A B-spline based fast wavefront reconstruction algorithm

Chen Hao; Wei Ling; Li Ende; He Yi; Yang Jinsheng; Li Xiqi; Fan Xinlong; Yang Zeping; Zhang Yudong

doi:10.12086/oee.2021.200160

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Chen H, Wei L, Li E D, et al. A B-spline based fast wavefront reconstruction algorithm[J]. Opto-Electron Eng, 2021, 48(2): 200160. doi: 10.12086/oee.2021.200160

Citation:

Chen H, Wei L, Li E D, et al. A B-spline based fast wavefront reconstruction algorithm[J]. Opto-Electron Eng, 2021, 48(2): 200160. doi: 10.12086/oee.2021.200160

A B-spline based fast wavefront reconstruction algorithm

1.
Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
2.
College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Jiangsu Key Laboratory of Medical Optics, Suzhou, Jiangsu 215163, China
4.
Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, Jiangsu 215163, China

Fund Project: National Natural Science Foundation of China (61605210, 61675226, 61378090), the National Instrumentation Program (2012YQ120080), and the National Key Research and Development Program of China (2016YFC0102500, 2017YFB0403700)

More Information

Corresponding author: Chen Hao, E-mail: chenhao114@mails.ucas.ac.cn

Received Date 11 May 2020

Revised Date 26 August 2020

Published Date 15 February 2021

Abstract

Abstract

Traditional schemes for Shack-Hartmann wavefront reconstruction can be classified into zonal and modal methods. The zonal methods are good at reconstructing the local details of the wavefront, but are sensitive to the noise in the slope data. The modal methods are much more robust to the noise, but they have limited capability of recovering the local details of the wavefront. In this paper, a B-spline based fast wavefront reconstruction algorithm in which the wavefront is expanded to the linear combination of bi-variable B-spline curved surfaces is proposed. Then, a method based on successive over relaxation (SOR) algorithm is proposed to fast reconstruct the wavefront. Experimental results show that the proposed algorithm can recover the local details of the wavefront as good as the zonal methods, while is much more robust to the slope noise.
- B-spline function /
- wavefront reconstruction /
- Hartmann wavefront sensor

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References

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Overview

Overview

Overview: Reconstructing wavefront from sampled slopes is the key to the slope sampling wavefront sensors, such as the Shack-Hartmann wavefront sensors and the pyramid wavefront sensors. Traditional reconstruction schemes can be classified into zonal and modal methods. The zonal methods reconstruct the wavefront by solving the slope differential-based least squares problem, in which the slopes are related to the wavefront data sampled in a predefined grid. These methods are good at reconstructing the local details of the wavefront, but are sensitive to the noise in the slope data. Besides, as it can only calculate the wavefront data in the grid, interpolation methods are needed to retrieve the wavefront data of higher spatial resolution, which may introduce additional error. The modal methods expand the wavefront to the linear combination of orthogonal polynomials, such as Zernike polynomials for the radical pupil and Legendre polynomials for the rectangle pupil. These methods are much more robust to the noise, but they have limited ability in recovering the local details of the wavefront. Hence, more polynomials are needed to recover the local details, but it will make the reconstruction process more ill-posed at the same time.

In this paper, a B-spline based fast wavefront reconstruction algorithm is proposed. The wavefront is expanded to the linear combination of bi-variable B-spline curved surfaces first. Then the reconstruction problem is converted from the least-mean squares of slopes to a Poisson problem, in which only the theoretical divergence and the measured divergence are utilized. The theoretical divergence can be calculated efficiently by the integration of divergences of the related B-spline bases, and the measured divergence can be easily estimated by the Taylor expanding of the local slopes. Then, the Poisson problem can be efficiently solved by employing successive over relaxation (SOR) method.

To evaluate the performance of the proposed method, an experiment of measuring the influence functions of the actuators of a piezoelectric deformed mirror is performed. Experimental results show that the proposed algorithm can recover the local details of the wavefront as good as the zonal methods, while is much more robust to the slope noise. Besides, thanks to the analytic solution of wavefront, it can retrieve the high spatial resolution data directly. As the proposed method separates the theory divergence calculation of the B-spline bases from the slopes, it can be easily extended to other reconstruction problems with different orders and control knots of B-spline surfaces utilized. Last but not least, the ability of recovering the local details and robustness to slope noise can be easily balanced by changing the layout of the knot and the calculation area of divergence estimation.