Case Study 2: Online Cophasing Optical Systems for Segmented Mirrors

Abstract

An online cophasing optical system for cophasing of segmented mirrors—a Mach–Zehnder interferometer equipped with the technique of dual-wavelength digital holography—is presented in this chapter. The principle and optical layout of this optical system is explicated mainly using wave optics. With this example, readers can better understand optical systems in view of wave optics. Compared with monolithic primary mirrors, segmented primary mirrors are more affordable and practical for ground-based astronomical telescopes with large apertures due to their low cost and easy fabrication. However, in order to use a segmented mirror to acquire a high image quality that is equivalent to the image quality using a monolithic mirror with the same aperture, cophasing of the segmented mirror is required. Cophasing, especially online cophasing, of segmented mirrors is a great challenge and has attracted much research interest. The process of cophasing a segmented mirror involves measuring and further removing height errors among all segments for the entire segmented mirror, including relative piston errors between adjacent segments and tip/tilt errors for each individual segment. A key step in this process is measuring these height errors (piston and tip/tilt errors). In optics, the height errors of a segmented mirror are generally determined by measuring the phase of light reflected from the segmented mirror. Due to the discontinuity of the segmented mirror and the existence of atmospheric turbulence, the problem of 2 pi ambiguities in the phase measurement makes measurement of the phase of light reflected from the segmented mirror very difficult. In this chapter, dual-wavelength digital holography, a technique commonly used for phase measurement and high-resolution imaging, is adopted to solve this problem.