No abstract

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 fast orthogonal search (FOS) algorithm has been shown to accurately model various types of time series by implicitly creating a specialized orthogonal basis set to fit the desired time series. When the data contain periodic components, FOS can find frequencies with a resolution greater than the discrete Fourier transform (DFT) algorithm. Frequencies with less than one period in the record length, called subharmonic frequencies, and frequencies between the bins of a DFT, can be resolved. This paper considers the resolution of subharmonic frequencies using the FOS algorithm. A new criterion for determining the number of non-noise terms in the model is introduced. This new criterion does not assume the first model term fitted is a dc component as did the previous stopping criterion. An iterative FOS algorithm called FOS first-term reselection (FOS-FTR), is introduced. FOS-FTR reduces the mean-square error of the sinusoidal model and selects the subharmonic frequencies more accurately than does the unmodified FOS algorithm.

No abstract

Algorithms and computational developments in recent years have yielded suitable techniques for overcoming the resolution limits imposed on conventional astronomical observations by atmospheric turbulence. The Knox-Thompson, triple-correlation, and phase-gradient algorithms are capable of reconstructing the diffraction-limited, complex spatial spectrum of an object from a sequence of short-exposure images. The basic principles of these techniques are reviewed with emphasis on photon-limited operation at visible wavelengths. Practical considerations, magnitude limits, and examples of recent applications are presented.