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A genetic algorithm (GA) is employed to determine the structure of measured, Shack-Hartmann data and its optimum artificial neural-network (ANN) predictor. In the GA approach there are no preordained architectures imposed. The NN architecture that evolves out of many generations of adaptation can also be interpreted as a mapping of the signal complexity. The GA approach inherently addresses the problems of generalization, over fitting of data, and the trade-off between ANN complexity and performance. One objective was to establish how much improvement could ideally be expected from NNs compared to linear techniques. The principal conclusions are: (i) The main input-output relationship is linear with only a small contribution from the nonlinear elements. (ii) The improvement achievable with ANNs compared to optimal linear predictors was less than a 10% reduction in predictor error. (iii) The optimum temporal input window of tip-tilt data corresponds to the time constant introduced by aperture averaging.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The low-frequency behavior of atmospherically distorted wavefronts is not accurately known at this time. It is expected that the phase delays will be a zero mean random process. A new zero-low-frequency model of spatial PSD of the phase distortions is presented in this paper. This model has a low frequency, called the roll-over frequency, for which the PSD starts to approach zero as the frequency decreases and approaches zero. This roll-over frequency is proportional to the outer-scale of turbulence. To verify the zero-low- frequency model, wavefront slope data was analyzed from the GSM experiment with a nonlinear modelling technique called Robust Orthogonal Search (ROS). One property of ROS is that it can detect frequency components at frequencies lower than the resolution of the discrete Fourier transform. This investigation consistently indicates a lowest frequency in the data for which any lower frequency components have lower power. This results supports the low-frequency model which rolls over and approaches zero for low spatial frequencies.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The simulation and performance evaluation of high-order, adaptive-optics (AO) corrective systems for the new, large telescopes require the generation of distorted wavefronts (WF) that accurately model the behavior of the real atmosphere. Roggemann et al. have introduced a method of accurately generating distorted wavefronts based on the covariance matrix of wavefront distortions and Cholesky factorization. Several authors have proposed fractional-Brownian-motion algorithms that are more computationally efficient as alternatives for generating distorted wavefronts but do not give accurate correlations. In this paper, the fractional Gaussian process (FGP) algorithm is introduced as a new method of generating distorted wavefronts. The algorithm is presented on both one and two dimensions. The correlation function and power spectra of simulated wavefronts are shown to compare well to the expected correlation and power spectra respectively. It is concluded that the FGP algorithm is an accurate and efficient method of generating simulated wavefronts.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Previous work has shown that atmospheric distortions are predictable. We present preliminary results which show that introducing predictors into the control loop of an adaptive optics system with a zero hysteresis segmented mirror improves systems performance.

Kolmogorov turbulence has a temporal behavior best described by fractional Brownian motion (FBM) with a self-similarity parameter of H equals 5/6. Non-Kolmogorov behavior, which has also been observed and reported, is characterized by H other than 5/6. Although FBM has strong inter-sample correlations, the signals arising in an adaptive optics control loop are not FBM, have weaker inter-sample correlation,and exhibit quite different characteristics with regard to predictability. One conclusion is that for greatest advantage, prediction within the loop should be introduced at the point where signals represent the reconstructed wavefront, i.e. mirror drive signals, and not at the level of the wavefront sensor output or wavefront error signals.

Restoration of depth images obtained by serial slicing of the image volume, is complicated by the fact that one part of an opaque 3D object can partially block another part from the view of the imaging lens. This type of obscuration makes the point spread function (PSF) object dependent. We present a general algorithm that adapts a transparent PSF to represent the effects of the opaque or semi-transparent object. Examples of its application are given using simulated annealing and modified iterative backprojection to carry out the iterative restoration.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Atmospherically-induced wavefront distortions that follow a Kolmogorov power spectral density has a spatial and temporal behaviour best described as a fractional Brownian motion (FBM) process. FBM is persistent and has a considerable degree of predictability, but its slopes are antipersistent and are not easily predicted by conventional means. However, previous measurements have shown that there is a exploitable degree of persistence and predictability in wavefront slopes. In this paper we describe how lowpass-filtered FBM can model the spectral, temporal and predictive properties of distorted wavefronts. Implications for closed-loop adaptive optics systems will be discussed.

The recovery of a stellar object's Fourier phase from the bispectrum of the atmospherically- degraded images has been investigated with respect to object complexity, a wide range of light levels, severity of the atmospheric effects and the number of bispectral subplanes used. The incremental improvement in the quality of the recovered phase as the number of near-axis subplanes increases is greatest for complex sources and when photon-noise dominates. At high signal-to-noise ratios it was found that the extended Knox-Thompson transfer function has a higher phase variance than the bispectral transfer function. Analysis has confirmed this difference in behavior.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The computational requirements of simulated annealing can be reduced by the use of an error backprojection operator to restrict the intensity perturbations to the area in which they will be most effective in decreasing the cost function. The use of cost function jitter and other diagnostic tools applicable to simulated annealing and/or area-adaptive simulated annealing is discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

When astronomical speckle images are truncated by the finite size of the image detector, important errors occur in the estimated power spectrum and the Knox-Thompson cross- spectra. The errors and their effect on image reconstruction are calculated for an 8-component and a 3-component star model. The distortions and negative artifacts seen in the reconstructions of the star ADS 11344 are explained by image truncation. A method of estimating an approximate error bound given the telescope, atmospheric seeing, detector size, and sampling rate is outlined.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Time delays inherent in the control systems of current and proposed adaptive optics systems could be eliminated by predicting atmospherically-distorted wavefronts a short time ahead. An error-backpropagation neural network trained on real astronomical data has demonstrated that time series of wavefront tips and tilts (slopes) in the visible, and piston (displacement) in the infrared, are predictable to a degree which would improve the operation of an adaptive optics telescope.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The triple correlation algorithm employing a minimum of computation is evaluated as a candidate process for near-real-time, quick-look, stellar image reconstruction at the telescope. Computational efficiency is gained by exploiting the binary nature of the photon-list images and by using a small number of high SNR bispectrum subplanes. When compared to the Knox-Thompson algorithm extended to 2, 4 and 6 subplanes, the fidelity of reconstruction by the TC process is better and less object dependent, even in the minimum-computation case of 2 planes.

Three dimensional images can be captured electronically by space-variant inversion or de-blurring of the intensity distribution measured in the volume behind the imaging lens. A computer simulation using a measured lens point-spread-function illustrates the effectiveness of the technique for incoherently-radiating objects with negligible internal scattering. 1 .

A simple least-squares algorithm for recovering stellar object phase from the bispectrum yields better phase estimates than the usual recursive method at low photon rates.

Three-dimensional incoherently illuminated scenes can be captured electronically by measuring the intensity distribution in a volume behind the lens. The 3-D image is reconstructed by an inversion algorithm employing the measured, space-variant, 3-D point spread function of the lens. A computer simulation using a measured PSF illustrates the effectiveness of the technique.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.