MIRROR DEFORMATION FOR PHASE COMPENSATION OF A THERMALLY BLOOMED LASER BEAM.

Under certain conditions phase errors develop over the cross section of an initially coherent beam of electromagnetic radiation propagating through the atmosphere. At the target the beam cross section is therefore enlarged and distorted. This phase error and beam divergence can be partially corrected by insertion of a compensating deformable mirror in the optical system. In this paper the root mean square (rms) error in phase compensation is calculated for a rather thick circular, initially flat mirror deformed by actuators. The inaccuracy in mirror deformations based on a simple thin plate model is evaluated by comparison with results obtained from a more elaborate model in which the mirror is treated as a solid of revolution discretized by means high-order isoparametric finite elements. It is found that for a given configuration of actuator positions, the actuator forces calculated with the two models differ as much as 25%, whereas the predicted rms phase compensation error differs by about 5%. Therefore, the computationally economical thin plate model is used in a parameter study to determine the optimum actuator configuration.