Inverse problems in astronomical adaptive optics

Adaptive optics (AO) is a technology used in ground-based astronomy to correct for the wavefront aberrations and loss of image quality caused by atmospheric turbulence. Provided some difficult technical problems can be overcome, AO will enable future astronomers to achieve nearly diffraction-limited performance with the extremely large telescopes that are currently under development, thereby greatly improving spatial resolution, spectral resolution and observing efficiency which will be achieved. The goal of this topical review is to present to the inverse problems community a representative sample of these problems. In this review, we first present a tutorial overview of the mathematical models and techniques used in current AO systems. We then examine in detail the following topics: laser guidestar adaptive optics, multi-conjugate and multi-object adaptive optics, high-contrast imaging and deformable mirror modeling and parameter identification.