Analyzing the encoding range of amplitude-phase coupled spatial light modulators

Most spatial light modulators (SLMs) 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 SLMs 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 SLMs 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 binary random distribution leads to methods of evaluating and geometrically interpreting the encoding range. Evaluations are presented of achieving fully complex encoding with SLMs that produce less than 2? 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.