MODAL COMPENSATION OF ATMOSPHERIC-TURBULENCE WITH THE USE OF ZERNIKE POLYNOMIALS AND KARHUNEN-LOEVE FUNCTIONS

Atmospheric Karhunen-Loeve functions are the optimal set of basis func tions for modal atmospheric compensation. They are seldom applied in p ractice on account of their nonanalytical nature. A pseudoanalytical s et of these functions is constructed with a least-squares-fitting proc edure. To produce an analytical expression for the optical resolution of modal atmospheric compensation, a modified form of structure functi ons is used and applied to the compensated wave front. This results in analytical residual phase structure functions for Zernike polynomials and pseudoanalytical residual phase structure functions for Karhunen- Loeve functions. With these structure functions it is found that the m odulation transfer function (MTF) after modal compensation is the prod uct of the telescope MTF and the uncompensated atmospheric MTF under t he assumption of isotropic compensating phase. Comparison with an accu rate numerical method shows that the approximated analytical method de veloped is much faster and gives reasonably accurate results, especial ly for high-order compensations. (C) 1995 Optical Society ofAmerica