Centroids analysis for circle of confusion in reverse Hartmann test

Zhu Zhao(赵柱), Mei Hui(惠梅), Zheng-Zheng Xia(夏峥铮), Yue-Jin Zhao(赵跃进)

1 Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, Beijing 100081, China; 2 School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

Centroids analysis for circle of confusion in reverse Hartmann test

Zhu Zhao(赵柱)^{1,2}, Mei Hui(惠梅)^{1,2}, Zheng-Zheng Xia(夏峥铮)^{1,2}, Yue-Jin Zhao(赵跃进)^{1,2}

1 Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, Beijing 100081, China; 2 School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

摘要 The point spread function (PSF) is investigated in order to study the centroids algorithm in a reverse Hartmann test (RHT) system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion (CoC) and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional (2D) Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional (1D) Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson's correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error (RMSE) by nearly one order of magnitude, thus achieving an accuracy of ～0.01 pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method.

Abstract：The point spread function (PSF) is investigated in order to study the centroids algorithm in a reverse Hartmann test (RHT) system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion (CoC) and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional (2D) Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional (1D) Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson's correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error (RMSE) by nearly one order of magnitude, thus achieving an accuracy of ～0.01 pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method.

基金资助:Project supported by the National Natural Science Foundation of China (Grant No. 61475018).

通讯作者:
Mei Hui
E-mail: huim@bit.edu.cn

引用本文:

赵柱, 惠梅, 夏峥铮, 赵跃进. Centroids analysis for circle of confusion in reverse Hartmann test[J]. 中国物理B, 2017, 26(5): 50204-050204.
Zhu Zhao, Mei Hui, Zheng-Zheng Xia, Yue-Jin Zhao. Centroids analysis for circle of confusion in reverse Hartmann test. Chin. Phys. B, 2017, 26(5): 50204-050204.