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

Effects of dead zones in multiple-quantum-well binary-phase modulators on optical interconnections

We investigate the effects of inactive regions [dead zones (DZ's)] in multiple-quantum-well binary-phase modulators used for free-space dynamic optical interconnection applications. Results, however, have implications for other types of pixelated spatial light modulators (SLM's). To our knowledge, the effects of DZ's in SLM's have not before been thoroughly studied in a context other than optical correlation. We investigate the DZ's (considered to be either opaque or transmissive) as a feature that may be exploited in system design, calculating light efficiency and fidelity as a function of DZ fractional width. It is shown that in particular cases an appropriate choice of DZ width would lead to an optical interconnection with substantially improved cross-talk performance.

Multiresolution correlator analysis and filter design

The concept of multiresolution optical correlators is formally introduced. A mathematical analysis is performed for a generalized multiresolution correlator that emphasizes the roles of both input and filter spatial light modulator resolutions. Conditions are derived for overlapping and nonoverlapping correlation orders. A simulation is performed in which it is shown that the predicted performance of composite binary-phase-only filters designed by the conventional design procedure is different from the actual performance when they are implemented in a real optical correlator. The training of filters on multiresolution approximations of high-resolution discrete Fourier transforms generated by multiresolution wavelet analysis (MWA) techniques is proposed. An analysis is performed that shows that training on MWA approximations results in filters whose performance is the same in a real correlator as that predicted by the design procedure. This analysis is confirmed by simulation. Further simulations show that the performance of reduced-resolution filters designed by MWA techniques is markedly superior to the performance of those designed by conventional means. Finally, an analysis is performed that explains why the ratio of zero- to higher-order correlation peak intensities is much greater for the former than the latter.

Analysis of spatial light modulator contrast ratios and optical correlation

We have performed a general analysis of optical correlators with spatal light modulators (SLM's) whose primary defect is a finite contrast ratio (CR). Our mathematical analysis identifies three noise terms that appear in addition to the correlation term. The filter SLM contains either a phase-only filter (POF) or a binary-phase-only filter (BPOF). Insertion of a dc block at the center of the filter SLM decreases the noise background in the correlator plane; this dc block is larger than that required for the same level of performance in a correlator whose SLM's have transmissive (or reflective) dead zones. With a noise-free input and the dc block, our computer simulations that show the peak intensity falling off as the CR decreases are in quantitative agreement with the correlation term of the mathematical model. For a cluttered, disjoint noise input this agreement is only qualitative, and at low CR's the dc block is definitely required for the BPOF correlator if the secondary peaks in the output are to be brought below the correlation peak.