Abstract

Projection operators form a basic building block for many mathematically optimal detection and estimation structures. For optical signal processing, a projector representation that is compatible with binary spatial light modulators is needed. When separating signals from significant amounts of additive noise, reduced-rank projectors outperform full-rank projectors. Thus, to attain optimal optical signal processing performance, the effects of rank reduction and quantization must be considered jointly. Rank reduction is a matter of deciding which orthogonal projector modes should be retained and which should be discarded. The quantization problem involves distributing the modes retained over a fixed number of binary spatial light modulators. We describe how the statistics of a stationary signal are used to build a projection operator that is matched to that signal. We then define a signal processing performance metric which indicates how well the projector separates that signal from additive noise. Our analysis tracks the effects of rank reduction and quantization, resulting in design equations for low-rank quantized projectors which are optimal under our metric. In effect, these design equations tell how to allocate a fixed amount of expensive hardware for best optical signal processing results.

© 1989 Optical Society of America