Simulation and optimization for a computer-controlled large-tool polisher

Large aspheric mirrors are ground and polished at the Steward Observatory Mirror Lab (SOML) using stressed-lap polishers under computer control.1,2 Stressed-lap polishing uses large stiff circular polishing tools, which are actively deformed under computer control forcing the lap to continually fit the aspheric mirror surface. The size of the tool is typically one-third to one-sixth the diameter of the minor. As the lap is translated across the rotating minor, the lap's horizontal speed and rotation rate, the total force on the lap, and applied moments to the lap are all dynamically controlled. In order to take full advantage of these many degrees of freedom, computer simulation and optimization software has been developed. The simulation is based on Preston's relation (local removal rate proportional to pressure and relative velocity) but allows the inclusion of non-linear effects based on measured results. The optimization of polishing parameters is accomplished by a damped least squares optimization algorithm which varies the polishing parameters to obtain a desired simulated removal profile. This software has been successfully used at SOML to guide grinding and polishing of numerous large primary and secondary telescope mirrors.3 The software was developed for the stressed lap polishers at the University of Arizona, but it can be used with equal effectiveness for other types of polishers.