Flattening of Convex Adaptive Secondary Mirrors Using Focal Plane Image Metrics

Abstract

Adaptive optics (AO) are essential in ground-based telescopes to correct atmospheric distortions and achieve high-resolution imaging; adaptive secondary mirrors (ASMs) integrate deformable mirrors directly into telescope optics but typically require a wavefront sensor (WFS) for calibration and flattening. When a WFS is unavailable or nonfunctional, alternative methods are needed. This thesis explores the feasibility of flattening the convex ASM of the UH-88 telescope without a WFS, using only a natural guide star and focal plane imaging. By developing a numerical model of the UH-88 system—including the deformable mirror, Mauna Kea atmospheric aberrations, and focal plane camera characteristics—we employed an image metric based on the second moment of intensity to evaluate image quality, adjusting Zernike mode coefficients via the Nelder-Mead simplex optimization algorithm to control mirror shape. Experimental validation using a laboratory setup that replicated key aspects of the UH-88 system confirmed that the ASM could be flattened to within 100 nm RMS surface error, meeting passive mirror operation requirements. The flattening was achieved within a 10-minute timeframe using only focal plane images of a natural guide star distorted by atmospheric turbulence. This study demonstrates that flattening a convex ASM without a WFS is feasible using focal plane image metric optimization, offering a practical solution when the WFS is unavailable or calibrated commands are outdated, thereby ensuring continued high-quality telescope operation.