent optical system is thus able to provide effective and cost-efficient parallel processing in reconstructing coherent Doppler tomograms.

An entirely optical method is proposed for solving many linear equations. A possible implementation of a simultaneous equation solver, (or equivalently an integral equation solver), is discussed. A method of matrix by matrix multiplication using random phase masks is proposed and shown to enable the optical solution of matrix equations, (or equivalently the solution of two dimensional integral equations).

Many of the linear algebra operations and algorithms possible on optical matrix-vector processors are reviewed. Emphasis is given to the use of direct solutions and their realization on systolic optical processors. As an example, implicit and explicit solutions to partial differential equations are considered. The matrix-decomposition required is found to be the major operation recommended for optical realization (since digital systems can easily solve the simplified matrix-vector problem that results). The pipelining and flow of data and operations are noted to be key issues in the realization of any algorithm on an optical systolic array processor. A realization of the direct solution by Householder OR decomposition is provided as a specific case study.

With the development of fast parallel optical matrix-vector multipliers and matrix-matrix multipliers, a need has arisen to reevaluate algorithms designed for electronic digital computers. Two examples are shown here. First, we discuss algorithms for eigenvector/eigenvalue problems using matrix-matrix multiplication. Second, we discuss relaxation and over relaxation methods for feedback in systolic array processors.

A new optical method, based on continuous-time relaxation methods, is presented for implicitly inverting the estimate of the covariance matrix associated with a set of signal waveforms. Complex valued signal information in conveyed by biased temporal -frequency carriers, a resonant electro-optic device serving both to evaluate the covariance matrix and (as a spatial light modulator, or SLM) to input that matrix for inversion.

An electrooptical engagement array architecture for performing matrix-matrix multiplication using incoherent light is presented. Key components of this newly proposed processing device include a single pulsed incoherent light source, two dynamic light valves, and a two-dimensional photodetector array.

Presented in this paper is a discussion on performing LU factorization, solution of simultaneous linear equations, matrix inversion, and QR factorization through repeated use of the basic operation of matrix-matrix multiplication. Electrooptical engagement array processing architectures appear well suited for implementing these higher order matrix algebra operations.

Optical systolic pipeline processors for polynomial evaluation can be built using Horner's rule. With integrated optics techniques, it will be possible to fabricate large order pipelines operating at very high speeds.

This paper discusses a new approach to coherently channelizing input rf signals that is similar to Bragg cell techniques but has the potential for operation at substantially higher bandwidths. The rf information from the environment is modulated on a laser beam. The modulated laser beam is then demultiplexed according to frequency by passing the beam through a dispersive device. The various channels are then each incident on the respective element of a detector array. Splitting a reference beam off from the main beam provides a local oscillator for heterodyne detection at the detector array. The optically encoded rf information is thereby translated back down to baseband or a common if band.