General treatment of spatial light modulator dead-zone effects on optical correlation. II. Mathematical analysis.

We present a general analytical treatment of optical correlation in correlators that use pixellated spatial light modulators with transmissive (or reflective) dead zones in both the input and filter planes. The active areas of the pixels modulate the light intensity while the dead zones transmit (or reflect) all of the light. Our model can predict the changes in the correlation peak and the signal-to-noise ratio with changes in dead zones, calculated in Part I [Appl. Opt. 32, 6527(1993)] from computer simulations. This model is also a general one: It applies to correlators in which one spatial light modulator contaions only opaque dead zones while the other contains only transmissive dead zones; it also applies to the case in which any one spatial light modulator contains both opaque and transmissive dead zones.