NIAOT OpenIR  > 中国科学院南京天文光学技术研究所  > 期刊论文
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
Source PublicationOptics Express
Volume27Issue:26Pages:37180-37196
Abstract
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.
Subject Area天文技术与方法
Language英语
WOS IDWOS:000507254300008
Citation statistics
Cited Times:0[WOS]
Document Type期刊论文
Identifierhttp://ir.niaot.ac.cn/handle/114a32/1669
Collection中国科学院南京天文光学技术研究所_期刊论文
大口径光学技术研究室_期刊论文
Affiliation1.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
Recommended Citation
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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