Evans C J, Kestner R N
Appl Opt. 1996 Mar 1;35(7):1015-21. doi: 10.1364/AO.35.001015.
Wave-front or surface errors may be divided into rotationally symmetric and nonrotationally symmetric terms. It is shown that if either the test part or the reference surface in an interferometric test is rotated to N equally spaced positions about the optical axis and the resulting wave fronts are averaged, then errors in the rotated member with angular orders that are not integer multiples of the number of positions will be removed. Thus if the test piece is rotated to N equally spaced positions and the data rotated back to a common orientation in software, all nonrotationally symmetric errors of the interferometer except those of angular order kNθ are completely removed. It is also shown how this method may be applied in an absolute test, giving both rotationally symmetric and nonsymmetric components of the surface. A general proof is given that assumes only that the surface or wave-front information can be described by some arbitrary set of orthognal polynomials in a radial coordinate r and terms in sin θ and cos θ. A simulation, using Zernike polynomials, is also presented.
波前或表面误差可分为旋转对称项和非旋转对称项。结果表明，如果在干涉测量中测试部件或参考表面绕光轴旋转到N个等间距位置，并对所得波前进行平均，那么旋转部件中角阶数不是位置数整数倍的误差将被消除。因此，如果将测试件旋转到N个等间距位置，并在软件中将数据旋转回共同方向，则干涉仪中除角阶数为kNθ的误差外，所有非旋转对称误差都将被完全消除。文中还展示了该方法如何应用于绝对测试，给出表面的旋转对称和非对称分量。给出了一个一般性证明，该证明仅假设表面或波前信息可以用径向坐标r以及sinθ和cosθ项中的一些任意正交多项式集来描述。还给出了使用泽尼克多项式的模拟。
