Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

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The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.

The effect of a uniform measurement bias, due to background light, stray light, detector dark current, or detector offset, on phase retrieval wavefront sensing algorithms is analyzed. Simulation results indicate that the root-mean-square error of the retrieved phase can be more sensitive to an unaccounted-for signal bias than to random noise in practical scenarios. Three methods for reducing the impact of signal bias are presented.