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Two-dimensional fractional Brownian motion (FBM) is a good model for stellar wave fronts distorted by Kolmogorov turbulence. However, the time series generated by the movement of such a wave front past an observation point does not explain the reported predictability of measured wave-front slopes. Rescaled-range analysis, a technique for detecting dependence among samples in a series, and a correlation-dimension algorithm that tests for the presence of deterministic chaos were applied to series of real, measured, stellar wavefront slopes. These tests suggest that the source of correlation and predictability is the low-pass spatial filtering of the FBM wave front by the lenslets of an adaptive-optics wave-front sensor and that the process is not chaotic. A simple modeling procedure is described for generating time series of measured wave-front slopes with the correct temporal characteristics.

A complication in three-dimensional image restoration is that one part of an opaque or semitransparent object can partially block another part from full view by the imaging lens. This type of obscuration alters the point-spread function relating the three-dimensional (3-D) image space and the 3-D object space, making it not only space variant but also object dependent. We describe image-restoration algorithms that can treat such situations, present the results of some simulations, and discuss the limitations of the algorithms.

It is shown that the triple-correlation bispectrum method of stellar image reconstruction has better dynamic range and resolution capabilities than the extended Knox–Thompson method when both are operating in the near-axis regime at high photon rates. Examples are given of the recovery success rate for companions 1/100 and 1/200 the strength of the primary object and of resolving close binaries.

Volume imaging, holography, and conoscopy are methods of recording three-dimensional images. We show that the dependence of the resolution cell size on distance is different for each system and determines the gray-level requirements of the detection and recording system in each case. Expressions are developed for the total number of resolution cells in the observable object volume. This is of interest in determining the total amount of data that must be processed by an electronic imaging system. Tables of performance figures are given for ideal and realistic conditions.

Least-squares phase recovery from the near-axis, triple-correlation bispectrum of atmospherically degraded stellar images has been studied for a wide range of light levels, increasing object complexity, different degrees of atmospheric severity, and number of bispectral subplanes used. As one would expect, image quality improves with increasing number of subplanes used, but this improvement is greatest in the region where photon noise dominates and the amount of improvement increases with object complexity. At high signal-to-noise ratios the near-axis Knox–Thompson transfer function has a higher phase variance than the triple-correlation transfer function. Simulation and analysis confirm this result.

Stellar speckle images are often truncated by the edges of the image detector. It is shown that even modest amounts of image truncation can cause important errors in the second-order spectra of speckle interferometry and the Knox–Thompson algorithm. A method is presented for estimating an approximate upper bound on the truncation error given the telescope, atmospheric seeing, detector size, and spatial sampling rate. Reconstructed images of the triple star ADS 11344 from simulations and from real data illustrate the distortions and negative artifacts caused by image truncations.

Accurate prediction of the short-term future behavior of atmospherically distorted wave fronts would permit the elimination of delays inherent in current adaptive-optics systems. It is shown by using astronomical image data that atmospherically induced wave-front distortions as represented by time series of wave-front tips and tilts measured in the visible and piston values measured in the infrared are predictable to a degree that would be useful in an adaptive-optics system. Adaptive linear predictors as well as predictors based on the back-propagation neural network are employed in this study.

The performance of a photon-address, subplane implementation of the triple-correlation (TC) algorithm is evaluated for application to near-real-time, stellar speckle imaging at low-light levels. A simple least-squares relaxation algorithm for recovering object phase from the bispectrum is proposed and found to be consistently better than the usual recursive method. Photon-address speckle data from six simulated objects of different degrees of complexity, and from the binary stars β Del and μ Ori, were used in this study. For real-time applications for which computational efficiency is critical, the relaxed two-plane TC algorithm offers excellent performance and rugged-ness with respect to object complexity.

The properties of the phase-gradient algorithm for retrieving the Fourier phase from stellar speckle images are examined with respect to random image motion, centroiding, photon noise, and stray photons. The phase gradient is found to be immune to the degradation from image motion and distortions at low photon levels that occur in the Knox–Thompson process. The signal-to-noise ratios of the two methods are found to be comparable. Bias terms that are due to stray photons caused by background light or detector noise are derived.

Sensitometry and the spatial-frequency response of a PROM SLM are evaluated with special emphasis on positive-mode operation. Spatial uniformity, the effects of crystal strain, and the readout decay characteristics are examined. The positive mode is 100 times more sensitive and has better linearity than the negative mode, but the spatial bandwidth is less by a factor of 0.17. Spatial variations of crystal strain cause deviations in γ of as much as 42% of its strain-free value.

A real-time optical correlator based on the principle of one-bit correlation, often used to facilitate the construction of real-time digital signal processors, is shown to have a greater immunity to mechanical noise than a comparable analog optical correlator. One-bit quantization also avoids some of the difficulties encountered with nonlinear light modulators. The one-bit optical correlator was studied by means of a computer simulation and an experimental system. Application of the technique to a multichannel correlator is discussed.