Wavefront response matrix for closed-loop adaptive optics system based on non-modulation pyramid wavefront sensor

Pyramid wavefront sensor (PWFS) is a kind of wavefront sensor with high spatial resolution and high energy utilization. In this paper an adaptive optics system with PWFS as wavefront sensor and liquid-crystal spatial light modulator (LC-SLM) as wavefront corrector is built in the laboratory. The wavefront response matrix is a key element in the close-loop operation. It can be obtained by measuring the real response to given aberrations, which is easily contaminated by noise and influenced by the inherent aberration in the optical system. A kind of analytic solution of response matrix is proposed, with which numerical simulation and experiment are also implemented to verify the performance of closed-loop correction of static aberration based on linear reconstruction theory. Results show that this AO system with the proposed matrix can work steadily in closed-loop operation.