6.1 – Optical Linear Algebra Processors

Abstract : This project considers the use of optical linear algebra processors for various applications in real time signal processing. The main thrusts of this project are: algorithms, architectures and applications for linear algebra optical processors. The work reported upon herein concerns two optical linear algebra processors and initial results obtained on each in the solution of very diverse engineering problems. The first system is a space integrating and frequency multiplexed processor applied to an iterative solution of linear algebraic equations for optimal control and to an explicit solution of the heat diffusion equation. The second system is a time and space integrating multi-channel acousto-optic processor applied to a finite element problem solution. The work reported here involves the first laboratory demonstrations of an optical linear algebra processor in a full engineering problem with new work in algorithms also involved. These include: an iterative algorithm linear algebraic equation solution, a nonlinear matrix solution, a frequency-multiplexed analog solution, high accuracy encoded explicit solution, and the first direct high-accuracy linear algebraic equation solution. New partitioning algorithms as well as parallel linear algebra algorithms are advanced and demonstrated on laboratory optical systems for the first time. These results are all significant original contributions in engineering, theory and the applications of linear algebra processors. They also form the framework for future research consideration.

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