相干合成中的随机并行梯度下降算法性能研究
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摘要
随机并行梯度下降算法(SPGD)是一种基于直接性能指标优化的相位控制方法,在自适应光学中有较好的适用性。该算法主要包含增益系数和随机扰动幅度两个可变参数,其取值对算法收敛性有很大的影响。对双边SPGD算法实现收敛时参数的取值要求进行研究,结合算法原理分析了算法参数的取值范围,并通过大量仿真实验找出所有使双边SPGD算法收敛的增益系数和随机扰动幅度值;得到随机扰动幅度的取值下限,理论和仿真分析了下限存在的原因及取值;在相干合成中存在相位噪声,研究了不同相位校正器参数的情况下可使算法收敛的参数的取值范围。
Stochastic parallel gradient descent algorithm(SPGD),aphase control method based on directly optimizing performance index,has good applicability in adaptive optics.The algorithm involves two variable parameters:gain coefficient and random perturbation amplitude,whose values have great influence on the convergence of the algorithm.The requirements of the parameter values for the convergence of SPGD algorithm are discussed,and the value range of parameters are analyzed by combining with the principle of the algorithm.Furthermore,a large number of simulations are conducted to analyze all the gain coefficients and the amplitude of random disturbance,which can ensure the convergency of bilateral SPGD.Meanwhile,the lower limit of the random disturbance amplitude is obtained,and the reason for its existence and the lower limit value are also analyzed theoretically and experimentally.With the existence of phase noise in coherent combination,the range of parameters for the algorithm to be convergent is analyzed with different phase corrector parameters.
Stochastic parallel gradient descent algorithm(SPGD),aphase control method based on directly optimizing performance index,has good applicability in adaptive optics.The algorithm involves two variable parameters:gain coefficient and random perturbation amplitude,whose values have great influence on the convergence of the algorithm.The requirements of the parameter values for the convergence of SPGD algorithm are discussed,and the value range of parameters are analyzed by combining with the principle of the algorithm.Furthermore,a large number of simulations are conducted to analyze all the gain coefficients and the amplitude of random disturbance,which can ensure the convergency of bilateral SPGD.Meanwhile,the lower limit of the random disturbance amplitude is obtained,and the reason for its existence and the lower limit value are also analyzed theoretically and experimentally.With the existence of phase noise in coherent combination,the range of parameters for the algorithm to be convergent is analyzed with different phase corrector parameters.
引文
1 Xiao Rui,Hou Jing,Jiang Zongfu.Experimental investigation of phase detection and compensation in coherent combining of fiber laser array[J].Acta Physica Sinica,2006,55(1):184-187.肖瑞,侯静,姜宗福.光纤激光器阵列相干合成中的位相探测与校正方法研究[J].物理学报,2006,55(1):184-187.
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4 Schuetz C A,Mirotznik M S,Shi S,etal.Applications of optical upconversion to sparse aperture millimeter-wave imaging[C].SPIE,2005,5989:59891C.
5 Schuetza C A,Mirotznikb M S,Shia S,et al.Optical techniques for sparse-aperture millimeter-wave imaging[C].SPIE,2006,6211:62110G.
6 He Y,Huang H,Jiang Y,et al.Optical phase control for MMW sparse aperture upconversion imaging[J].Chinese Optics Letters,2014,12(5):051101.
7 Wang X L,Zhou P,Ma H,et al.Synchronization and coherent combining of two pulsed fiber ring lasers based on direct phase modulation[J].Chinese Physics Letters,2009,26(5):054211-054212.
8 Xiao Rui.Coherent combining technology of master oscillator power amplifier fiber arrays[D].Changsha:National University of Defense Technology,2007:1-56.肖瑞.主振荡功率放大器方案光纤激光相干合成技术[D].长沙:国防科学技术大学,2007:1-56.
9 Goodno G D,McNaught S J,Rothenberg J E,et al.Active phase and polarization locking of a 1.4kW fiber amplifier[J].Optics Letters,2010,35(10):1542-1544.
10 Liu L,Loizos D N,Vorontsov M A.Coherent combining of multiple beams with multi-dithering technique:100kHz closed-loop compensation demonstration[C].SPIE,2007,6708:67080D.
11 Shay T M,Benham V.A novel technique for phase locking optical fiber arrays[C].SPIE,2004,5550:313-319.
12 Zhou P,Wang X,Ma Y,et al.Stable coherent beam combination by active phasing a mutual injection-locked fiber laser array[J].Optics Letters,2010,35(7):950-952.
13 Vorontsov M A,Weyrauch T,Beresnev L A,et al.Adaptive array of phase-locked fiber collimators:Analysis and experimental demonstration[J].IEEE Journal of Selected Topics in Quantum Electronics,2009,15(2):269-280.
14 Kansky J E,Charles X Y,Murphy D V,et al.Beam control of a 2Dpolarization maintaining fiber optic phased array with high-fiber count[C].SPIE,2006,6306:63060G.
15 Liu Zejin,Zhou Pu,Hou Jing,et al.Research of coherent beam combining using actively phase-controlling[J].Chinese JLasers,2009,36(3):518-524.刘泽金,周朴,侯静,等.主动相位控制光纤激光相干合成的研究[J].中国激光,2009,36(3):518-524.
16 Li X,Ma Y,Zhou P,et al.Coherent beam combining with double stochastic approximation based on logic comparison algorithm[J].Optics Express,2009,17(2):385-394.
17 Mu Jie,Jing Feng,Wang Xiao,et al.Error control of piston and tilt based on SPGD in coherent beam combination[J].Chinese J Lasers,2014,41(6):0602002.母杰,景峰,王逍,等.相干合成中基于SPGD算法的平移误差和倾斜误差控制[J].中国激光,2014,41(6):0602002.
18 Cheng Bo,Yang Jing,Li Xinyang,et al.Adaptive optics control technique based on orthogonal mode perturbance gradient descent algorithm[J].Acta Optica Sinica,2015,35(8):0801004.陈波,杨靖,李新阳,等.基于正交模式扰动梯度下降算法的自适应光学控制技术[J].光学学报,2015,35(8):0801004.
19 Wang Xiaolin.Study on optimization algorithm based adaptive optics in laser phased array[D].Changsha:National University of Defense Technology,2011:3-20.王小林.激光相控阵中的优化式自适应光学研究[D].长沙:国防科学技术大学,2011:3-20.
20 Zhou Pu,Liu Zejin,Wang Xiaolin,et al..Theoretical and experimental investigation on coherent beam combining of fiber lasers using SPGD algorithm[J].Acta Optica Sinica,2009,29(8):2232-2237.周朴,刘泽金,王小林,等.随机并行梯度下降算法用于光纤激光相干合成的理论与实验研究[J].光学学报,2009,29(8):2232-2237.
21 Wang Xiaolin,Zhou Pu,Ma Yanxing,et al.Phase control of coherent fiber laser array using stochastic parallel gradient descent algorithm and its application[J].Acta Optica Sinica,2010,30(10):2874-2878.王小林,周朴,马阎星,等.SPGD算法在光纤激光相干阵列光束控制中的应用[J].光学学报,2010,30(10):2874-2878.
22 Fan Ling,Qiao Chunhong,Feng Xiaoxing,et al.Elementary study turbulence effects resulted from laser propagation in the atmosphere based on the stochastic parallel gradient descent algorithm[J].Journal of Atmospheric and Environmental Optics,2009,4(3):183-189.范玲,乔春红,冯晓星,等.基于SPGD算法的激光大气传输湍流效应校正的初步研究[J].大气与环境光学学报,2009,4(3):183-189.
23 Chen Bo,Li Xinyang,Jiang Wenhan.Optimization of stochastic parallel gradient descent algorithm for adaptive optics in atmospheric turbulence[J].Chinese J Lasers,2010,37(4):959-964.陈波,李新阳,姜文汉.大气湍流自适应光学随机并行梯度下降算法的优化[J],中国激光,2010,37(4):959-964.
24 Peng Hao.Research of the stochastic parallel gradient descent algorithm for wavefront control technique[D].Changsha:National University of Defense Technology,2008:19-35.彭浩.随机并行梯度下降波前控制算法研究[D].长沙:国防科学技术大学,2008:19-35.
25 Vorontsov M A,Carhart G W,Cohen M,et al.Adaptive optics based on analog parallel stochastic optimization:Analysis and experimental demonstration[J].Journal of the Optical Society of America A,2000,17(8):1440-1453.
26 Fu Q,Pott J U,Shen F,et al.Stochastic parallel gradient descent optimization based on decoupling of the software and hardware[J].Optics Communications,2014,310:138-149.
27 Vorontsov M A,Carhart G W.Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters[J].Journal of the Optical Society of America A,2006,23(10):2613-2622.
28 Vorontsov M A,Sivokon V P.Stochastic parallel gradient descent technique for high resolution wave-front phasedistortion correction[J].Journal of the Optical Society of America A,1998,15(10):2745-2758.
29 Vorontsov M A.Decoupled stochastic parallel gradient descent optimization for adaptive optics:Integrated approach for wave-front sensor information fusion[J].Journal of the Optical Society of America A,2002,19(2):356-368.
30 Liu Lei.Research on laser beam shaping technique based on stochastic parallel gradient descent algorithm[D].Changchun:Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,2013:13-34.刘磊.基于随机并行梯度下降算法的激光束整形技术研究[D].长春:中国科学院长春光学精密机械与物理研究所,2013:13-34.
31 Spall J C.Multivariate stochastic approximation using a simultaneous perturbation gradient approximation[J].IEEETransactions on Automatic Control,1992,37(3):332-341.
32 Dembo A,Kailath T.Model-free distributed learning[J].IEEE Transactions on Neural Networks,1990,1(1):58-70.
2 Liang Yonghui,Wang Sanhong,Long Xuejun,et al.Experimental explorations of the laser beam cleanup system based on stochastic parallel gradient descent algorithm[J].Acta Optica Sinica,2008,28(4):613-618.梁永辉,王三宏,龙学军,等.随机并行梯度下降光束净化实验研究[J].光学学报,2008,28(4):613-618.
3 Wang Sanhong,Liang Yonghui,Long Xuejun,et al.Multilevel wavefront correction technique based on stochastic parallel gradient descent algorithm[J].Chinese J Lasers,2009,36(5):1091-1096.王三宏,梁永辉,龙学军,等.基于随机并行梯度下降算法的多级波前校正技术[J].中国激光,2009,36(5):1091-1096.
4 Schuetz C A,Mirotznik M S,Shi S,etal.Applications of optical upconversion to sparse aperture millimeter-wave imaging[C].SPIE,2005,5989:59891C.
5 Schuetza C A,Mirotznikb M S,Shia S,et al.Optical techniques for sparse-aperture millimeter-wave imaging[C].SPIE,2006,6211:62110G.
6 He Y,Huang H,Jiang Y,et al.Optical phase control for MMW sparse aperture upconversion imaging[J].Chinese Optics Letters,2014,12(5):051101.
7 Wang X L,Zhou P,Ma H,et al.Synchronization and coherent combining of two pulsed fiber ring lasers based on direct phase modulation[J].Chinese Physics Letters,2009,26(5):054211-054212.
8 Xiao Rui.Coherent combining technology of master oscillator power amplifier fiber arrays[D].Changsha:National University of Defense Technology,2007:1-56.肖瑞.主振荡功率放大器方案光纤激光相干合成技术[D].长沙:国防科学技术大学,2007:1-56.
9 Goodno G D,McNaught S J,Rothenberg J E,et al.Active phase and polarization locking of a 1.4kW fiber amplifier[J].Optics Letters,2010,35(10):1542-1544.
10 Liu L,Loizos D N,Vorontsov M A.Coherent combining of multiple beams with multi-dithering technique:100kHz closed-loop compensation demonstration[C].SPIE,2007,6708:67080D.
11 Shay T M,Benham V.A novel technique for phase locking optical fiber arrays[C].SPIE,2004,5550:313-319.
12 Zhou P,Wang X,Ma Y,et al.Stable coherent beam combination by active phasing a mutual injection-locked fiber laser array[J].Optics Letters,2010,35(7):950-952.
13 Vorontsov M A,Weyrauch T,Beresnev L A,et al.Adaptive array of phase-locked fiber collimators:Analysis and experimental demonstration[J].IEEE Journal of Selected Topics in Quantum Electronics,2009,15(2):269-280.
14 Kansky J E,Charles X Y,Murphy D V,et al.Beam control of a 2Dpolarization maintaining fiber optic phased array with high-fiber count[C].SPIE,2006,6306:63060G.
15 Liu Zejin,Zhou Pu,Hou Jing,et al.Research of coherent beam combining using actively phase-controlling[J].Chinese JLasers,2009,36(3):518-524.刘泽金,周朴,侯静,等.主动相位控制光纤激光相干合成的研究[J].中国激光,2009,36(3):518-524.
16 Li X,Ma Y,Zhou P,et al.Coherent beam combining with double stochastic approximation based on logic comparison algorithm[J].Optics Express,2009,17(2):385-394.
17 Mu Jie,Jing Feng,Wang Xiao,et al.Error control of piston and tilt based on SPGD in coherent beam combination[J].Chinese J Lasers,2014,41(6):0602002.母杰,景峰,王逍,等.相干合成中基于SPGD算法的平移误差和倾斜误差控制[J].中国激光,2014,41(6):0602002.
18 Cheng Bo,Yang Jing,Li Xinyang,et al.Adaptive optics control technique based on orthogonal mode perturbance gradient descent algorithm[J].Acta Optica Sinica,2015,35(8):0801004.陈波,杨靖,李新阳,等.基于正交模式扰动梯度下降算法的自适应光学控制技术[J].光学学报,2015,35(8):0801004.
19 Wang Xiaolin.Study on optimization algorithm based adaptive optics in laser phased array[D].Changsha:National University of Defense Technology,2011:3-20.王小林.激光相控阵中的优化式自适应光学研究[D].长沙:国防科学技术大学,2011:3-20.
20 Zhou Pu,Liu Zejin,Wang Xiaolin,et al..Theoretical and experimental investigation on coherent beam combining of fiber lasers using SPGD algorithm[J].Acta Optica Sinica,2009,29(8):2232-2237.周朴,刘泽金,王小林,等.随机并行梯度下降算法用于光纤激光相干合成的理论与实验研究[J].光学学报,2009,29(8):2232-2237.
21 Wang Xiaolin,Zhou Pu,Ma Yanxing,et al.Phase control of coherent fiber laser array using stochastic parallel gradient descent algorithm and its application[J].Acta Optica Sinica,2010,30(10):2874-2878.王小林,周朴,马阎星,等.SPGD算法在光纤激光相干阵列光束控制中的应用[J].光学学报,2010,30(10):2874-2878.
22 Fan Ling,Qiao Chunhong,Feng Xiaoxing,et al.Elementary study turbulence effects resulted from laser propagation in the atmosphere based on the stochastic parallel gradient descent algorithm[J].Journal of Atmospheric and Environmental Optics,2009,4(3):183-189.范玲,乔春红,冯晓星,等.基于SPGD算法的激光大气传输湍流效应校正的初步研究[J].大气与环境光学学报,2009,4(3):183-189.
23 Chen Bo,Li Xinyang,Jiang Wenhan.Optimization of stochastic parallel gradient descent algorithm for adaptive optics in atmospheric turbulence[J].Chinese J Lasers,2010,37(4):959-964.陈波,李新阳,姜文汉.大气湍流自适应光学随机并行梯度下降算法的优化[J],中国激光,2010,37(4):959-964.
24 Peng Hao.Research of the stochastic parallel gradient descent algorithm for wavefront control technique[D].Changsha:National University of Defense Technology,2008:19-35.彭浩.随机并行梯度下降波前控制算法研究[D].长沙:国防科学技术大学,2008:19-35.
25 Vorontsov M A,Carhart G W,Cohen M,et al.Adaptive optics based on analog parallel stochastic optimization:Analysis and experimental demonstration[J].Journal of the Optical Society of America A,2000,17(8):1440-1453.
26 Fu Q,Pott J U,Shen F,et al.Stochastic parallel gradient descent optimization based on decoupling of the software and hardware[J].Optics Communications,2014,310:138-149.
27 Vorontsov M A,Carhart G W.Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters[J].Journal of the Optical Society of America A,2006,23(10):2613-2622.
28 Vorontsov M A,Sivokon V P.Stochastic parallel gradient descent technique for high resolution wave-front phasedistortion correction[J].Journal of the Optical Society of America A,1998,15(10):2745-2758.
29 Vorontsov M A.Decoupled stochastic parallel gradient descent optimization for adaptive optics:Integrated approach for wave-front sensor information fusion[J].Journal of the Optical Society of America A,2002,19(2):356-368.
30 Liu Lei.Research on laser beam shaping technique based on stochastic parallel gradient descent algorithm[D].Changchun:Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,2013:13-34.刘磊.基于随机并行梯度下降算法的激光束整形技术研究[D].长春:中国科学院长春光学精密机械与物理研究所,2013:13-34.
31 Spall J C.Multivariate stochastic approximation using a simultaneous perturbation gradient approximation[J].IEEETransactions on Automatic Control,1992,37(3):332-341.
32 Dembo A,Kailath T.Model-free distributed learning[J].IEEE Transactions on Neural Networks,1990,1(1):58-70.