Models of atmospheric turbulent distortions for images and super-resolution

Fedor V. Shugaev; Evgeni N. Terentiev; Ludmila S. Shtemenko; Elena A. Bratinkova

doi:10.1117/12.487747

21 August 2003 Models of atmospheric turbulent distortions for images and superresolution

Fedor V. Shugaev, Evgeni N. Terentiev, Ludmila S. Shtemenko, Elena A. Bratinkova

Proceedings Volume 5087, Laser Systems Technology; (2003) https://doi.org/10.1117/12.487747
Event: AeroSense 2003, 2003, Orlando, Florida, United States

Abstract

As known, the problem of compensation of turbulent distortions is an ill-posed one. Regularization methods are found to be inefficient. The problem can be solved by using local-linear super-resolution method. Its main feature consists in diminishing of problem dimensions. We use the terminology of multi sensors (rays) systems for this purpose and a new concept of resolving function R. Each linear device which forms image is characterized by two functions: PSF O and MTF M on observation area D. The function R resolves a function O, if their cyclical product (or convolution) is equal (or near) to d - delta function: R*O = O*R = d on D. The resolving image R*I on D can be presented as measured one by fine “registering system” with narrower PSF R*O that cannot be achieved physically. If area D is as small as one of O, then the corresponding values of M are relatively large ones and there is no problem for compensation of distortions. The special arrangement of local subareas of D is obtained by solving the next multi sensors (rays) problem: to separate the image I and the distorting PSF O on the observation area D so that at small quantity of data the resolution problem with R could be solved strictly and with the minimum border effect. Grid-generated turbulence in a shock tube was chosen as an example of homogeneous and isotropic turbulence. Statistical properties of this flow have been investigated experimentally. We found the correlation function and structure function for the fluctuations of refractive index. In our case of grid-generated turbulence the statistical properties are distinct from the Kolmogorov's two-thirds law. We modeled laser beam propagation through turbulent atmosphere and obtained the numerical results for the distortions of images. The distortion O (r) of PSF and the set of resolving functions R were found according to the structure function. The problem of compensation of distortions caused by turbulence was solved with the aid of a new local-linear super-resolution method. This method allows to resolve turbulent distortions of PSF at low signal-to-noise ratio.

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Fedor V. Shugaev, Evgeni N. Terentiev, Ludmila S. Shtemenko, and Elena A. Bratinkova "Models of atmospheric turbulent distortions for images and superresolution", Proc. SPIE 5087, Laser Systems Technology, (21 August 2003); https://doi.org/10.1117/12.487747

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KEYWORDS

Point spread functions

Turbulence

Atmospheric modeling

Super resolution

Correlation function

Modulation transfer functions

Refractive index

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