Estimating the contribution of different parts of the atmosphere to optical wavefront aberration

Abstract

Current adaptive optical telescope designs use a single deformable mirror (DM), usually conjugated to the aperture plane, to compensate for the cumulative effects of optical turbulence. The corrected field of view (FOV) of an adaptive optics system could theoretically be increased through the use of multiple DMs conjugated to a like number of corresponding planes which sample the turbulence region in altitude. Often, the atmospheric turbulence responsible for the degradation of long-exposure telescope images is concentrated in several relatively strong layers. The logical location for the planes of correction in a multiconjugate adaptive optics (MCAO) system would be the same as these “seeing layers.” Each DM would correct for the component of the total wavefront contributed by its associated turbulent layer. However, there is no known method of isolating a particular layer so that its component may be measured. Somehow, the individual components must be estimated using available measurements of the cumulative wavefront at the aperture of the telescope. This paper presents a theoretical analysis of a signal processing technique for determining these phase contributions. The method takes advantage of the spatial diversity of wavefront sensor (WFS) measurements from two or more reference sources. These separate wavefront sensor measurements are processed via minimum mean square error filtering to yield an estimate of the phase perturbation caused by a particular turbulent layer of the atmosphere. Our results indicate that multiple wavefront corrector adaptive optics systems will require much brighter reference sources than single wavefront corrector systems.