Wavefront compensation based on stochastic parallel gradient descent algorithm for Earth observation telescope

Wavefront compensation techniques that do not require wavefront sensors are demanded in the on-orbit telescopes on Earth observation satellites. This is especially true for segmented or sparse aperture telescopes that could realize unprecedented high angular resolution. A promising wavefront sensorless approach is the stochastic parallel gradient descent (SPGD) algorithm. The wavefront correction by the SPGD optimization relies only on the intensity data in the acquired image. However, many previous observation targets are point light sources, not the extended ground scenes generally acquired by Earth observation satellites. This paper derives an efficient wavefront control method for imaging systems for the fast SPGD optimization. Wavefront compensation has been demonstrated by experiment on extended objects in single aperture optics, in which a microelectrome- chanical system deformable mirror controls the wavefront. Subsequent numerical simulations are reported for multi-aperture imaging systems. The paper also discuses a method to reduce the computational cost of SPGD optimization.