Binary phase-only filters: implications of bandwidth and uniqueness on performance

Abstract

The use of binary phase-only filter (BPOF) concepts in conjunction with recently developed spatial light modulator technology offers the potential for real-time image processing.1 Thus BPOFs have been suggested as a replacement for matched filters in pattern recognition problems.2 However, there are several design issues to be explored in using the BPOF. First, the standard BPOF design approach does not explicitly define the BPOF bandwidth. We define a figure of merit for BPOFs which references the signal-to-noise performance of matched filters and investigates the relationship of BPOF resolution and noise performance as a function of filter bandwidth. Second, since the standard BPOF is equivalent to a phase-only filter (POF) matched to only the even part of the reference image, its response is not unique. We discuss the consequences of image positivity on uniqueness and BPOF filter design. We develop a relationship between a two-channel configuration (to match both the even and odd parts of the reference) and the POF. We show that the two-channel configuration effectively reduces the uniqueness problem to that for POFs.