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Surface analysis of an actively controlled telescope primary mirror under static loads.

The performance of an actively controlled mirror with an aspect ratio of 63:1 is modeled by a large scale software system. The model allows generalized static disturbances to be applied to the mirror, generates a corrective force field, and tests the result through a finite element simulation. For convenience in input, disturbances may be in the form of a force field or a displacement field. Use of a displacement field is easier, for example, if one wishes to distort the mirror with a particular aberration term for which the disturbing forces are unknown. The user must have established a particular actuator set to be used in counteracting the disturbance, whereupon the actuator forces for this set are determined by a modal truncation method. These computed actuator forces are then reapplied to the mirror model along with the disturbance to evaluate the corrected behavior of the model. Comparisons are made of the rms surface errors and energy concentrations as predicted by modal truncation and computed via the finite element method. Numerical examples, including some bordering on the pathological, are employed to show that the corrected mirror performance under the action of computed actuator forces and external disturbances agrees generally with the mirror surface as predicted by modal truncation.