Control of a Thermal Deformable Mirror: Correction of a Static Disturbance with Limited Sensor Information

This research considers the control of a Thermal Deformable Mirror (TDM), which is used to correct a static aberration in a light beam. The TDM is a cheap, but relatively slow, deformable mirror suited for the correction of static and thermal aberrations. Correction of quasi-static disturbances can, for example, be used to enhance microscope images, or to improve the quality of femto-second light wave packages. The control objective is to maximize the light power that drops through a pinhole after focusing of the beam in a minimal time span. Only the light power behind the pinhole is available for feedback. The slow dynamics of the mirror and the lack of measurement information complicate the control task. The optimization algorithm (OA) used to maximize the light power is based on consecutive line searches in the direction of several Zernike modes. The OA operates on the surface shape of the mirror, rather than the mirror input voltages. To speed up and to improve the performance of the algorithm, model predictive control (MPC) is used to adjust the mirror shape to the shape provided by the OA. The effectiveness of using MPC has been experimentally validated. The disturbance in the experiments consists of a focus and tilt misalignment, and the zero-input shape of the TDM. Without MPC, the light power reaches 40% of the maximum light power within 3000 iterations. When applying the MPC controller, 40% of the maximum intensity is obtained within 700 iterations, and 50% within 2200 iterations.