Enhancing wavefront estimation accuracy by using higher-order iterative compensations in the Southwell configuration

Abstract

Accurate wavefront integration based on gradient fields is crucial for various indirect measurement techniques, such as Shack-Hartmann sensing, shearography, and the fringe reflection technique. In this paper, a higher-order iterative compensation algorithm is proposed to enhance the reconstruction accuracy for the finite-difference-based least-squares integration (FLI) method. In this method, higher-order gradient fields are reconstructed and the calculated residual gradient fields compensate the truncation error with the traditional FLI by iterations. A comparison of different FLI methods, including traditional FLI, iterative FLI, higher-order FLI, and the proposed FLI method, is conducted. The result shows that the reconstructed wavefront with the proposed method is more accurate than those with other FLI methods. In addition, the impact of the gradient measurement noise is also discussed.

Wavefront measurement of a multilens optical system based on phase measuring deflectometry

“…From Eq. ( 1), the wavefront can be obtained by numerical integration [1,12,13] . The solutions of parameters x 2 , B, and x 1 in Eq.…”

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

“…Li et al proposed an optimized reconstruction method by using high-order numerical differentiation formats [ 77 ]. Guang et al presented a higher-order iterative finite-difference-based least-squares integration (HIFLI) method to improve the accuracy and convergence rate of shape reconstruction [ 78 ]. The HIFLI method is a hybrid of the iterative finite-difference-based least-squares integration (IFLI) method and a higher-order gradient reconstruction method.…”