Statistical moments of the transmittance of phase-only spatial light modulators

Robert W. Cohn; R. J. Nonnenkamp

doi:10.1117/12.138892

13 January 1993 Statistical moments of the transmittance of phase-only spatial light modulators

Robert W. Cohn, R. J. Nonnenkamp

Proceedings Volume 1751, Miniature and Micro-Optics: Fabrication and System Applications II; (1993) https://doi.org/10.1117/12.138892
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

The monochromatic diffraction patterns from phase-only spatial light modulators, such as deformable mirror- and liquid crystal-SLMs, are routinely modeled using the fast Fourier transform. Random errors in phase have typically been evaluated by Monte Carlo analysis. This can require the averaging of numerous runs to find the expected value of intensity and its standard deviation. However, the pixel structure of current modulators, which allows each pixel to apply arbitrary piston or tilt modulation, greatly simplifies the form of the expectations. Specifically, we assume that the parameters of piston, and likewise tilt, describing the entire SLM transmittance are Gaussian, independent, and identically distributed random variables. Expressions for the expected value of the Fourier plane intensity spectrum and its standard deviation, and for propagation of the intensity pattern to any arbitrary observation plane using the angular spectrum of waves formulation are presented. Each expression reduces to a small number of Fourier transform operations that may be efficiently calculated by the FFT.

Citation Download Citation

Robert W. Cohn and R. J. Nonnenkamp "Statistical moments of the transmittance of phase-only spatial light modulators", Proc. SPIE 1751, Miniature and Micro-Optics: Fabrication and System Applications II, (13 January 1993); https://doi.org/10.1117/12.138892

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