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A new method of evaluating the MTF of a Kolmogorov turbulence phase aberration Zernike modal compensating system using an approximation of the correlation of the residual phase aberration and the compensating phase distribution is described. This approach enables the extension of our previous results to cases including high-order terms in the compensating phase function. The Karhunen-Loeve expansion is discussed along with its relation to the Zernike polynomial expansion. Calculation of the optical resolution, or correlation quality, and the relative structure content, shows the Karhunen-Loeve expansion to be noticeably better than the Zernike expansion when terms through third and fifth order are included in the compensating phase distribution.
Wang et al. (1978) studied this question.