Matrix multiplication has been performed by optical analog methods using the scheme of Heinz et al. The most critical element was Ƒ(a), the spatial filter corresponding to the two-dimensional Fourier transform of a. In the operation c = b × 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 Ƒ(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.
D. P. Jablonowski, R. A. Heinz, and J. O. Artman, "Matrix Multiplication by Optical Methods: Experimental Verification," Appl. Opt. 11, 174-178 (1972)