Improved difference model applied in the Fourier-transform-based integration method based on Taylor theory.

Abstract

The two-dimensional Fourier-transform-based integration algorithm is widely used in shape or wavefront reconstruction from gradients. However, its reconstruction accuracy is limited by the truncation error of the difference model. The truncation error is affected by the distribution of the sampling points. It increases when the sampling points are unevenly distributed and arranged irregularly. For improving, a novel way to calculate the difference is proposed based on Taylor expansion theory of binary functions. The first-order partial derivative terms are used to estimate the second- and third-order partial derivative terms for reducing the truncation error. The proposed difference model is applied to Fourier-transform-based integration. The reconstruction results show that it can get better results when the sampling points are irregularly distributed.