剪切干涉测量中基于Zernike多项式的自适应波前重建

提出一种剪切干涉测量中被测波前重建的新方法，该方法基于Zernike多项式最小二乘拟合的基本原理，通过自适应的方式来确定波前重建表达式。推导出剪切相位Zernike多项式系数与被测波前Zernike多项式系数的直接转换矩阵，提出了自适应确定多项式级次的新算法，给出了相应的波前重建数学模型。对算法进行了计算机模拟，并应用于实际剪切干涉测量，结果证明该方法具有可靠的波前重建精度。

A Zernike Polynomial Based Adaptive Wavefront Reconstruction Method for Lateral Shearing Interferometry

To solve the problem involved in the shearing interferometry that the wavefronts are not directly reflected in the interferograms, an accurate reconstruction algorithm and procedure will be required. Utilizing the first order derivatives of the surface under measurement, an adaptive algorithm and a reconstruction procedure are proposed for such purpose together with the relevant models. The algorithm is based on the least squares principle and the Zernike polynomials. A direct transformation between the coefficients for the tests wavefront and the ones for the shearing phase is proposed. Computational and experimental tests show the proposed algorithm and the models are effective and accurate.