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Yi Zheng, Shanshan Sun, and Ying Li
Yi Zheng,1,2 Shanshan Sun,1,3,* and Ying Li1,2
1National Astronomical Observatories/Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China
2Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, China
3University of Chinese Academy of Sciences, Beijing 100049, China
*Corresponding author: sssun@niaot.ac.cn
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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 wavefront decomposition, LSI interferogram reconstruction, and SST overlap domain evaluation.
© 2016 Optical Society of America
4 May 2016: Corrections were made to Refs.6, 16, 17, and 20–23.
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Orthonormal Zernike Circle Polynomials Z j ( ρ , θ )
Orthonormal Vertical Elliptical Polynomials in Terms of Zernike Circle Polynomials
Zernike Olivary Polynomials in Terms of Zernike Circle Polynomials
Zernike Olivary Polynomials Coefficient Functions ( 0.20 ≤ b ≤ 1.00 ) (Error- Ratio < 0.1 % )
ZOPs Coefficients and Corresponding ZEPs Coefficients When an Olivary Wavefront with an Aspect Ratio b = 0.8 is Fitted with a Different Number of Polynomials j Showing the Independence of the Former but Dependence of the Latter on j a