Influence function is one of the most important parameters for the correction of aberrations with deformable mirrors. When deformable mirrors are loaded with laser irradiation, the influence function will be affected by the heat-induced thermoelastic deformation, which would lower the aberration correction ability and effectiveness. On occasions when they are applied in laser systems, the influence of laser-induced thermoelastic deformation is significant, it would cause a considerable change in the influence function. We have analyzed the changes in the surface shape of a 37-element deformable mirror caused by laser induced thermoelastic deformation, and calculated the changes of influence function. The dependence of influence function on the arrangement of actuators, material properties of the actuators and the base and the heat flux is analyzed, with the actuator layout being square and hexagonal, different material properties and the heat flux varied from 0.005W/mm<sup>2</sup> to 0.01W/mm<sup>2</sup>, using the finite element method. The results indicate that all of the previous factors will affect the influence function. Thus, in order to reduce the change of influence function caused by laser induced surface shape, the material and parameters of the deformable mirror should be chosen carefully.
Laser-induced static surface shape changes of deformable mirrors will cause difficulties for beam control of the laser system. The overall peak and valley (PV) value of the deformable mirror (DM) will reach the scale of micrometer when irradiated by high power lasers. We have investigated changes in the static surface shape of a 37-element DM caused by laser-induced thermoelastic deformation. It is found that the laser-induced profile change of the mirror shows a high-order characteristic. In this paper the finite element method is used to analyze the surface shape of the DM when it is irradiated by high power lasers. The surface shape is fitted using the Zernike polynomials and the influence functions to see the characteristic of it and the DM’s ability to compensate it. The fitting results show that the lower-order aberrations can be corrected by the DM itself with the cost of a reduced ability of aberration correction, as the available amount of stroke will decrease. In addition, changes of the influence functions are simulated and the modified influence functions are calculated. Furthermore, the performances of the DM in three different situations are simulated to reveal the impact of thermoelastic deformation on the DM’s aberration correcting ability.