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The Shack-Hartmann wavefront sensor (SHWFS) is an optical detection device based on the measurements of wavefront slopes. It is widely used in an adaptive optics system due to its simple structure and strong environment adaptability. The measuring accuracy of the SHWFS depends mainly on the accuracy of the spot image centroid in each sub-aperture. There are many centroid algorithms including the center of gravity algorithm, Gauss fitting algorithm, and correlation algorithm. As to the simplicity, robustness, high accuracy and stability, the center of gravity algorithm is more widely used. However, the accuracy of gravity algorithm is sensitive to the noise including discretization, aliasing, photon noise, readout noise, stray light, and direct current bias. To improve the accuracy of centroid, the output signals of SHWFS must be pre-processed to suppress the noise effect by using the method of thresholding in general. Many threshold methods have been presented to reduce the error of centroid and there theoretically exists an optimum threshold which causes the minimum error of centroid based on the characteristics of SHWFS and noise. However, it is difficult to separate the signals from the noises, and the optimum threshold cannot be estimated accurately in real time in the SHWFS systems. In this paper aiming at noises in SHWFS, which vary with time and space rapidly, a method based on the noise weighted function of the mean value of pixels and the local gradient direction of image signals in the moving windows is presented according to the characteristics of the Gaussian spot and noise distributions. Moreover, the theory and parameters determination of the method are analyzed. The method utilizes the probability that the pixels in the moving windows belong to the noise, and the probability is inversely proportional to the mean value of pixels and the local gradient direction of image signals, and so the monotonically reducing probability function of pixels is constructed. Finally, the standard deviation and mean value of noise can be obtained, and the estimation value of optimum threshold is equal to the mean value of noise plus three times the standard deviation of noise. To investigate the effects of the optimum threshold estimation with the different spot sizes, spot strengths and noise levels, the proposed algorithm is compared with traditional methods. The simulation and experimental results show that the proposed method could achieve higher accuracy, and the error between the threshold obtained by the method presented in this paper and theoretical optimum threshold is less than 10%, which is less than those from the traditional methods.
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Keywords:
- Shack-Hartmann wavefront sensor /
- Gaussian spot /
- optimum thresh /
- weighted function
[1] Li J, Gong Y, Hu X R, Li C C 2014 Chin. J. Laser 41 0316002 (in Chinese) [李晶, 巩岩, 呼新荣, 李春才 2014 中国激光 41 0316002]
[2] Baik S H, Park S K, Kim C J, Cha B 2007 Opt. Laser Technol. 39 262
[3] Zhu Z Y, Li D Y, Hu L F, Mu Q Q, Yang C L, Cao Z L, Xuan L 2016 Chin. Phys. B 25 090702
[4] Gao C Q, Gao M W, Weber H 2004 Chin. Phys. Lett. 21 2191
[5] Wei L, Shi G H, Lu J, Yang J S, Li X Q, Zhang Y D 2013 J. Opt. 15 055702
[6] Chen L H, Rao C H 2011 Acta Phys. Sin. 60 090701 (in Chinese) [陈林辉, 饶长辉 2011 60 090701]
[7] Li C H, Xian H, Jiang W H, Rao C H 2007 Acta Phys. Sin. 56 4289 (in Chinese) [李超宏, 鲜浩, 姜文汉, 饶长辉 2007 56 4289]
[8] Ares J, Arines J 2001 Opt. Lett. 26 1831
[9] Ma X Y, Rao C H, Zheng H Q 2009 Opt. Express 17 8525
[10] Liang C, Liao W H, Shen J X, Zhou Y 2009 Chin. J. Laser 36 430 (in Chinese) [梁春, 廖文和, 沈建新, 周宇 2009 中国激光 36 430]
[11] Ren J F, Rao C H, Li M Q 2002 Opto-Electron. Eng. 29 1 (in Chinese) [任剑峰, 饶长辉, 李明全 2002 光电工程 29 1]
[12] Thatiparthi C, Ommanib A, Burmanc R, Thapa D, Hutchings N, Lakshminarayanan V 2016 Proc. SPIE 9693 969321
[13] Thomas S 2004 Proc. SPIE 5490 1238
[14] Nightingale A M, Gordeyev S 2013 Opt. Eng. 52 071413
[15] Shen F, Jiang W H 1999 High Power Laser and Particle Beams 11 27 (in Chinese) [沈锋, 姜文汉 1999 强激光与粒子束 11 27]
[16] Li Y K, Zhang J Z, Zhang F Z 2014 Proc. SPIE 9242 92421V
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[1] Li J, Gong Y, Hu X R, Li C C 2014 Chin. J. Laser 41 0316002 (in Chinese) [李晶, 巩岩, 呼新荣, 李春才 2014 中国激光 41 0316002]
[2] Baik S H, Park S K, Kim C J, Cha B 2007 Opt. Laser Technol. 39 262
[3] Zhu Z Y, Li D Y, Hu L F, Mu Q Q, Yang C L, Cao Z L, Xuan L 2016 Chin. Phys. B 25 090702
[4] Gao C Q, Gao M W, Weber H 2004 Chin. Phys. Lett. 21 2191
[5] Wei L, Shi G H, Lu J, Yang J S, Li X Q, Zhang Y D 2013 J. Opt. 15 055702
[6] Chen L H, Rao C H 2011 Acta Phys. Sin. 60 090701 (in Chinese) [陈林辉, 饶长辉 2011 60 090701]
[7] Li C H, Xian H, Jiang W H, Rao C H 2007 Acta Phys. Sin. 56 4289 (in Chinese) [李超宏, 鲜浩, 姜文汉, 饶长辉 2007 56 4289]
[8] Ares J, Arines J 2001 Opt. Lett. 26 1831
[9] Ma X Y, Rao C H, Zheng H Q 2009 Opt. Express 17 8525
[10] Liang C, Liao W H, Shen J X, Zhou Y 2009 Chin. J. Laser 36 430 (in Chinese) [梁春, 廖文和, 沈建新, 周宇 2009 中国激光 36 430]
[11] Ren J F, Rao C H, Li M Q 2002 Opto-Electron. Eng. 29 1 (in Chinese) [任剑峰, 饶长辉, 李明全 2002 光电工程 29 1]
[12] Thatiparthi C, Ommanib A, Burmanc R, Thapa D, Hutchings N, Lakshminarayanan V 2016 Proc. SPIE 9693 969321
[13] Thomas S 2004 Proc. SPIE 5490 1238
[14] Nightingale A M, Gordeyev S 2013 Opt. Eng. 52 071413
[15] Shen F, Jiang W H 1999 High Power Laser and Particle Beams 11 27 (in Chinese) [沈锋, 姜文汉 1999 强激光与粒子束 11 27]
[16] Li Y K, Zhang J Z, Zhang F Z 2014 Proc. SPIE 9242 92421V
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