Hernández-Gómez Geovanni, Malacara-Doblado Daniel, Malacara-Hernández Zacarías, Malacara-Hernández Daniel
Appl Opt. 2014 Nov 1;53(31):7422-34. doi: 10.1364/AO.53.007422.
Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. Frequently, a least squares fit of the transverse aberrations in the x direction and a least squares fit of the transverse aberrations in the y direction is performed to obtain the wavefront. In this work, we briefly describe a modal method to integrate Hartmann and Shack-Hartmann patterns by means of a single least squares fit of the transverse aberrations simultaneously instead of the traditional x-y separate method. The proposed method uses monomial calculation instead of using Zernike polynomials, to simplify numerical calculations. Later, a method is proposed to convert from monomials to Zernike polynomials. An important obtained result is that if polar coordinates are used, angular transverse aberrations are not actually needed to obtain all wavefront coefficients.
哈特曼测试和夏克 - 哈特曼测试测量的是波前斜率，而非波前变形，波前斜率等同于光线横向像差。文献中描述了许多积分方法，用于从这些测量结果中获取波前变形。基本上，它们可分为两类，即模态法和区域法。通常，会分别对x方向的横向像差进行最小二乘拟合以及对y方向的横向像差进行最小二乘拟合，以获得波前。在这项工作中，我们简要描述一种模态方法，通过对横向像差进行单次同时最小二乘拟合来整合哈特曼和夏克 - 哈特曼图案，而不是采用传统的x - y分别拟合方法。所提出的方法使用单项式计算而非泽尼克多项式，以简化数值计算。随后，提出了一种从单项式转换为泽尼克多项式的方法。一个重要的结果是，如果使用极坐标，实际上并不需要角向横向像差来获得所有波前系数。
