This dissertation discusses a certain aspect of opitcal data processing--namely the concept of performing a convolution operation of an incoherent optical light field with a specified processing kernel. The theory that shows that an incoherent imaging system performs a convolution by the very process of imaging is reviewed. The constraints on the form of processing kernel are discussed. The most severe constraint is the restriction of positive real kernels. Methods for extending the versatility of incoherent systems to include bipolar and even complex kernels are described. The most promising methods are those that encode the bipolar or complex information on either a spatial or temporal carrier frequency. The dissertation includes a presentation of two systems that are applicable to the demodulation of the signals generated by a temporal carrier approach. One of the systems introduces the concept of bipolar detection, which may have a strong influence on the performance of incoherent optical processing systems in the future. The other system is a synergism of optical and digital components that produces a hybrid system capable of high performance. The main motivation of this investigation was an outgrowth of our interest in developing a computed tomography system based on film recording of the projection data. The theory of computed tomography is reviewed in this text and an optical processing system based in part on the hybrid approach to the filtering operation is presented. This system represents a very concrete example of the capabilities of an incoherent optical processor.

This dissertation covers theoretical and experimental work on applying optical processing techniques ot the operation of a Boltzmann machine. A Boltzmann machine is a processor that solves a problem by iteratively optimizing an estimate of the solution. The optimization is done by finding a minimum of an energy surface over the solution space. The energy function is designed to consider not only data but also a priori information about the problem to assist the optimization. The dissertation first establishes a generic line-of-approach for designing an algorithmic optical computer that might successfully operate using currently realizable analog optical systems for highly-parallel operations. Simulated annealing, the algorithm of the Boltzmann machine, is then shown to be adaptable to this line-of-approach and is chosen as the algorithm to demonstrate these concepts throughout the dissertation. The algorithm is analyzed and optical systems are outlined that will perform the appropriate tasks within the algorithm. From this analysis and design, realizations of the optically-assisted Boltzmann machine are described and it is shown that the optical systems can be used in these algorithmic computations to produce solutions as precise as the single-pass operations of the analog optical systems. Further considerations are discussed for increasing the usefulness of the Boltzmann machine with respect to operating on larger data sets while maintaining the full degrees of parallelism and to increasing the speed by reducing the number of electronical-optical transducers and by utilizing more of the available parallelism. It is demonstgrated how, with a little digital support, the analog optical systems can be used to produce solutions with digital precision but without compromising the speed of the optical computations. Finally there is a short discussion as to how the Boltzmann machine may be modelled as a neuromorphic system for added insight into the computational functioning of the machine.

The subject of this dissertation is an electro-optical processing (EOP) concept which, in its basic configuration, computes a discrete linear transform such as Fourier, Laplace, Hilbert, etc., as well as convolutions and correlations. It accepts input signals through an incoherent light source, performs high speed analog multiplications via a two-dimensional array of apertures in a chrome mask on the surface of a charge-coupled device (CCD), shifts and integrates intermediate results within the CCD, and presents the transformed signal as a data stream from the output shift register of the CCD. The EOP concept is described in detail where both serial and parallel configurations are developed. It is seen to be an efficient computer of matrix-vector products, matrix-matrix products, and multichannel correlations. The inclusion of feedback and a changeable CCD mask yields an architecture for higher order matrix operations such as matrix inversion, solution of simultaneous equations, etc. A functional model of an EOP matrix-vector multiplier is presented which describes the accumulated effect of errors in system elements from the LED through the CCD. Also described is removal of error introduced by biasing required of input and mask modulation functions in order that they represent bipolar quantities. An EOP spectrum analyzer based upon direct implementation of the discrete Fourier transform (DFT) is described and use of a Kaiser-Bessel window function applied to the CCD mask is described as a solution to the "spectral leakage" problem caused by sharp discontinuities at each end of a normal window of sampled data. Finally, application of a parallel EOP configuration to the synthetic aperture radar (SAR) problem is offered. An architecture utilizing separate in-phase and quadrature EOP channels is described. The system shows potential for providing at least modest resolution SAR imagery with an economy of size, weight, and power consumption.

QC 351 A7 no. 82 / The object of this study was to determine the utility of polarization -discrimination techniques for active optical processing. A baseline of static performance must be established before these techniques can be applied to real -time processing. The theoretical foundation for an alternative to the Vander Lugt technique of re- cording complex spatial filters had been laid by Marathay in 1969. On the basis of his theory, a photosensitive Vectograph TM technique was investigated, in which the image is produced as a polarization pattern rather than as the silver grain image of conventional photography. (1) Photographic characteristics of sensitized Vectographs were determined. The resolution ( >700 1p /mm) and the gray scale achieved indicate that the Vectograph material can also be used for recording Vander Lugt filters. (2) Theoretical analysis showed that the technique can be used to image and process objects in the same system without removal of the filter. It can also be used to generate halfwave plates for the pupil functions described by Toraldo di Francia for superresolution. (3) The Vectograph can perform addition and subtraction of functions recorded on it; it also is suitable for recording real -bipolar filter functions. (4) Variable- contrast images can be recorded. A variable-contrast Vectograph tar- get (VCVT), developed for optical testing, can not only vary the contrast of the recorded image but also reverse its contrast. In a similar fashion, a spatially variable birefringent filter (SVBF) was developed that permits spatial control of the wave- length of the transmitted light. Static and dynamic electro-optical properties of liquid crystal mixtures of cholesteryl-chloride, cholesteryl-nonanoate, and cholesteryl-oleyl-carbonate were studied to determine their feasibility as the modulator in a proposed photoconductor-liquid crystal sandwich, which would be used as a reversible recording medium. (1) Previous research had indicated that cholesteric liquid crystals are circularly dichroic in a narrow wavelength band. The present work showed that light transmitted within this band is actually elliptically polarized. The degree of ellipticity depends on the relationship between the probing wavelength and the wavelength at which the sample becomes circularly dichroic. Outside this narrow wavelength band, the crystals exhibited pure optical activity. (2) The dynamic electro-optical properties of the cholesteric trimixture were measured. An alternating electric field applied parallel to the helical axis of the liquid crystals resulted in a hysteresis in the electro-optical rotatory power of the crystals. The magnitude of the hysteresis would limit cycling of these liquid crystals to a maximum frequency of ^0.10 Hz. (3) A bias voltage applied to the crystals in an attempt to improve the frequency response resulted in a field- induced memory. When the bias voltage was maintained, the optical rotatory power failed to stabilize. Prolonged exposure to the bias voltage severely diminished the electro-optical rotatory power of the crystals.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Description based on print version record. Includes bibliographies.

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