Control of the optical surface of a thin, deformable primary mirror with application to an orbiting astronomical observatory

A significant technological problem associated with the orbital operation of large astronomical telescopes is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror. In this paper the discrete control of linear distributed systems is considered. In particular the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory is presented. Modal techniques are employed to represent the distortion of the mirror surface. This distortion is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each actuator acts upon the mirror through a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number, equal to the number of actuators, of the most significant modes. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.