The utilization of coherent optical correlation techniques in the performance of matrix multiplication by-optical analog methods has been investigated mathematically. Although the basic concepts have been known for some time, we have not been able to find explicit analyses in the existing literature. Since many correlations other than those corresponding to the desired matrix multiplication terms exist, methods of isolating the desired from the undesired terms are presented. Various spatial configurations for both the input and output arrays are discussed. For the special cases of 2 × 2 matrices the analyses are presented in greater detail. Using simple circ function distributions, the effects of finite-sized array elements and detector apertures are investigated.
R. A. Heinz, J. O. Artman, and S. H. Lee, "Matrix Multiplication by Optical Methods," Appl. Opt. 9, 2161-2168 (1970)