The piston error recognition technique used in the modified Shack–Hartmann sensor

Segmented telescopes and multi-aperture telescopes are effective ways to realize high-resolution observations in astronomy. An important work for the high-resolution observations with segmented telescopes and multi-aperture telescopes is phasing the multiple segmented mirrors or sub-apertures. Modified Shack–Hartmann sensor is proposed for piston error detection. The signal of the modified Shack–Hartmann sensor is the interference pattern created by a lens placed across two adjacent pupils in the exit pupil plane. The information of piston error is encoded in the interference pattern. Many methods are proposed to extract piston error from the interference pattern. In this paper, three existing piston error extraction methods are introduced and reproduced. The influence of the offset of the lens in modified Shack–Hartmann​ sensor on the three methods is analyzed. The offset lens causes the three methods failed in high accuracy piston error detection. We propose a piston error recognition technique based on phase retrieval technology to resolve the problem caused by the offset lens. The proposed piston error recognition technique can recognize not only the piston error but also the offset value of the lens. Therefore, the proposed technique can also be used to debug the modified Shack–Hartmann sensor. By means of simulations we show that the proposed method shows improved performance and it works well in noise and sub-pupil aberration situations. • Three existing piston error extraction methods used in the modified Shack–Hartmann sensor are introduced, analyzed and reproduced. • Simulation and comparison of three existing piston error extraction methods under ideal and offset lens situations are conducted respectively. • The influence of the offset of the lens in modified Shack–Hartmann sensor on the three existing methods is analyzed. From the theoretical analysis and simulation results, it is proved that the offset lens causes the three methods failed in high accuracy piston error detection. • A piston error recognition technique based on phase retrieval technology to resolve the problem caused by the offset lens is proposed. The proposed piston error recognition technique can recognize not only the piston error but also the offset value of the lens. • The proposed method is compared with the existing methods through simulation and the results show that the proposed method shows improved performance and it works well in noise and sub-pupil aberration situations.