Incoherent optical image processing with acousto-optic pupil-plane filtering.

We describe an incoherent image processor that uses orthogonally oriented one-dimensional acoustooptic cells to implement dynamic, arbitrary bipolar point-spread functions (PSF's). Arbitrary PSF's are implemented as a linear superposition in time of separable PSF's. The use of incoherent illumination increases the input field of view over that provided by coherent illumination, and implementation of the PSF by a pupil-plane filter yields a simple, compact single-lens imaging system. The acousto-optic cells offer a faster PSF update rate than that of conventional spatial light modulators, which is a critical issue for the implementation of a bipolar PSF as a subtraction between its positive and rectified negative parts. Initial experimental results are presented that demonstrate the realization of an arbitrary nonseparable PSF, image convolution with a bipolar PSF, two-dimensional image correlation, and an increased processor field of view.

Apodized pixel lenses in compact shadow-casting correlators.

We present a compact two-dimensional shadow-casting correlator that can perform correlation between inputs of size 256 × 256 and a point-spread function of size 32 × 32. A two-dimensional array of mutually incoherent sources is used to encode the point-spread function, and each source is individually steered to improve the light uniformity and the light-utilization efficiency. The geometric optics constraint requires that the shadow region be very close to the input plane. This constraint is removed by the introduction of apodized pixel lenses in the input spatial light modulator. The pixel lenses move the shadow plane to their Fourier plane, and pixel apodization reduces the interchannel cross talk, thereby improving the signal-to-noise ratio. Simulation and experimental results verifying these concepts are presented.

Cross-talk analysis and reduction in fully parallel matrix-matrix multipliers.

Analog optical processors that calculate a product of two matrices in a single clock cycle are analyzed for cross talk. It is determined that the sidelobes from the sinc function corresponding to the individual pixels of the spatial light modulator that encodes the first matrix are the main source of the cross talk. This cross talk can be reduced substantially by the use of an apodizing function for individual pixels of the spatial light modulator. This scheme for cross-talk reduction is verified by computer simulation. Initial experimental results are presented that demonstrate the gray-scale performance of the matrix-matrix multiplier as well as sidelobe suppression with apodization.

Time-integrating correlator based on fiber-optic delay lines.

A time-integrating correlator based on techniques of fiber-optic delay-line signal processing is described. We show that the time-integrating architecture does not suffer from limitations associated with previously demonstrated space-integrating fiber-optic correlators. Experimental results from an eight-channel time-integrating correlator are presented, demonstrating real-time autocorrelation of a 5-MHz square wave. Limitations of the experimental correlator are discussed, and an alternative design is proposed, with a potential time-bandwidth product of the order of 10(8).

Fully parallel analog optical calculation of multiple outer products.

An analog optical processor for evaluating weighted sums of outer products in parallel is described. It uses a linear array of light sources oriented along the diagonal, two-dimensional spatial light modulators to encode input vectors, a two-dimensional detector array to generate the output, and conventional spherical and cylindrical lenses. This system can be used to multiply two matrices as well as to evaluate a weighted rank-1 synthesis of images in a single clock cycle of the processor. Initial experimental results are presented, and factors limiting the performance are described. Implications of this architecture to optical signal- and image-processing systems are discussed.

MOSAIC: a space-multiplexing technique for optical processing of large images.

A technique for Fourier processing of images larger than the space-bandwidth products of conventional or smart spatial light modulators and two-dimensional detector arrays is described. The technique involves a spatial combination of subimages displayed on individual spatial light modulators to form a phase-coherent image, which is subsequently processed with Fourier optical techniques. Because of the technique's similarity with the mosaic technique used in art, the processor used is termed an optical MOSAIC processor. The phase accuracy requirements of this system were studied by computer simulation. It was found that phase errors of less than λ/8 did not degrade the performance of the system and that the system was relatively insensitive to amplitude nonuniformities. Several schemes for implementing the subimage combination are described. Initial experimental results demonstrating the validity of the mosaic concept are also presented.

Performance analysis of optical shadow-casting correlators.

We analyze the performance of two optical shadow-casting image correlators that use two-dimensional source arrays to encode the system point-spread function (PSF). The analysis of a standard shadowcasting correlator suggests that the angular divergence of the source array is a critical parameter in the determination of the maximum space-bandwidth product of the image and of the PSF that can be used with such a system. Further, the energy efficiency of a standard shadow-casting correlator is related inversely to the size of the PSF. We show that the constraints on energy efficiency and on the space-bandwidth product of the PSF can be overcome by beam steering the source elements. A modified shadow-casting correlator is proposed that uses phase-only blazed gratings to beam steer the sources. Experimental results generated by a mechanically beam-steered array are presented.

Optical implementation of numerical inequality detection and its applications to database machines.

Two approaches for numerical-inequality-detection optical circuits are described. These circuits, which work with parallel-access optical memory (disks or holographic), form a critical component of an optical database machine.

Acousto-optic processing with electronic image feedback for morphological filtering.

An optical morphological processor is described and demonstrated in which the structuring element is generated by means of an acousto-optic cell in the Fourier plane of a coherent optical correlator. A magneto-optic spatial light modulator is employed in the input plane. A single PC generates the drive signals for the acousto-optic cell, processes the output image, and controls the input magneto-optic spatial light modulator. Complex morphological operations of opening and closing are experimentally demonstrated by using electronic image feedback. The results of a morphological noise-removal algorithm implemented by using the optical processor are compared with computer simulations, possible sources of discrepancies are proposed, and potential remedies are discussed.

Crossed Bragg cell implementation of a Fourier-plane filter for optical image correlators.

A two-dimensional optical image processor is described and demonstrated in which the point-spread function is generated by crossed acousto-opticells in the Fourier plane of a coherent optical correlator. Coherence effects and generation of nonseparable point-spread functions are considered.

Numerical optical computing in the residue number system with outer-product lookup tables.

An optical outer-product architecture is presented that performs residue arithmetic operations with position-coded lookup tables. The architecture can implement arbitrary integer-valued functions of two independent variables in a single gate delay. The outer-product configuration possesses spatial complexity (a gate count) that grows linearly with the size of the modulus, and therefore with the system's dynamic range, in contrast to traditional residue lookup tables, which have quadratic growth in spatial complexity. The use of linear arrays of sources and modulators leads to power requirements that also grow linearly with the size of the modulus.

Optical computing: introduction by the guest editors to the feature in the 1 May 1988 issue.

The feature in the 1 May 1988 issue of Applied Optics includes a collection of papers originally presented at the 1987 Lake Tahoe Topical Meeting on Optical Computing. These papers emphasize digital optical computing systems, optical interconnects, and devices for optical computing, but analog optical processing is considered as well.

Sorting with optical compare-and-exchange modules.

Sorting is central to the solution of many knowledge-based and switching problems in advanced computation and communication systems. Parallel-pipelined sorting algorithms are appropriate for applications that demand high throughput, low delay, and many data channels. One such algorithm, the bitonic sort, can be implemented with passive perfect shuffle interconnects between active stages of compare-and-exchange (C&E) elements. In this paper we focus on optical hardware to implement the C&E operation and show that, by taking advantage of a distinctive feature of optical logic, namely, bistability, comparison circuits of remarkable simplicity are attainable. We describe implementations of C&E in a variety of optical device technologies capable of performing latching and nonlatching logic. Based on the device characteristics we outline potential application areas for each technology.