Eigenvector determination by iterative optical methods

Direct and implicit optical matrix-vector algorithms

New direct and implicit algorithms for optical matrix-vector and systolic array processors are considered. Direct rather than indirect algorithms to solve linear systems and implicit rather than explicit solutions to solve second-order partial differential equations are discussed. In many cases, such approaches more properly utilize the advantageous features of optical systolic array processors. The matrix-decomposition operation (rather than solution of the simplified matrix-vector equation that results) is recognized as the computationally burdensome aspect of such problems that should be computed on an optical system. The Householder QR matrix-decomposition algorithm is considered as a specific example of a direct solution. Extensions to eigenvalue computation and formation of matrices of special structure are also noted.

Hybrid optical-digital signal processing applied to an optimal nonlinear phase estimator

An electrooptical realization of an optimal phase estimator for phase modulated communication signals is described in this work. The realization uses an electrooptical processor to perform a 1-D convolution in a 2-D space and a computer to complete the calculations. The processor is a realization of the time domain recursive nonlinear filter. This paper describes the nonlinear filter theory, the electrooptical realization,and the performance of the processor.

Acoustooptic transducers in iterative optical vector-matrix processors

The use of acoustooptic transducers that are commercially available in iterative optical vector-matrix processors is considered. Deconvolvers using space and time integration are described. The use of multichannel systems to solve large vector-matrix equations in which the matrices are banded is also addressed.

Microprocessor-based fiber-optic iterative optical processor

The design and fabrication of an iterative optical vector-matrix processor are described. Microprocessor feedback is used to produce an iterative processor capable of solving simultaneous linear equations. It also facilitates scaling and biasing of the data and the handling of bipolar and complex-valued data as well as correction for selected system error sources. Fiber-optic interconnections are used to improve the system's alignment and to reduce its size, weight, and errors. The design, fabrication, and performance of the system are analyzed.