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Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering
Zheng Y(郑奕)1,2; Wei K(魏凯)1,3; Liang B(梁斌)1,2; Li Y(李颖)1,2; Chu XH(褚鑫辉)1,3
2019-12
发表期刊Optics Express
卷号27期号:26页码:37180-37196
摘要
Zernike circular polynomials (ZCP) are widely used in optical testing, fabrication and adaptive optics. However, their ability to characterize information on spherical cap is often
limited by aperture angle, with highly curved surface being particularly challenging. In this study,we propose a simple and systematic process to derive Zernike like functions that are applicable to all types of spherical cap. The analytical expressions of three function sets are calculated using Gram-Schmidt algorithm. They are hemispherical harmonics (HSH), Zernike spherical function (ZSF) and longitudinal spherical function (LSF). HSH satisfies Laplacian equation and composes a subset of spherical harmonics (SH). ZSF and LSF can be applied to arbitrary spherical cap and their orthogonality is invariant to aperture. The achieved functions, with their complete and orthogonal performance, can serve as essential tools for surface characterization required for a wide range of applications like large-angle lenses description in illumination design,aberration analysis in high aperture systems, human cornea measurement fitting, geomagnetic field modelling, etc. Moreover, they are important for graphics rendering in virtual reality and games by solving the reflectance equation efficiently.
学科领域天文技术与方法
语种英语
WOS记录号WOS:000507254300008
引用统计
被引频次:4[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.niaot.ac.cn/handle/114a32/1669
专题期刊论文
作者单位1.南京天文光学技术研究所
2.天文光学技术重点实验室
3.中国科学院大学
推荐引用方式
GB/T 7714
Zheng Y,Wei K,Liang B,et al. Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering[J]. Optics Express,2019,27(26):37180-37196.
APA Zheng Y,Wei K,Liang B,Li Y,&Chu XH.(2019).Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering.Optics Express,27(26),37180-37196.
MLA Zheng Y,et al."Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering".Optics Express 27.26(2019):37180-37196.
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