Abstract. Atmospheric turbulence is a fundamental problem in imaging through long slant ranges, horizontalrange 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.
nt Transmitted e t ni cos of -nt cos et r1 = rll = ni cos ei + nt cos et nt cos ei -ni cos et ni cos et + nt cos ei where nt = 1.33 for water nt = 1.47 for vegetable oil nt = 1.47 -1.57 for crude ABSTRACTIntegrity Applications Incorporated (IAI) collected electro-optical polarimetric imagery (PI) to evaluate its effectiveness for detecting oil on water. Data was gathered at multiple sun angles for vegetable oil and crude oil to demonstrate PI sensitivity to different liquids and collection geometries. Unique signatures for oil relative to water were observed. Both oils consistently displayed higher degree of linear polarization (DOLP) values than water, which was expected based on the lower index of refraction of water (1.33) relative to vegetable oil and crude oil (1.47 and 1.47-1.57, respectively). The strength of the polarimetric signatures was found to vary as a function of collection angle relative to the sun, with peak linear polarizations ranging from 40-70% for crude oil and 20-50% for vegetable oil. IAI found that independentlyscaled DOLP was particularly useful for discriminating these liquids, because it demonstrated the least sensitivity to collection angle, compared to other PI products. Specifically, the DOLP signature of vegetable oil was approximately 20% lower than for crude oil, regardless of collection angle. This finding is consistent with the lower index of refraction values for vegetable oil compared to crude. Based on the promising results presented here, IAI recommends further testing and development of PI for oceanic remote sensing applications such as oil spill/leak detection and for supporting oil cleanup efforts. With additional work, PI may also be applicable to other oceanic environmental issues such as detection of agricultural runoff or effluent from industrial facilities or watercraft.
Abstract. A common method for synthesizing turbulent imagery is to model phase perturbations on a wavefront and then propagate the wavefront to the entrance pupil of an imaging system. The point spread function (PSF) that results from the wavefront in the pupil is then computed and used to synthesize images by the usual means of convolution. In a recent publication, a method was disclosed using sparse and redundant dictionaries of turbulent characteristics to construct PSFs directly in the image plane and simulate image formation without making phase models and computing wavefront propagation. However, the dictionary method, as disclosed in the recent publication, is limited to modeling PSFs characterized by the Fried parameter of the data used to construct the dictionary. Herein, we demonstrate that a dictionary constructed from data with a given Fried parameter can be scaled to construct turbulent PSFs corresponding to larger and smaller values of the Fried parameter. This enables a single dictionary, or a small number of dictionaries, to serve for the simulation of turbulent images over a range of turbulence conditions. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
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