Wavefront reconstruction in square region based on improved two-dimension Legendre polynomials

Zhen Wu; Zhilin Xia; Xuyu Li; Qing Lu; Chaoyang Wei; Jianda Shao

doi:10.1117/12.2506234

18 January 2019 Wavefront reconstruction in square region based on improved two-dimension Legendre polynomials

Zhen Wu, Zhilin Xia, Xuyu Li, Qing Lu, Chaoyang Wei, Jianda Shao

Proceedings Volume 10839, 9th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test, Measurement Technology, and Equipment; 1083915 (2019) https://doi.org/10.1117/12.2506234
Event: Ninth International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT2018), 2018, Chengdu, China

Abstract

In optical testing, such as the fringe reflection technology and Shack-Hartman wavefront sensor technology, slope of a surface is measured instead, from which the faithful surface of the test optic is obtained. Therefore, a gradient data-based wavefront reconstruction is needed. This paper shows the use of the Gram-Schmidt process for orthonormalizing the gradients of the two-dimensional Legendre polynomials. After a set of orthonormalized vector polynomials is generated in a square region, these polynomials can be used to fit the gradient data in the region. By a simple linear transformation, the fitting coefficients can be derived and transformed to the wavefront description of the two-dimension Legendre polynomials, and the wavefront and primary aberration are then obtained. Based on the zonal method, this can effectively reconstruct the high-frequency component by fitting the difference of the high-frequency error, which cannot be done by polynomial fitting. According to the computer simulation, this algorithm can primely realize the reconstruction of wavefront.

Citation Download Citation

Zhen Wu, Zhilin Xia, Xuyu Li, Qing Lu, Chaoyang Wei, and Jianda Shao "Wavefront reconstruction in square region based on improved two-dimension Legendre polynomials", Proc. SPIE 10839, 9th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test, Measurement Technology, and Equipment, 1083915 (18 January 2019); https://doi.org/10.1117/12.2506234

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