Abstract
Atmospheric turbulence is a fundamental problem in imaging through long slant ranges, horizontal-range paths, or uplooking astronomical cases through the atmosphere. An essential characterization of atmospheric turbulence is the point spread function (PSF). Turbulence images can be simulated to study basic questions, such as image quality and image restoration, by synthesizing PSFs of desired properties. In this paper, we report on a method to synthesize PSFs of atmospheric turbulence. The method uses recent developments in sparse and redundant representations. From a training set of measured atmospheric PSFs, we construct a dictionary of “basis functions” that characterize the atmospheric turbulence PSFs. A PSF can be synthesized from this dictionary by a properly weighted combination of dictionary elements. We disclose an algorithm to synthesize PSFs from the dictionary. The algorithm can synthesize PSFs in three orders of magnitude less computing time than conventional wave optics propagation methods. The resulting PSFs are also shown to be statistically representative of the turbulence conditions that were used to construct the dictionary.
Highlights
Introduction and BackgroundIn any long-range imaging case, turbulence degrades the imagery by inducing both warping and blurring
We shall refer to the reserved data as the test set point spread function (PSF). The purpose of these comparisons was to determine if the synthesized PSFs possessed characteristics that were comparable with PSFs from the same atmospheric conditions, but which were never used in training the custom PSF dictionary
Using point source data collected under deep turbulence conditions, we constructed a custom sparse dictionary containing 256 atoms and verified its ability to represent turbulent PSF data using 64 coefficients or less
Summary
In any long-range imaging case, turbulence degrades the imagery by inducing both warping and blurring. MFBD algorithms assume that the image frames have a common source, namely the object from which radiation propagated to the optical system, and they use this assumption to infer the turbulent PSFs impacting each image.[9] Each inferred PSF is used to correct the corresponding distorted image frame. In this way, MFBD algorithms model the instantaneous atmospheric turbulence in the entrance pupil of the optical system.
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