A new method of reconstructing and predicting an unknown probability density function (PDF) characterizing the
statistics of intensity fluctuations of optical beams propagating through atmospheric turbulence is presented in this
paper. The method is based on a series expansion of generalized Laguerre polynomials ; the expansion coefficients are
expressed in terms of the higher-order intensity moments of intensity statistics. This method generates the PDF from
the data moments without any prior knowledge of specific statistics and converges smoothly. The utility of
reconstructed PDF relevant to free-space laser communication in terms of calculating the average bit error rate and
probability of fading is pointed out. Simulated numerical results are compared with some known non-Gaussian test
PDFs: Log-Normal, Rice-Nakagami and Gamma-Gamma distributions and show excellent agreement obtained by the
method developed. The accuracy of the reconstructed PDF is also evaluated.
An image reconstruction approach is developed that makes joint use of image sequences produced by a conventional imaging channel and a Shack-Hartmann (lenslet) channel. Iterative maximization techniques are used to determine the reconstructed object that is most consistent with both the conventional and Shack-Hartmann raw pixel-level data. The algorithm is analogous to phase diversity, but with the wavefront diversity provided by a lenslet array rather than a simple defocus. The log-likelihood cost function is matched to the Poisson statistics of the signal and Gaussian statistics of the detector noise. Addition of a cost term that encourages the estimated object to agree with a priori knowledge of an ensemble averaged power spectrum regularizes the reconstruction. Techniques for modeling FPA sampling are developed that are convenient for performing both the forward simulation and the gradient calculations needed for the iterative maximization. The model is computationally efficient and accurately addresses all aspects of the Shack-Hartmann sensor, including subaperture cross-talk, FPA aliasing, and geometries in which the number of pixels across a subaperture is not an integer. The performance of this approach is compared with multi-frame blind deconvolution and phase diversity using simulations of image sequences produced by the visible band GEMINI sensor on the AMOS 1.6 meter telescope. It is demonstrated that wavefront information provided by the second channel improves image reconstruction by avoiding the wavefront ambiguities associated with multiframe blind deconvolution and to a lesser degree, phase diversity.
Image restoration algorithms compensate for blur induced attenuation of frequency components that correspond to fine
scale image features. However, for Fourier spatial frequency components with low signal to noise ratio, noise
amplification outweighs the benefit of compensation and regularization methods are required. This paper investigates a
generalization of the Wiener filter approach developed as a maximum a priori estimator based on statistical expectations
of the object power spectrum. The estimate is also required to agree with physical properties of the system, specifically
object positivity and Poisson noise statistics. These additional requirements preclude a closed form expression. Instead,
the solution is determined by an iterative approach. Incorporation of the additional constraints results in significant
improvement in the mean square error and in visual interpretability. Equally important, it is shown that the performance
has weak sensitivity to the weight of the prior over a large range of SNR values, blur strengths, and object morphology,
greatly facilitating practical use in an operational environment.
KEYWORDS: Staring arrays, Wavefronts, Sensors, Image processing, Point spread functions, Data modeling, Telescopes, Signal to noise ratio, Image acquisition, Convolution
Ideally phase diversity determines the object and wavefront that are consistent with two images taken identically except that the wavefront of the diversity channel is perturbed by a known additive aberration. In practice other differences may occur such as image rotation, magnification, changes in detector response, and non-common image motion. This paper develops a mathematical forward model for addressing magnification changes and a corresponding maximumlikelihood implementation of phase diversity. Performance using this physically correct forward model is compared with the more simple approach of resampling the data of the diversity channel.
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