Four-beam sparse phase retrieval algorithm for sheared-beam imaging

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.