Earth observation satellite with a large mirror telescope has been studied in Japan Aerospace Exploration Agency to offer a fine ground sampling distance from geostationary orbit. Our latest optical design has a 3.6-m primary mirror and thus aims to obtain a ground sampling distance of sub-10 m from an altitude of 36,000 km at visible wavelengths. To achieve diffraction-limited performance in such optics on orbit, the telescope equips with not only actuators to control primary and secondary mirrors but also a deformable mirror (DM) at the exit pupil plane for the fine phasing. For on-orbit wavefront correction with a deformable mirror, a wavefront sensorless image-based aberration correction scheme is advantageous from the viewpoint of severely limited hardware resources in satellites. Phase diversity (PD) and stochastic parallel gradient descent (SPGD) optimization are known for promising image-based approaches. The former is model-based and thus the estimation accuracy of wavefront aberration significantly depends on the model accuracy, while the other requires many measurements to compensate for large aberration. To alleviate these issues, we propose sequential use of PD and SPGD optimization to efficiently reduce wavefront correction. We first developed an optical testbed with an incoherent light source, a MEMS DM, and extended image targets, and then a wavefront correction experiment was carried out. As a result, the proposed method successfully achieved diffraction-limited imaging performance with a small number of measurements. We will also discuss the image dependence of the wavefront correction performance.
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