<title>Algorithm to choose which pixels to zero out in a zero and phase filter</title>

Abstract

An algorithm to choose which pixels to zero out in an otherwise phase-only filter is presented. This algorithm involves a simple thresholding technique applied to the general spatial filter described in previous work. Having fixed those pixels which are to be set equal to 0 in the filter, one can then view the remaining phases as free parameters and design a good 0 and continuous phase filter by optimizing the filter's signal-to-clutter ratio using the author's techniques. One can the discretize this zero and phase filter into one whose entries are 0 or one of the nth roots of unity. For example, ternary (0, +1, and -1) filter are of this form as are filters whose entries are 0 and the sixteenth roots of unity. Examples of such are given. This paper together with its ancestor provides a completely automatic way to start with a training set of true and false targets of any size and automatically and without human intervention produce optimized filters for use in extant spatial light modulators.