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进行星间激光通信的光学发射天线光束整形器设计时, 首要解决的问题是根据输入光场及理想的输出光场, 确定整形器的相位分布, 其核心就是相位恢复. 基于角谱传播理论, 在传统 Gerchberg-Saxton (G-S)迭代算法的基础上, 提出了一种幅度梯度加成迭代算法, 给出了算法的详细流程与分析. 与G-S相比, 新算法利用迭代过程, 构建光场幅度反馈回路, 利用梯度搜索最佳迭代路径, 两者的联合作用加速其迭代收敛进程. 数值仿真表明, 新算法的单位迭代次数所引起迭代误差下降的速度是G-S算法的1.7倍, 其收敛速度明显优于G-S算法; 对不同的随机初始相位, 新算法都能进行有效迭代, 表现出适应性强, 且收敛一致性好的优点. 幅度梯度加成迭代算法为复杂光场的高效相位恢复提供了一种新思路, 为设计各种衍射光学元件提供了技术支持.For designing the light beam shaper in the optical transmitting antenna in inter-satellite optical communication system, the essential problem is, according to the input optical field and ideal output light field, to determine the shaper of phase distribution, in which its core is in phase recovery. Based on the traditional Gerchberg-Saxton (G-S) iterative algorithm, using the angular spectrum propagation theory, a kind of amplitude gradient addition iterative algorithm is proposed, and the detailed algorithm process and analysis are given. Compared with G-S algorithm, the new one using iterative process, constructs the light field amplitude feedback loop, and searches out the optimal iteration path using the gradient; their joint action accelerates the convergence process. Numerical simulation shows that the iterative error-drop speed caused by unit iterations in the new algorithm is 1.7 times that of the G-S algorithm, its convergence rate is obviously superior to the G-S algorithm; for different random initial phase, the new algorithm can effectively carry out iteration, show the advantages of the strong adaptability and the good convergent consistency. Amplitude gradient addition iterative algorithm gives a new effective way of recovering the complex optical field phase, and provides technical support for designing all kinds of diffraction optical element.
[1] Huang L X, Yao X, Cai D M, Guo Y K, Yao J, Gao F H 2010 Chin. J. Laser. 37 1218 (in Chinese) [黄利新, 姚新, 蔡冬梅, 郭永康, 姚军, 高福华 2010 中国激光 37 1218]
[2] Yu J J, Tan L Y, Ma J, Han Q Q, Yang Y Q, Li M 2009 Chin. J. Laser. 36 581 (in Chinese) [俞建杰, 谭立英, 马晶, 韩琦琦, 杨玉强, 李密 2009 中国激光 36 581]
[3] Wu R,Hua N, Zhang X B, Cao G W, Zhao D F, Zhou S L 2012 Acta Phys. Sin. 61 224202 (in Chinese) [邬融, 华能, 张晓波, 曹国威, 赵东峰, 周申蕾 2012 61 224202]
[4] Yu B, Peng X, Tian J D, Niu H B 2005 Acta Phys. Sin. 54 2034 (in Chinese) [于斌, 彭翔, 田劲东, 牛憨笨 2005 54 2034
[5] Deng X P, Zhao D M 2011 Appl. Opt. 50 6019
[6] Gerchberg R W, Saxton W O 1972 Optik 35 237
[7] Fienup J R 1982 Appl. Opt. 21 2758
[8] Lu Y, Li Q, Dong Y H, Gao H D, Ma Z G 2001 J. Opt. Laser 12 365 (in Chinese) [鲁建业, 李琦, 董蕴华, 高惠德, 马祖光 2001 光电子激光 12 365]
[9] Fang L, Ye Y T, Wu Y F, Lu J J, Yang X M, Cheng Z Q Opt 2006 Opt. El. Eng. 33 42 (in Chinese) [方亮, 叶玉堂, 吴云峰, 陆佳佳, 杨先明, 成志强 2006 光电工程 33 42]
[10] Li S L, Li H T, Yang X J 2008 J. Appl. Opt. 29 758 (in Chinese) [李社蕾, 李海涛, 杨喜娟 2008 应用光学 29 758]
[11] Yang G Z, Gu B Y 1981 Acta Phys. Sin. 30 410 (in Chinese) [杨国桢, 顾本源 1981 30 410]
[12] Goodman J W 1996 Introduction to Fourier Optics (2nd EdN.) (New York: McGraw-Hill) p55
[13] Li J C 2009 Acta Opt. Sin. 29 1163 (in Chinese) [李俊昌 2009 光学学报 29 1163]
[14] Biggs D S C, Andrews M 1997 Appl. Opt. 36 1766
[15] Wen C L, Ji J R, Dou W H, Song Y S 2010 Acta Opt. Sin. 30 2473 (in Chinese) [温昌礼, 季家镕, 窦文华, 宋艳生 2010 光学学报 30 2473]
[16] Deng X G, Li Y P, Qiu Y, Fan D Y 1995 Chin. J. Laser B 4 447
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[1] Huang L X, Yao X, Cai D M, Guo Y K, Yao J, Gao F H 2010 Chin. J. Laser. 37 1218 (in Chinese) [黄利新, 姚新, 蔡冬梅, 郭永康, 姚军, 高福华 2010 中国激光 37 1218]
[2] Yu J J, Tan L Y, Ma J, Han Q Q, Yang Y Q, Li M 2009 Chin. J. Laser. 36 581 (in Chinese) [俞建杰, 谭立英, 马晶, 韩琦琦, 杨玉强, 李密 2009 中国激光 36 581]
[3] Wu R,Hua N, Zhang X B, Cao G W, Zhao D F, Zhou S L 2012 Acta Phys. Sin. 61 224202 (in Chinese) [邬融, 华能, 张晓波, 曹国威, 赵东峰, 周申蕾 2012 61 224202]
[4] Yu B, Peng X, Tian J D, Niu H B 2005 Acta Phys. Sin. 54 2034 (in Chinese) [于斌, 彭翔, 田劲东, 牛憨笨 2005 54 2034
[5] Deng X P, Zhao D M 2011 Appl. Opt. 50 6019
[6] Gerchberg R W, Saxton W O 1972 Optik 35 237
[7] Fienup J R 1982 Appl. Opt. 21 2758
[8] Lu Y, Li Q, Dong Y H, Gao H D, Ma Z G 2001 J. Opt. Laser 12 365 (in Chinese) [鲁建业, 李琦, 董蕴华, 高惠德, 马祖光 2001 光电子激光 12 365]
[9] Fang L, Ye Y T, Wu Y F, Lu J J, Yang X M, Cheng Z Q Opt 2006 Opt. El. Eng. 33 42 (in Chinese) [方亮, 叶玉堂, 吴云峰, 陆佳佳, 杨先明, 成志强 2006 光电工程 33 42]
[10] Li S L, Li H T, Yang X J 2008 J. Appl. Opt. 29 758 (in Chinese) [李社蕾, 李海涛, 杨喜娟 2008 应用光学 29 758]
[11] Yang G Z, Gu B Y 1981 Acta Phys. Sin. 30 410 (in Chinese) [杨国桢, 顾本源 1981 30 410]
[12] Goodman J W 1996 Introduction to Fourier Optics (2nd EdN.) (New York: McGraw-Hill) p55
[13] Li J C 2009 Acta Opt. Sin. 29 1163 (in Chinese) [李俊昌 2009 光学学报 29 1163]
[14] Biggs D S C, Andrews M 1997 Appl. Opt. 36 1766
[15] Wen C L, Ji J R, Dou W H, Song Y S 2010 Acta Opt. Sin. 30 2473 (in Chinese) [温昌礼, 季家镕, 窦文华, 宋艳生 2010 光学学报 30 2473]
[16] Deng X G, Li Y P, Qiu Y, Fan D Y 1995 Chin. J. Laser B 4 447
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