Theoretical and numerical analysis of wavefront error caused by atmospheric turbulence through deformable mirrors

In the development process of satellite control systems and solar sensors, conventional solar simulators can't show variations in the solar shape and intensity in the state of solar occultation, so we set up a solar simulation and test platform. A method is put forward to simulate the wavefront error based on deformable mirror (DM). In this paper, the main relevant parameters which describe the atmospheric turbulence are introduced. The statistic characteristics of optical wavefront phase influenced by atmospheric turbulence are presented, and analyzed by the method of Zernike modes. A piezoelectric DM with 109 electrodes manufactured by OKO is used as the wavefront phase modulator. The important technology parameter about the deformable mirror is tested. Owing to the linear superposition, we have a research in the optical influence function and voltage deflection. The method of Karhunen-Loeve function is used in the simulation of optical wavefront, because it is statistically independent and can be expanded into the form of Zernike polynomials. We can get the coefficient matrix of random turbulence wavefront, and then link up with surface of the mirror. According to the relationship between deformation of the mirror and the voltage, we can deduce the voltage control matrix, and change the surface of the mirror as we conceive. The numerical results indicate that wavefront error can be introduced to the distribution maps of solar shape and intensity in different orbital position and any tangent point by DM in the light path.