5 February 1990 Matrix-Tensor Multiplication Using Phase-Coded Optical Correlation
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Abstract
We present a parallel optical method of multiplying a two-dimensional input array by an arbitrary fourth-rank tensor to produce a 2-D output array. This process is equivalent to a crossbar interconnection of the input and output arrays. The algorithm works by arranging the interconnection tensor into a 2-D phase-coded image. The input is pre-coded by transmission through a conjugate phase mask, and then optically correlated with the connection image. The correlation plane contains the output array values in a noisy background. We show how the output signal to noise ratio (SNR) can be traded in for connection image size and complexity, and give theoretical calculations of average output SNR, along with computer simulations supporting these predictions. We describe a proposed reconfigurable optical interconnection system using this matrix-tensor multiplier implemented with four-wave mixing in photorefractive materials.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Joseph E. Ford, Joseph E. Ford, Groff Bittner, Groff Bittner, Sing H. Lee, Sing H. Lee, Shaya Fainman, Shaya Fainman, } "Matrix-Tensor Multiplication Using Phase-Coded Optical Correlation", Proc. SPIE 1151, Optical Information Processing Systems and Architectures, (5 February 1990); doi: 10.1117/12.962221; https://doi.org/10.1117/12.962221
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