Description of complex optical surface based on sparse radial basis function approximation with spatially variable shape parameters

Xiangdong Zhou; Jian Bai; Xiao Huang; Lei Zhao; Chen Wang; Yujie Luo

doi:10.1117/12.2506450

30 January 2019 Description of complex optical surface based on sparse radial basis function approximation with spatially variable shape parameters

Xiangdong Zhou, Jian Bai, Xiao Huang, Lei Zhao, Chen Wang, Yujie Luo

Author Affiliations +

Proceedings Volume 10841, 9th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Meta-Surface-Wave and Planar Optics; 108410O (2019) https://doi.org/10.1117/12.2506450
Event: Ninth International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT2018), 2018, Chengdu, China

Abstract

It is necessary to fit the discrete sampling value of the optical element surface obtained by measuring equipment, because the results of fitting are useful for manufacturing and optical design. The commonly used fitting methods are X-Y polynomial approximation, Zernike polynomial approximation and radial basis function (RBF) approximation. Compared with others, radial basis function is more suitable to fit the complex optical surface. However, the further improvement of fitting accuracy and cost are limited by the fixed shape parameter of the classic RBF approximation. In this paper, we propose the sparse radial basis function approximation with spatially variable shape parameters to fit discretely sampled optical surfaces. Our main purpose is to improve fitting accuracy and to reduce computational cost. Then, we analyze the impact of the spatial distribution of RBF nodes on fitting. Finally, we compare the accuracy and cost between the classic RBF approximation and the sparse RBF approximation with spatially variable shape parameters by fitting various complex surface.

Citation Download Citation

Xiangdong Zhou, Jian Bai, Xiao Huang, Lei Zhao, Chen Wang, and Yujie Luo "Description of complex optical surface based on sparse radial basis function approximation with spatially variable shape parameters", Proc. SPIE 10841, 9th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Meta-Surface-Wave and Planar Optics, 108410O (30 January 2019); https://doi.org/10.1117/12.2506450

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available