The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-250

“Cellular Hypercube Optical Interconnections for Optoelectronic Smart Pixel Cellular Arrays”

by Charles Benedict Kuznia

May 1994

This dissertation investigates the cellular hypercube interconnection network and its photonic implementation in a smart-pixel cellular array architecture. The smart-pixel cellular array uses electronic technologies for processing and memory functions, and optical and photonic technologies for the interconnection function. The cellular hypercube is a space-invariant extension of the hypercube network used in multiprocessor systems. The space-invariant property allows cellular hypercube realization by a full-aperture imaging system. The cellular hypercube is a multi-hop network that can communicate data between cells of an N x N array in O(logN) hops. This work compares the cellular hypercube with the mesh, hypercube and perfect shuffle in the performance of 'frequently used permutations' (FUPs) on an N x N array. Due to the regularity of the data movements within most algorithms, a family of four permutations labeled FUPs describe the majority of useful permutations. FUPs recur in algorithms such as FFT, histogramming, convolution, matrix operations, and divide-and-conquer routines. The descriptions of FUPs in binary image algebra (BIA) language gives insight to the dependence of permutation performance on the interconnection network topology.

This works describes the use of computer generated gratings (CGGs) as a means of creating optical interconnection patterns. A Fourier imaging system uses a CGG to diffract light from the optical source of each cellular processor into diffraction orders and images these orders onto detector windows of spatially separated cells in the image plane. A spatial phase function represents the CGG surface profile that determines the diffraction pattern. For most diffraction patterns, there is no closed form solution to the CGG phase function that produces it. This work describes iterative numerical techniques for finding CGG phase functions for producing a desired interconnection pattern. We show results for the cellular hypercube pattern and define CGG performance parameters.

The last section of this dissertation describes several optical imaging systems for combining a reflective smart-pixel array, lens and CGG into a single compact structure. In a reflective smart-pixel array all optical sources and detectors are on the same side of the array plane. This work describes an optical system in which the object and image planes are coplanar and the system magnification is positive. This arrangement returns the image point back to the object point source. The CGG diffracts light energy out of the image point and onto detector windows of surrounding cells according to the interconnection pattern.

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