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Advantages of optics over electronics in signal processing derive from the fact that many operations, such as addition, multiplication, correlation, and filtering, can be performed in parallel on two-dimensional data samples. However, this advantage is attainable only if information can be input/output or processed at sufficient speed and space bandwidth. Although acousto-optic devices have been used to provide impressive throughput, they are inherently one-dimensional and do not possess any information-storage capability beyond the acoustic transit time (≤50 μs). Hence, a high-resolution high-speed two-dimensional transducer (or spatial light modulator, SLM) with real-time update capability is required. Unfortunately, none of the existing SLMs perform well enough to fully utilize the inherent speed and parallelism of the optics. This dissertation addresses the development of an SLM that has the potential to meet most of the performance requirements of advanced optical information-processing applications--the photoemitter membrane light modulator (PEMLM). At the heart of the PEMLM is a microchannel plate (MCP) with a flexible membrane covering each pore. In operation, the write image incident on a photocathode, which is placed on the input side of the MCP, creates an electron image. This electron image is then amplified by the MCP and deposited onto the membrane array. The membrane elements, which are electrically and mechanically isolated from each other, are deflected by the induced electrostatic forces. These deflections represent the stored information. Readout of stored information is accomplished by sensing the phase changes induced in an optical-readout beam reflected from the deformed membrane array. A sandwich-type electrostatic grid structure positioned between the MCP and membrane greatly enhances the versatility of the PEMLM by facilitating the use of secondary emission for active electron removal and various intrinsic operations. The theoretical analysis and experimental characterizations performed on prototype devices indicates that PEMLM is capable of higher throughput than most other SLMs, with expected resolutions approaching 50 lp/mm over 10⁷ resolution elements and framing rates greater than 1 KHz. MCP gains provides quantum-limited sensitivity. The PEMLM also promises information-storage times of minutes to hours, greater than 2π phase modulation, good image quality, and an option for serial addressing. In addition, the PEMLM can intrinsically perform operations such as intensity thresholding, contrast modification, edge enhancement, binary logic, synchronous detection, and image addition/subtraction.

This dissertation considers a method for processing two-dimensional (2-D) signals (e.g. imagery) by transformation to a coordinate space where the 2-D operation separates into orthogonal 1-D operations. After processing, the 2-D output is reconstructed by a second coordinate transformation. This approach is based on the Radon transform, which maps a two-dimensional Cartesian representation of a signal into a series of one-dimensional signals by line-integral projection. The mathematical principles of this transformation are well-known as the basis for medical computed tomography. This approach can process signals more rapidly than conventional digital processing and more flexibly and precisely than optical techniques. A new formulation of the Radon transform is introduced that employs a new transformation--the central-slice transform--to symmetrize the operations between the Cartesian and Radon representations of the signal and to aid in analyzing operations that may be susceptible to solution in this manner. It is well-known that 2-D Fourier transforms and convolutions can be performed by 1-D operations after Radon transformation, as proven by the central-slice and filter theorems. Demonstrations of these operations via Radon transforms are described. An optical system has been constructed to derive the line-integral projections of 2-D transmissive or reflective input data. Fourier transforms of the projections are derived by a surface-acoustic-wave chirp Fourier transformer, and filtering is performed in a surface-acoustic-wave convolver. Reconstruction of the processed 2-D signal is performed optically. The system can process 2-D imagery at approximately 5 frames/second, though rates to 30 frames/second are achievable if a faster image rotator is added. Other signal processing operations in Radon space are demonstrated, including Labeyrie stellar speckle interferometry, the Hartley transform, and the joint coordinate-frequency representations such as the Wigner distribution function. Other operations worthy of further study include derivation of the 2-D cepstrum, and several spectrum estimation algorithms.

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