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Among all kinds of wavefront reconstruction algorithms in adaptive optical systems, the standard and mostly used algorithm is the direct gradient wavefront reconstruction algorithm. As the number of sub-apertures in Shack-Hartmann wavefront sensor and the actuators for deformable mirror increases, the reconstruction matrix in direct gradient wavefront reconstruction algorithm takes too much space and the number of multiplication in the algorithm increases sharply. So, the iterative algorithm is adopted in wavefront reconstruction for the high-resolution adaptive optical system. The number of multiplication and the required space of the iterative algorithm are directly related to the sparseness of both iterative matrix and slope response matrix. In an adaptive optical system, the sparseness of these two matrixes is connected with the system parameters. Therefore, it is necessary to study how to choose the proper parameters for an adaptive optical system when it uses iterative wavefront reconstruction algorithm. In this paper, the sparseness of slope response matrix and iterative matrix are analyzed based on a 613-actuator adaptive optical system. The influence of the Gaussian function index of deformable mirror on the sparsenesses of slope response matrix, iterative matrix, stability and correction qualities of the adaptive optical system are also studied under the condition of constant actuator spacing and coupling coefficient. A larger Gaussian function index results in a lower sparseness of the slope response matrix and the iterative matrix. Too large or too small a Gaussian function index will degrade the stability and the correction quality of an adaptive optical system. Finally, the optimal range of the Gaussian function index is provided by balancing the sparseness of slope response matrix, the correction quality, and the stability of the adaptive optical system.
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Keywords:
- Gaussian function index /
- iterative matrix /
- slope response matrix /
- sparseness
[1] Jiang W H, Zhang Y D, Rao C H, Ling N, Guan C L, Li M, Yang Z P, Shi G H 2011 Acta Optica Sinaca 31 9 (in Chinese) [姜文汉, 张雨东, 饶长辉, 凌宁, 官春林, 李梅, 杨泽平, 史国华 2011 光学学报 31 9]
[2] Jiang W H 2006 Chinese Journal of Nature 28 1 (in Chinese) [姜文汉 2006 中国自然杂志 28 1]
[3] Zhang L Q, Gu N T, Rao C H 2013 Acta. Phys. Sin. 62 169501 (in Chinese) [张兰强, 顾乃庭, 饶长辉 2013 62 169501]
[4] Ren Z J, Liang X Y, Liu M B, Xia C Q, Lu X M, Li R X, Xu Z Z 2009 Chin. Phys. Lett. 26 124203
[5] Yu L H, Liang X Y, Ren Z J, Wang L, Xu Y, Lu X M, Yu G T 2012 Chin. Phys. B 21 014201
[6] Li X Y, Jiang W H 2003 Acta Optica Sinaca 23 6 (in Chinese) [李新阳, 姜文汉 2003 光学学报 23 6]
[7] Jiang W H, Li H G 1990 Proc. SPIE The Hague, Netherlands, March 01, 1990 p82
[8] Feng L, Fedrigo E, Bechet C 2012 Applied Optics 51 3564
[9] Antonin H B 2010 Proc. SPIE San Diego, CA, August 02, 2009 p1
[10] Luc G, Curtis R, Vogel, Brent L 2002 J. Opt. Soc. Am. A 19 1817
[11] Eric T, Michel T 2010 J. Opt. Soc. Am. A 27 1046
[12] Cheng S Y, Chen S Q, Dong L Z, Liu W J, Wang S, Yang P, Ao M W, Xu B 2014 Acta Phys. Sin. 63 074206 (in Chinese) [程生毅, 陈善球, 董理治, 刘文劲, 王帅, 杨平, 敖明武, 许冰 2014 63 074206]
[13] Zhu Y G 2010 Matrix Analysis and Calculation (Beijing: National Defense Industry Press) pp160-183 (in Chinese) [朱元国 2010 矩阵分析与计算(北京: 国防工业出版社)第160-183页]
[14] Curtis R V 2004 Proc. of SPIE Bellingham WA, June 21, 2004 p1327
[15] John M C, John G 2004 Science, The International Journal of High Performance Computing Applications 18 225
[16] Dong L Z, Yang P, Xu B 2009 Applied Physics B 96 527
[17] Ning Y, Yu H, Zhou H, Rao C H, Jiang W H 2009 Acta Phys. Sin. 58 4717 (in Chinese) [宁禹, 余浩, 周虹, 饶长辉, 姜文汉 2009 58 4717]
[18] Noll R J 1976 J. Opt. Soc. Am. A 66 207
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[1] Jiang W H, Zhang Y D, Rao C H, Ling N, Guan C L, Li M, Yang Z P, Shi G H 2011 Acta Optica Sinaca 31 9 (in Chinese) [姜文汉, 张雨东, 饶长辉, 凌宁, 官春林, 李梅, 杨泽平, 史国华 2011 光学学报 31 9]
[2] Jiang W H 2006 Chinese Journal of Nature 28 1 (in Chinese) [姜文汉 2006 中国自然杂志 28 1]
[3] Zhang L Q, Gu N T, Rao C H 2013 Acta. Phys. Sin. 62 169501 (in Chinese) [张兰强, 顾乃庭, 饶长辉 2013 62 169501]
[4] Ren Z J, Liang X Y, Liu M B, Xia C Q, Lu X M, Li R X, Xu Z Z 2009 Chin. Phys. Lett. 26 124203
[5] Yu L H, Liang X Y, Ren Z J, Wang L, Xu Y, Lu X M, Yu G T 2012 Chin. Phys. B 21 014201
[6] Li X Y, Jiang W H 2003 Acta Optica Sinaca 23 6 (in Chinese) [李新阳, 姜文汉 2003 光学学报 23 6]
[7] Jiang W H, Li H G 1990 Proc. SPIE The Hague, Netherlands, March 01, 1990 p82
[8] Feng L, Fedrigo E, Bechet C 2012 Applied Optics 51 3564
[9] Antonin H B 2010 Proc. SPIE San Diego, CA, August 02, 2009 p1
[10] Luc G, Curtis R, Vogel, Brent L 2002 J. Opt. Soc. Am. A 19 1817
[11] Eric T, Michel T 2010 J. Opt. Soc. Am. A 27 1046
[12] Cheng S Y, Chen S Q, Dong L Z, Liu W J, Wang S, Yang P, Ao M W, Xu B 2014 Acta Phys. Sin. 63 074206 (in Chinese) [程生毅, 陈善球, 董理治, 刘文劲, 王帅, 杨平, 敖明武, 许冰 2014 63 074206]
[13] Zhu Y G 2010 Matrix Analysis and Calculation (Beijing: National Defense Industry Press) pp160-183 (in Chinese) [朱元国 2010 矩阵分析与计算(北京: 国防工业出版社)第160-183页]
[14] Curtis R V 2004 Proc. of SPIE Bellingham WA, June 21, 2004 p1327
[15] John M C, John G 2004 Science, The International Journal of High Performance Computing Applications 18 225
[16] Dong L Z, Yang P, Xu B 2009 Applied Physics B 96 527
[17] Ning Y, Yu H, Zhou H, Rao C H, Jiang W H 2009 Acta Phys. Sin. 58 4717 (in Chinese) [宁禹, 余浩, 周虹, 饶长辉, 姜文汉 2009 58 4717]
[18] Noll R J 1976 J. Opt. Soc. Am. A 66 207
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