Zernike-polynomial expansion of turbulence-induced centroid anisoplanatism.

An expansion of image centroid position after propagation through atmospheric turbulence in terms of Zernike-polynomial coefficients is shown to consist of a tilt term plus coma terms. Centroid anisoplanatism therefore arises from turbulence-induced coma distortions. By correcting for coma effects to a sufficiently high order, the deleterious effects of centroid anisoplanatism can be reduced to any desired level. The Strehl ratio is given by the asymptotic formula [1 + A(D/r(0))(5/3)](-1), where A = 0.018(I + 1)(-7/3) and I is the number of coma terms corrected.