Ms. Merfit Assad Profile

Merfit Assad

Research Engineer at Lockheed Martin Missiles and Fire Control

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Proceedings Article | 12 February 2007 Paper

On the use of Gaussian filter functions for adaptive optics

Merfit Assad, Larry Andrews

Proceedings Volume 6457, 64570Q (2007) https://doi.org/10.1117/12.699677

KEYWORDS: Gaussian filters, Scintillation, Adaptive optics, Zernike polynomials, Atmospheric turbulence, Monochromatic aberrations, Atmospheric optics, Statistical analysis, Optical filters, Atmospheric propagation

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For adaptive optic systems, the use of aperture filter functions calculated using various Zernike modes can be useful in describing lower-order aberrations caused by atmospheric turbulence. Traditionally, these filter functions are calculated using the step function depicting a hard aperture that introduces integrals that are sometimes difficult to integrate and must be done numerically. The Gaussian method, equivalent to the ABCD matrix method, can be used in place of the conventional method for calculating the aperture filter functions. Evaluation of the Gaussian approximation for modeling a finite receiver aperture can be made by comparison of reduction in phase variance with results achieved using the conventional method. The validity of Gaussian approximation in this application is demonstrated by the consistency of results between the two methodologies. Comparison of reduction in scintillation by the two methodologies reveals several benefits derived from utilization of Gaussian approximation. The Gaussian approximation produces data that can be interpreted analytically. This paper will first examine the use of statistical models for predicting atmospheric turbulence and then the use of Zernike polynomials in adaptive optics. Next, this paper compares the reduction of phase variance and scintillation using the conventional method with the Gaussian approximation to evaluate the effectiveness of the new filter functions. The results of these comparisons are presented both as mathematical expressions and graphically.

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