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 × 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.
© 1972 Optical Society of America
Original Manuscript: July 8, 1971
Published: January 1, 1972
D. P. Jablonowski, R. A. Heinz, and J. O. Artman, "Matrix Multiplication by Optical Methods: Experimental Verification," Appl. Opt. 11, 174-178 (1972)