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Sheared-beam imaging (SBI) is an effective way of imaging through turbulent medium, such as atmosphere or scattering liquid. Traditionally, the imaging is based on the laser transmitter array consisting of three beams or five beams for coherent illumination to the remote object. Compared with the existing SBI methods, the four-beam sparse sampling imaging method has been proposed, which may have more advantages; it not only sparses the detector elements but also reduces the number of emitted beams. However, the traditional phase retrieval algorithms are not suitable for the four-beam sparse sampling imaging. We propose a four-beam sparse phase retrieval (F-BSPR) algorithm, which uses the phase differences from both horizontal and vertical components and the phase differences from other components when the phase is retrieving. The proposed phase retrieval algorithm can better connect the phase difference and improve the accuracy of the phase retrieval. Furthermore, the imaging quality is improved. Simulation and experimental results show that the proposed algorithm is effective and feasible when the number of detector elements is sparse by 50%. Compared to the traditional four-beam phase retrieval method, the proposed F-BSPR method has better imaging quality and robustness. [ABSTRACT FROM AUTHOR]

In the field of the active wavefront correction for off-axis telescopes, the sensitivity matrix and damped least squares method are widely employed to calculate the misalignment. Improper selection of the damping coefficient will lead to bad wavefront correction results. Moreover, the calculated misalignment is referenced on the optical coordinate system, which cannot be directly applied as the control quantity. The article has two innovative points to solve these problems. First, an adaptive damping least squares method is proposed. The method considers the mirror surface error, uses Python + Zemax cosimulation to perform closed-loop reverse verification, and selects the optimal damping coefficient. Simulation is carried out for verification. Second, the article deduces the mathematical relationship between the calculated misalignment and the mechanism control quantity. Based on the above research, the wavefront active correction experiment has been completed. The optical component is actively adjusted with the wavefront quickly converging to RMS = 0. 055λ @ 632. 8 nm. The results verify the correctness of the proposed method. [ABSTRACT FROM AUTHOR]