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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.