Abstract
Shaping aspheric surfaces on ultra-thin spherical mirrors is a new idea which combines optical fabrication and measurement, elasticity mechanics, active optics, etc. It can relieve pressures of fabrication, test and cost using large-aperture aspherical mirrors. Both appropriate actuator arrangement and efficient loads are the keys to achieve shaping aspheric surfaces. In order to determine the best actuator loads, the optimization of actuator forces is studied in this paper. Firstly, an example of shaping aspheric surfaces on a large off-axis ultra-thin mirror is presented, and its actuator arrangement and preliminary actuator loads satisfying surface accuracy have been given. Secondly, the corresponding relation between actuator forces and aspherical figure are analyzed, and the optimization objective is set up. Finally, the sequential quadratic programming (SQP) method for nonlinear constraint problem is applied to calculate best actuator forces. Simulation results indicate that the RMS aspheric surface error is significantly improved, and the number of actuators is also obviously decreased when the RMS error remains unchanged.
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