Acta Optica Sinica, Volume. 32, Issue 9, 922002(2012)
Description of Free-form Optical Curved Surface Using Two-Variable Orthogonal Polynomials
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.
Get Citation
Copy Citation Text
Wang Qingfeng, Cheng Dewen, Wang Yongtian. Description of Free-form Optical Curved Surface Using Two-Variable Orthogonal Polynomials[J]. Acta Optica Sinica, 2012, 32(9): 922002
Category: Optical Design and Fabrication
Received: Mar. 12, 2012
Accepted: --
Published Online: Jul. 9, 2012
The Author Email: Qingfeng Wang (qfwanglz@163.com)