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High-resolution retinal imaging requires dilating the pupil, and therefore exposing more aberrations that blur the image. We developed an image processing technique that takes advantage of the natural movement of the eye to average out some of the high-order aberrations and to oversample the retina. This method was implemented on a long sequence of retinal images of subjects with normal vision. We were able to resolve the structures of the size of single cells in the living human retina. The improvement of resolution is independent of the acquisition method, as long as the image is not warped during scanning. Consequently, even better results can be expected by implementing this technique on higher-resolution images.

Wavefronts reconstructed from measured gradients are composed of a straightforward integration of the measured data, plus a correction term that disappears when there are no measurement errors. For regions of any shape, this term is a solution of Poisson's equation with Dirichlet conditions (V = 0 on the boundaries). We show that for rectangular regions, the correct solution is not a periodic one, but one expressed with Fourier cosine series. The correct solution has a lower variance than the periodic Fourier transform solution. Similar formulas exist for a circular region with obscuration. We present a near-optimal solution that is much faster than fast-Fourier-transform methods. By use of diagonal multigrid methods, a single iteration brings the correction term to within a standard deviation of 0.08, two iterations, to within 0.0064, etc.

We propose a method for separating the contribution of atmospheric turbulence layers at different elevations above a telescope. To sample this volume, we create a periodic fringe pattern in the sodium layer, then image it with an extended Hartmann sensor at many viewing angles. Low-layer turbulence causes overall shift of the fringe pattern in each lenslet, and high-altitude turbulence results in internal deformations in the imaged patterns. Parallel Fourier analysis allows separation of the atmospheric layers. Two mirrors, one conjugate to a ground layer and the other to a single high-altitude layer, are shown to widen the field of view significantly to tens of arcseconds and more. The feasibility of this method is analyzed regarding energy requirements, computational costs, camera size, and other parameters. Extensive error analysis and imaging simulations are presented.

The applicability of wave-front correction by means of a bimorph mirror in conjunction with a curvature sensor is described. We use Zernike polynomials to describe the quality of the atmospheric-turbulence correction analytically. The match is limited by boundary conditions of the mirror and by the discreteness of the electrodes. The correction is limited by coupling of lower- and higher-order Zernike polynomials and necessitates an interfacing computer between the wave-front sensor and the bimorph mirror.

We identify wave fronts that have passed through atmospheric turbulence as fractal surfaces from the Fractional Brownian motion family. The fractal character can be ascribed to both the spatial and the temporal behavior. The simulation of such wave fronts can be performed with fractal algorithms such as the Successive Random Additions algorithm. An important benefit is that wave fronts can be predicted on the basis of their past measurements. A simple temporal prediction reduces by 34% the residual error that is not corrected by adaptive-optics systems. Alternatively, it permits a 23% reduction in the measurement bandwidth. Spatiotemporal prediction that uses neighboring points and the effective wind speed is even more beneficial.

The weighted-shift-and-add speckle imaging technique is analyzed using simple assumptions. The end product is shown to be a convolution of the object with a typical point-spread function (psf) that is similar in shape to the telescope psf and depends marginally on the speckle psf. A filter can be applied to each data frame before locating the maxima, either to identify the speckle locations (matched filter) or to estimate the instantaneous atmospheric psf (Wiener filter). Preliminary results show the power of the technique when applied to photon-limited data and to extended objects.

An image-reconstruction technique for astronomical speckle interferometric data is described. This variant of the shift-and-add algorithm originally developed by Lynds et al. [ Astrophys. J.207, 174 ( 1976)] utilizes a weighted impulse distribution of speckle positions to extract an average speckle for a data set. This is done by means of a weighted deconvolution procedure, similar in form to a Weiner filter, which deconvolves the specklegram by the impulse distribution. Results show that this method appears to be self-calibrating for seeing effects. It yields point-spread functions, for observations of an unresolved star, that compare quantitatively with computed Airy patterns for both simple apertures and the fully phased multiple mirror telescope array. Images of the resolved object Alpha Orionis show evidence of an extended stellar envelope.