Pseudorandom phase-only encoding of real-time spatial light modulators

Applied Optics (Impact Factor: 1.78). 05/1996; 35(14):2488-98. DOI: 10.1364/AO.35.002488
Source: PubMed


We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326°modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.

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    ABSTRACT: Most spatial light modulators (SLM) are limited in that they cannot produce arbitrary complex modulations. Because phase and amplitude are usually coupled, it is difficult to computer design appropriate modulation patterns fast enough for the real-time applications for which SLM's are suited. Dramatic computational speedups can be achieved by using encoding algorithms that directly translate desired complex values into values that the modulator can produce. For coherently illuminated SLM's in a Fourier transform arrangement pseudorandom encoding can be used. Each SLM pixel is programmed in sequence by selecting a single value of pixel modulation from a random distribution having an average that is identical to the desired fully complex modulation. While the method approximates fairly arbitrary complex modulations, there are always some complex values that are outside the encoding range for each SLM coupling characteristic and for each specific pseudorandom algorithm. Using the binomial distribution leads to methods of evaluating and geometrically interpreting the encoding range. Evaluations are presented of achieving fully complex encoding with SLM's that produce less than 2π of phase shift, identifying an infinite set of encoding algorithms that encode the same value, identification of the maximum encoding range, and geometric interpretation of encoding errors.
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