Active Control of Large Telescopes: Adaptive Optics

Abstract

This chapter begins with a brief description of the requirements for image quality, the measurement of the wavefront aberration with a Shack–Hartmann (SH) sensor and its decomposition in a set of orthogonal functions named the Zernike modes. Next, the Kolmogorov turbulence model is used, together with the assumption of frozen turbulence shape transported by the wind to evaluate the RMS value of the phase error, the image quality, and the power spectral density of the various Zernike modes. The next section discusses the main features of deformable mirrors for adaptive optics, with a special attention to the bimorph piezoelectric mirrors in various actuator configurations (keystone and honeycomb). The following section is devoted to the feedback control using a frequency-shaped singular value decomposition (SVD) controller and assuming a quasi-static response of the deformable mirror; the closed-loop response of the various Zernike modes and the RMS phase error is evaluated as a function of the control bandwidth. Next, a dynamical model of the mirror is used and the control-structure interaction is analyzed, leading to spillover; the importance of the structural damping of the vibration modes is pointed out. The damping augmentation via passive piezo shunt and active damping using modal filtering is then analyzed. The chapter concludes with some remarks on manufacturing and a list of references.