Kewei E, Zhang Chen, Li Mengyang, Xiong Zhao, Li Dahai
Opt Express. 2015 Aug 10;23(16):20267-79. doi: 10.1364/OE.23.020267.
Based on the Legendre polynomials expressions and its properties, this article proposes a new approach to reconstruct the distorted wavefront under test of a laser beam over square area from the phase difference data obtained by a RSI system. And the result of simulation and experimental results verifies the reliability of the method proposed in this paper. The formula of the error propagation coefficients is deduced when the phase difference data of overlapping area contain noise randomly. The matrix T which can be used to evaluate the impact of high-orders Legendre polynomial terms on the outcomes of the low-order terms due to mode aliasing is proposed, and the magnitude of impact can be estimated by calculating the F norm of the T. In addition, the relationship between ratio shear, sampling points, terms of polynomials and noise propagation coefficients, and the relationship between ratio shear, sampling points and norms of the T matrix are both analyzed, respectively. Those research results can provide an optimization design way for radial shearing interferometry system with the theoretical reference and instruction.
基于勒让德多项式表达式及其性质，本文提出了一种新方法，可根据RSI系统获得的相位差数据，对方形区域上激光束的被测畸变波前进行重构。仿真结果和实验结果验证了本文所提方法的可靠性。推导了重叠区域相位差数据随机含有噪声时的误差传播系数公式。提出了矩阵T，用于评估由于模式混叠高阶勒让德多项式项对低阶项结果的影响，其影响大小可通过计算T的F范数来估计。此外，分别分析了剪切比、采样点、多项式项数与噪声传播系数之间的关系，以及剪切比、采样点与T矩阵范数之间的关系。这些研究结果可为径向剪切干涉测量系统提供一种优化设计方法，具有理论参考和指导意义。
