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Zernike olivary polynomials for applications with olivary pupils

机译：Zernike多项式多项式，适用于有橄榄的学生

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摘要

Orthonormal polynomials have been extensively applied in optical image systems. One important optical pupil, which is widely processed in lateral shearing interferometers (LSI) and subaperture stitch tests (SST), is the overlap region of two circular wavefronts that are displaced from each other. We call it an olivary pupil. In this paper, the normalized process of an olivary pupil in a unit circle is first presented. Then, using a nonrecursive matrix method, Zernike olivary polynomials (ZOPs) are obtained. Previously, Zernike elliptical polynomials (ZEPs) have been considered as an approximation over an olivary pupil. We compare ZOPs with their ZEPs counterparts. Results show that they share the same components but are in different proportions. For some low-order aberrations such as defocus, coma, and spherical, the differences are considerable and may lead to deviations. Using a least-squares method to fit coefficient curves, we present a power-series expansion form for the first 15 ZOPs, which can be used conveniently with less than 0.1% error. The applications of ZOP are demonstrated in wave-front decomposition, LSI interferogram reconstruction, and SST overlap domain evaluation. (C) 2016 Optical Society of America
机译：正交多项式已广泛应用于光学图像系统。在横向剪切干涉仪（LSI）和子孔径针迹测试（SST）中广泛处理的一种重要的光学瞳孔是两个彼此偏移的圆形波阵面的重叠区域。我们称它为橄榄色学生。在本文中，首先介绍了一个单位圆中的一个椭圆形瞳孔的归一化过程。然后，使用非递归矩阵方法，获得Zernike多项式（ZOP）。以前，泽尼克（Zernike）椭圆多项式（ZEP）被认为是对橄榄瞳孔的近似值。我们将ZOP与他们的ZEP对等进行比较。结果表明，它们共享相同的成分，但比例不同。对于某些低阶像差，例如散焦，彗形像差和球面像差，差异很大，并且可能导致偏差。使用最小二乘法拟合系数曲线，我们给出了前15个ZOP的幂级数展开形式，可以方便地使用，误差小于0.1％。 ZOP的应用在波前分解，LSI干涉图重建和SST重叠域评估中得到了证明。 （C）2016美国眼镜学会

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