There are significant optical wavefront perturbational effects in the use of lasers and in imaging through atmospheric turbulence. In adaptive optics, an active element such as a deformable mirror is used to eliminate the phase aberrations of an optical wavefront. Diagnostics to determine the phase distortions are obtained by various methods. The deformable mirror is used in a feedback loop in order to cancel the unwanted phase distortions. This paper considers what is known as a modal approach to the adaptive optics problem in which the wavefront distortions are expanded into a spatial set of polynomials. The coefficients of the polynomials are temporally varying and represent the time varying phenomenological perturbations such as atmospheric turbulence, thermal blooming, and mirror distortions. The measurement devices for the wavefront are either a shearing interferometer or a Hartman array. The shearing interferometer displaces or shears the wavefront and then interferes the sheared image with the unsheared image. The Hartman array yields a linear measurement of the aberration coefficients through an effective measurement of the gradient of the wavefront. Since the wavefront is temporally varying, state space models for the aberration coefficients are obtained. An adaptive estimator is developed in order to adapt upon the atmospheric turbulence structure constant and the bandwidth of the atmospheric turbulence, and to then obtain a minimum mean square estimator for the aberration coefficients. (Author).

Project 2304. Also available as ADA041135.