Optical polynomial processing based on the bilinear transform
Shing-Hong Lin, Thomas F. Krile, John F. Walkup · Annual Meeting Optical Society of America · 1986
With the motivation to extend linear/bilinear operators to a more general class of nonlinear operators via a Volterra series (polynomial) approximation, we look into optical polynomial implementations using a factored representation so that presently known bilinear techniques can be employed. Since there are two inputs and one kernel in the generalized bilinear transform, the two inputs act as polynomial input variables and the elements in the kernel represent coefficients of the quadratic polynomial. Thus higher polynomial processing can be realized by iterating the bilinear transform. A dual-LCLV system is proposed to form such a quadratic polynomial. With electronic or optical feedback, a general optical polynomial processor is achievable. The work has been extended to perform bipolar complex analog and binary digital polynomial operations. The analog operations are performed by using separate parallel channels for real/imaginary and positive/negative numbers and making use of triple matrix-matrix product processing. Systolic and wavefront processors and a triple product processor are used to implement binary digital polynomial processing.