Optical Bilinear Transformations: General Properties

Abstract

Because of the quadratic relation between the optical field and intensity, an inherent non-linearity exists in almost all optical systems. A class of non-linear transformations which we call bilinear (quadratic with memory) is defined; its properties and relevance to optical imaging systems are discussed. For space-invariant systems, a generalized transfer function is defined which characterizes the bilinear system completely. We also examine the approximate linearization of bilinear systems for low-contrast images, and the propagation of noise through such systems. Special emphasis is given to the partially coherent system which is but a special case of this general bilinear system.