On the modulation transfer function for an atmosphere-telescope combination with adaptive compensation for random wavefront tilt

A discussion is given of the problem of recording a long-exposure, averaged image of an object viewed through the turbulent atmosphere by means of adaptive compensation for the seeing excursion of the instantaneous image. Analytic expressions are derived for the modulation transfer function of an atmosphere-telescope system involving adaptive compensation for random wavefront tilts, and the compensated tilt is estimated for a telescope aperture of arbitrary shape. The general relations yield MTF's for systems having circular and annular telescope apertures, refining the results of D. L. Fried and A. T. Young.