Optimization-based correction of a segmented optical telescope using image-plane sensing

The apertures of many optical telescopes are constructed of multiple mirror segments. To attain the performance of a monolithic mirror, the segments must be corrected in tip, tilt, and piston. In this paper we consider a three-segment optical telescope and develop an optimization based algorithm for determining the initial error of the segmented aperture through a sequence of displacements, thereby facilitating correction of the initial error. The optimization algorithm is used to investigate the effects of sensor quantization on the achievable correction accuracy.