Description of free-form optical curved surface using two-variable orthogonal polynomials

Qingfeng Wang, Dewen Cheng*, Yongtian Wang

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

16 引用 (Scopus)

摘要

The orthogonal polynomials of two variables are generated on the unit circle and unit square, and a detailed analysis of the free-form fitting precision is carried out using the orthogonal polynomials with three different sampling grids, which are uniformly pseudo-random grid, array grid and circular grid. To ensure the universality of the fitting analysis, many experiments are conducted on rotationally symmetric aspheric surfaces, free-form surfaces and Peaks free-form surfaces. According to the experiments, among the three sampling grids, the array sampling grid is suitable for most fitting situations. XY-polynomial and orthogonal XY-polynomial give better fitting precision than other surface types in most cases on the wave-front fitting, the orthogonal Zernike polynomial has advantage in circle or square domain and orthogonal Chebyshev is the best polynomial when fitting is required on a square domain using the array sampling grid.

源语言英语
文章编号0922002
期刊Guangxue Xuebao/Acta Optica Sinica
32
9
DOI
出版状态已出版 - 9月 2012

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Wang, Q., Cheng, D., & Wang, Y. (2012). Description of free-form optical curved surface using two-variable orthogonal polynomials. Guangxue Xuebao/Acta Optica Sinica, 32(9), 文章 0922002. https://doi.org/10.3788/AOS201232.0922002