Computation of Farfield Diffraction Characteristics of Radial and Annular Walsh Filters on the Pupil of Axisymmetric Imaging Systems

Abstract

Pupil plane filtering by Walsh filters is a convenient technique for tailoring the intensity distribution of light near the focal plane of a rotationally symmetric imaging system. Walsh filters, derived from Walsh functions, form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or −1 values of the Walsh functions over prespecified annular regions of the circular filter. Order of these filters is given by the number of zero-crossings, or equivalently phase transitions within the domain over which the set is defined. In general, Walsh filters are binary phase zone plates, each of them demonstrating distinct focusing characteristics. With a backdrop of pupil plane filtering for image enhancement and a brief description of different types of zone plates for manipulation of axial intensity distribution, this chapter puts forward the inherent potential of Walsh filters in this context. The mathematical formulation utilized for computing the transverse and axial intensity distributions in and around the image/focal plane, when radial and annular Walsh filters are placed on the exit pupil of an axisymmetric imaging system, is presented.