Effects of systematic phase errors on phase-only correlation

The performance of phase-only optical correlators is usually reduced if the filter-plane phase differs from that prescribed for the classical matched filter. Current spatial light modulators, which frequently produce less than 2π phase modulation, and interface circuits, which quantize or incorrectly amplify signals placed on the spatial light modulator, both can produce systematic phase errors. We examine these effects using a model of correlation-peak amplitude as a function of phase error. The correlation peak is reasonably approximated as the product of an average of unity-amplitude error phasors multiplied by the average amplitude across the filter plane. The trends predicted by this new model compare favorably with computer simulations that use gray-scale images.