OPTIMAL MODAL WAVE-FRONT COMPENSATION FOR ANISOPLANATISM IN ADAPTIVE OPTICS

We examine how modal aberration measurements degraded by turbulence-in duced anisoplanatism may be used to optimally conjugate atmospheric ph ase aberrations. By examining the form of the aperture-averaged mean s quare residual phase error, we show that atmospheric compensation is s uboptimal when the measured coefficients from off-axis or finite-altit ude guide stars are applied directly. The optimal compensation is obta ined only when conjugate phase coefficients are estimated, given the g uide-star measurements and knowledge of the spatial correlation of the on-axis and measured phase coefficients, by use of a minimum-mean-squ are-error (MMSE) estimator. The form of this estimator is outlined, th us motivating the need to quantify the spatial cross correlation of th e Zernike coefficients of the phase aberrations. With a knowledge of t he modal cross correlation, we show that wave-front compensation perfo rmance can be enhanced by use of the MMSE estimator over use of the be acon measurements directly for all orders of correction. For high-orde r off-axis natural-guide-star correction, equivalent imaging performan ce is obtained at a beacon offset 10% larger than when beacon measurem ents are used directly. For high-order laser-guide-star correction, eq uivalent imaging performance is obtained at laser-guide-star altitudes 20% lower when the MMSE estimator is employed. (C) 1998 Optical Socie ty of America.