The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. The objective is to demonstrate the operation of an optical processor designed to minimize computation time in performing a practical computing application. This is done by using the large array of processing elements in a Hughes liquid crystal light valve, and relying on the residue arithmetic representation, a holographic optical memory, and position coded optical look-up tables. In the design, all operations are performed in effectively one light valve response time regardless of matrix size. The features of the design allowing fast computation include the residue arithmetic representation, the mapping approach to computation, and the holographic memory. In addition, other features of the work include a practical light valve configuration for efficient polarization control, a model for recording multiple exposures in silver halides with equal reconstruction efficiency, and using light from an optical fiber for a reference beam source in constructing the hologram. The design can be extended to implement larger matrix arrays without increasing computation time
