Fast and Highly Accurate Zonal Wavefront Reconstruction from Multi-Directional Slope and Curvature Information Using Subregion Cancelation

The wavefront reconstruction is a crucial step in determining the performance of wavefront detection instruments. The wavefront reconstruction algorithm is primarily evaluated in three dimensions: accuracy, speed, and noise immunity. In this paper, we propose a hybrid zonal reconstruction algorithm that introduces slope and curvature information in the diagonal, anti-diagonal, horizontal, and vertical directions by dividing the neighbor sampling points into subregions in groups of four. By canceling the same parameters in integration equations, an algorithm using multi-directional slope–curvature information is achieved with only two sets of integration equations in each subregion, reducing the processing time. Simulation experiments show that the relative root-mean-square reconstruction error of this algorithm is improved by about 4 orders of magnitude compared with existing algorithms that use multi-directional slope information or slope–curvature information alone. Compared with the hybrid multi-directional slope–curvature algorithm, the proposed algorithm can reduce computation time by about 50% as well as provide better noise immunity and reconstruction accuracy. Finally, the validity of the proposed algorithm is verified by the null test experiment.