任意形状孔径的干涉图像波面拟合的数学矢量模型

文中利用移相干涉术的特点提出了自动检测任意形状孔径中有干涉条纹区域的方法，测试中，当测试波前相对于参考滤前的光程差是照明波长的整数倍时形成干涉条纹，它此而形成的二维图就是干涉图像。干涉术是一种从干涉图像提取测试波面信息的光学测试技术，它包括对干涉图像的采样、条纹定级次和波面拟合三步。这里提出了一个对干涉图像拟合处理的线性代数矢量模型，应用线性代数矢量矩阵的知识详细地推导出了一种对干涉图像的处理带有一般性的矢量拟合公式，由最小二乘法逼近多项式拟合的相位值数据，用Ｇｒａｎ－Ｓｃｈｍｉｄｔ算法正交化处理多项式组，用反向替代法技术来求解最初多项式组的权因子系数。

Mathematical vector model for interferogram of arbitrary apertures of the fitting process

Based on phase\|shifting interferometry, the method can detect the interference fringes of interferogram. Fringes are formed when the optical difference (OPD) between a reference wave front and a test wave front based on the interference of light is an integral multiple of the illuminating wavelength. The resultant two\|dimensional fringes pattern is called an interferogram. Interferometry is an optical testing technique in which information of a test surface is extracted from an interferogram. This is accomplished through a three\|step process of sampling, ordering and fitting. A linear\|algebra vector notation is developed, which clearly and concisely describes the interferogram fitting process. The development is completely general. The approach performs a least\|squares fit of the phase data to the polynomial set, orthogonalizes this result with a Gram\|Schmidt algorithm, and solves for the final weighting coefficients of the initial polynomial set with a backsubstitution technique.