Microprocessor-based fiber-optic iterative optical processor

Acoustooptic linear heterodyned complex-valued matrix-vector processor

A new analog (linear) optical vector-inner-product and matrix-vector processor architecture is described. It employs linear input laser-diode arrays and a multichannel acoustooptic cell. Attention is given to the selection of the operating modes for all devices, error correction, the ability of the system to operate on complex-valued data, and its stability with respect to temperature, data history, and component variations. Laboratory data are provided verifying the potential of the system architecture to achieve 9-10-bit accuracy and complex-valued multiplication.

Acoustooptical matrix-vector product processor: implementation issues

An acoustooptic technique was used to design and construct a prototype of a processor capable of multiplying a 128 x 128 complex-element matrix by a 128 complex-element vector. The device was specified to execute 10(5) matrix-vector products per second with 8-bit resolution. The performance of each component of the prototype was evaluated, as was the impact of component performance on system performance.

Matrix preconditioning: a robust operation for optical linear algebra processors

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

Optical system for real-time multiplication of the multiple matrix with a 2-D light source array

An optical system for real-time multiplication of the multiple matrix is proposed. A 2-D light source array enables this system to perform a triple matrix multiplication without the unidirectional diffuser that was essential in the former system we proposed. The performance of this system is discussed based on a simplified model to show the guidelines for designing the system. The preliminary experiments of multiplying three 3 x 3 matrices are successfully carried out with a mean error of 2.0%. A method to multiply the multiple matrix with binary elements using our system is also shown.

Optical matrix-matrix multiplication method demonstrated by the use of a multifocus hololens

A method of optical matrix-matrix multiplication is presented. The feasibility of the method is also experimentally demonstrated by the use of a dichromated-gelatin multifocus holographic lens (hololens). With the specific values of matrices chosen, the average percentage error between the theoretical and experimental data of the elements of the output matrix of the multiplication of some specific pairs of 3 x 3 matrices is 0.4%, which corresponds to an 8-bit accuracy.

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.

Feedback methods for optical systolic and engagement matrix processors

The matching of the feedback circuitry to the optical systolic or engagement processor permits simple pipelining of stationary iterative algorithms as well as on-the-fly scale adjustment similar in effect to floating-point calculation.

Rapid unbiased bipolar incoherent calculator cube

Presented in this paper is one of several possible electrooptical engagement array architectures for performing matrix-matrix multiplication using incoherent light. Essential components of this new signal-processing device include two dynamic light valves operating in a reflection mode, a 2-D photodetector array, and a single polarizing beam splitter.

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.