General treatment of spatial light modulator dead-zone effects on optical correlation. I. Computer simulations

In Part I we present an approximate mathematical analysis and exact computer simulations for optical correlation in correlators having pixellated spatial light modulators with transmissive (or reflective) dead zones in both the input and filter planes. We show that the correlation amplitude consists of four terms: a true correlation plus three different types of noise terms originating from the transmissive dead zones in both spatial light modulators; we describe the role that each of these terms plays in the correlation process. We calculate peak intensity, signal-to-noise ratio, and energy throughput efficiency as a function of dead-zone area in both spatial light modulators using either phase-only or matched filters. We utilize a dc block in the filter plane for noise reduction. We also use a filter reference image smaller than the input spatial light modulator size to reduce false correlation peaks. We discuss the effects of fabricating a filter from a filter reference image whose center has been offset rom optic axis. In Part II [Appl. Opt. 32,6536 (1993)] we present a general analytical treatment of our model that can justify the simulation results of Part I. This analysis is applicable even to mixed cases of opaque and transmissive dead zones.