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

Abstract

Abstract. 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. © 1999Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99) 01702-X]

Improved-fidelity error diffusion through blending with pseudorandom encoding

“…[3][4][5][6][7][8] We also have reported SNR to provide comparisons with the work of other authors. However, since ED does not uniformly distribute noise of the full NRB, we also calculate a reduced-bandwidth SPR.…”

“…This definition of encoding error differs from that in our previous papers. [1][2][3][4][5][6][7][8] In the earlier studies the average error contribution resulting from encoding a single pixel was evaluated rather than the actual contribution. This distinction is important because while several PRE algorithms have been developed for phase-only SLM's, they produce identical average errors and diffraction patterns of essentially identical performance.…”

“…This distinction is important because while several PRE algorithms have been developed for phase-only SLM's, they produce identical average errors and diffraction patterns of essentially identical performance. 7 However, when these various algorithms are blended with ED, (1) the actual error contributions are error diffused and (2) the performance of the diffraction patterns differs depending on which PRE algorithm is used.…”

“…With PRE it is possible to encode only values of magnitude less than or equal to unity. 7 Therefore for PRE alone we normally scale the complex values of the desired function so that ␥ equals unity. PRE also permits encoding for values of ␥ that are less than zero, but this produces increased levels of speckle noise and lower diffraction efficiency.…”

“…[1][2][3][4][5][6][7][8] The focus of the study has been to develop algorithms that can be computed in real or near-real time and that demonstrate good (rather than optimal) optical performance within the available time constraints for practical spatial light modulators (SLM's). These constraints frequently include that the SLM represents only a limited range of complex values (e.g., phase-only, quantized phase-only, coupled amplitude-phase) and that the SLM has a relatively small number of pixels [or equivalently, space-bandwidth product (SBWP)] compared with fixed-pattern diffractive optical elements and holograms.…”