Hybrid wavefront reconstruction from multi-directional slope and full curvature measurements using integral equations with higher-order truncation errors for wavefront sensors

Wavefront reconstruction is one of the most important steps in zonal wavefront sensors and has great influence on measurement accuracy. An improved hybrid wavefront reconstruction algorithm that adds two diagonal slope and curvature values at each grid point is proposed to improve reconstruction accuracy and noise immunity. Hybrid reconstruction equations with smaller truncation errors in diagonal and anti-diagonal directions are deduced. Furthermore, multi-directional hybrid reconstruction equations incorporating vertical, horizontal, diagonal and anti-diagonal directions are also formulated. Numerical experiments show that the relative reconstruction errors of the proposed algorithms are reduced by about four orders of magnitude compared with the existing hybrid reconstruction algorithm with noise ignored. Considering the measurement noise, the proposed algorithms have better noise immunity and reconstruction accuracy, especially for the reconstruction of high-order aberrations.