Wavefront control and correction with adaptive segmented mirrors

Ground-based astronomical telescopes suffer a severe limitation in the form of atmospheric turbulence. This refers to the random, time-varying distribution of the index of refraction of the air that an optical wavefront will experience on passage through the atmosphere. The result of this is a degradation of the image and resolution produced by the telescope, compared to that attainable with a homogeneous atmosphere. Consequently, there has been much work directed toward mitigating the effects of such turbulence in telescope systems. The basic approach is to make the telescope mirror active or adaptive, rather than passive. An adaptive mirror is characterized by its ability to change in shape or deform in some manner, thus allowing the possibility of correcting for some wavefront errors by introducing conjugate errors in the mirror itself. One type of adaptive element is the segmented mirror, in which the overall mirror is composed of many independent segments, each of which has three degrees of freedom to move.; In this thesis, segmented mirror adaptive optics systems are studied. The study is divided into three main sections. In the first part, we discuss and evaluate two different correction algorithms, namely the zonal and modal approaches. The efficiencies of each at correcting atmospheric turbulence aberrations are found for ideal and non-ideal situations. The second main part of the thesis is concerned with optimizing the correction algorithm for a general segmented mirror in the presence of both atmospherically-induced wavefront errors and simple misalignment errors of the mirror itself, as well as wavefront measurement errors. The forms and statistics of both kinds of aberration are assumed to be known in addition to the measurement noise statistics. In the third section we consider using an optical linear algebra processor to perform the control computations in an adaptive segmented mirror system. The accuracy requirements of such a processor are evaluated and the system is compared with an adaptive mirror system with a conventional electronic digital processor. A re-optimization of the correction algorithm is also presented that accounts for the errors introduced by the optical processor.