Abstract

Matrix-vector multiplication is a fundamental operation in linear algebra. A large variety of optical processors for performing matrix multiplication have been proposed and some experimentally demonstrated. We propose the use of a pinhole hologram to perform matrix-vector multiplication. The method is capable of storing and addressing a large number of holograms inside a photorefractive crystal, and achieving better resolution while performing the multiplication. On recording, each matrix (M × N) pattern passes through a pinhole and then stores its hologram in a photorefractive crystal. A phase-conjugate beam is used to read the holograms. Among them the desired one, say matrix A, is selected by opening a corresponding pinhole. An NX1 vector B is illuminated by the selected matrix pattern. The overlap of matrix A and B produces a matrix C. Using a cylindrical lens we can convert the M × N matrix C into a MX1 vector c which is the product of A and B. A 2-D detector array is used to detect the intensity distribution of vector c and to decide its value according to some preset threshold value. This method can be programmed to implement a parallel real-time matrix-vector processor.

© 1991 Optical Society of America