Adaptive optics: Wavefront reconstruction by adaptive filtering and control

This dissertation concerns a class of adaptive optics problems in which phase distortions due to atmospheric turbulence are corrected by adaptive wavefront reconstruction with a deformable mirror—i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, rather than the linear time-invariant control loops used in conventional “adaptive optics”. The basic problem is posed here as an adaptive disturbance rejection problem with many channels.; Chapter 2 provides some necessary mathematical background of Fourier Optics. In the same chapter the three key components of an adaptive optical system are discussed, which are deformable mirror (DM), wavefront sensor (WFS), and controller design. Chapter 3 discusses in detail how the AO system is modeled. The ideas of reparameterization for channel number reduction and the many constant matrices used in the AO system are defined. Chapter 4 introduces the active noise cancellation (ANC) concept and explains how the AO system adopts the ANC systems. The solution given here is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. In Chapter 5, the simulation results using eigenvectors of a Gramian matrix are presented for a one-meter telescope with both one-layer and two-layer atmospheric turbulence profile. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared to a classical linear time-invariant control loop. Chapter 6 first introduces the Zernike polynomials then two different simulation results by adopting the Zernike polynomials for a one-meter telescope and a 3.5-meter telescope are included. These polynomials provide the physical meanings of the atmospheric turbulence and those two simulations provide the possible control and reference channel reduction for the AO system which leads to feasible real-time systems for nowadays computing power. Chapter 7 explains how the Gramian matrix W is computed. Chapter 8 concludes this dissertation.