Matrix multiplication by optical methods: experimental verification.

Matrix multiplication has been performed by optical analog methods using the scheme of Heinz et al. The most critical element was F(a), the spatial filter corresponding to the two-dimensional Fourier transform of a. In the operation c = b x a, errors in the c elements were 1-2% when the a elements were all approximately the same. Very large errors occurred when the a elements differed significantly, and these were used directly [instead of the F(a) derived values] in the numerical comparisons. These errors were attributed to the limited linear range of the amplitude transmittance characteristic of the film used. Suggestions for future work are made.

Matrix multiplication by optical methods.

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 x 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.