基于瀑布型多重网格加速的复指数波前复原算法
|
摘要
激光在大气中传输时,由于强湍流或长传输距离的影响,畸变波前中出现由相位起点组成的不连续相位,现有波前复原算法不能有效复原不连续相位,使得自适应光学系统校正效果下降甚至失效.本文分析了最小二乘波前复原算法不能复原相位奇点的原因,提出了基于瀑布型多重网格加速的复指数波前复原算法,给出了复指数波前复原算法中迭代计算、降采样、插值计算的实现方式.研究了该方法对不连续相位和随机连续相位的复原能力,数值分析了采用复指数波前复原算法的自适应光学系统对大气湍流像差的校正效果.仿真结果表明,同等复原精度下,相比直接迭代过程,该方法所需浮点乘数目减少了近2个数量级,且随着夏克-哈特曼波前传感器子孔径数目增加,其在计算量上的优势更加明显. Rytov方差较大时,相比直接斜率法,自适应光学系统采用复指数波前复原算法后校正光束Strehl比提升1倍.
When laser beam propagates through the turbulent atmosphere, there are branch points in wavefront,which are caused by deep turbulence or long propagation distance. Conventional least-square reconstruction algorithms cannot restore the discontinuous wavefront, which severely limits correction performance of an adaptive optics system. If the incoming wavefront contains a branch cut, there is 2 nπ difference between the measured phase difference and the principle phase difference, which is the reason why conventional least-square reconstruction algorithms cannot reconstruct wavefront with branch points. The complex exponential reconstructor is developed to restore the discontinuous wavefront with phase difference replaced by complex exponents. However, thousands of iterations are required by the complex exponential reconstructor before converging to an acceptable solution. In order to speed up the iterative calculation, the cascadic multigrid method(CMG) is introduced in the process of wavefront reconstruction. The proposed method can be used to restore discontinuous wavefront with lower residual error similar to those reconstructed by the direct iteration.The number of float point multiplications required by the CMG method is nearly 2 orders of magnitude lower than that required by the direct iteration. The acceleration of the CMG method increases with the number of subapertures increasing. The performance of CMG method to recover continuous wavefront is also investigated and compared with conventional wavefront reconstruction algorithm based on successive over-relaxation. It is shown that the CMG method has good capability for wavefront reconstruction with high precision and low computation cost no matter whether it is applied to discontinuous or continuous wavefront. Furthermore, the CMG method is used in the adaptive optics for correcting the turbulence aberration. The direct slope wavefront reconstruction algorithm based on the assumption that the measured slope and the control voltage satisfy the linear relationship cannot restore the wavefront with branch points. As a result, the adaptive optics system with the CMG method doubles the correction quality evaluated by the Strehl ratio compared with that with the direct slope wavefront reconstruction algorithm.
When laser beam propagates through the turbulent atmosphere, there are branch points in wavefront,which are caused by deep turbulence or long propagation distance. Conventional least-square reconstruction algorithms cannot restore the discontinuous wavefront, which severely limits correction performance of an adaptive optics system. If the incoming wavefront contains a branch cut, there is 2 nπ difference between the measured phase difference and the principle phase difference, which is the reason why conventional least-square reconstruction algorithms cannot reconstruct wavefront with branch points. The complex exponential reconstructor is developed to restore the discontinuous wavefront with phase difference replaced by complex exponents. However, thousands of iterations are required by the complex exponential reconstructor before converging to an acceptable solution. In order to speed up the iterative calculation, the cascadic multigrid method(CMG) is introduced in the process of wavefront reconstruction. The proposed method can be used to restore discontinuous wavefront with lower residual error similar to those reconstructed by the direct iteration.The number of float point multiplications required by the CMG method is nearly 2 orders of magnitude lower than that required by the direct iteration. The acceleration of the CMG method increases with the number of subapertures increasing. The performance of CMG method to recover continuous wavefront is also investigated and compared with conventional wavefront reconstruction algorithm based on successive over-relaxation. It is shown that the CMG method has good capability for wavefront reconstruction with high precision and low computation cost no matter whether it is applied to discontinuous or continuous wavefront. Furthermore, the CMG method is used in the adaptive optics for correcting the turbulence aberration. The direct slope wavefront reconstruction algorithm based on the assumption that the measured slope and the control voltage satisfy the linear relationship cannot restore the wavefront with branch points. As a result, the adaptive optics system with the CMG method doubles the correction quality evaluated by the Strehl ratio compared with that with the direct slope wavefront reconstruction algorithm.
引文
[1]Fried D L, Vaughn J L 1992 Appl. Opt. 31 2865
[2]Fried D L 1998 JOSA A 15 2759
[3]Primmerman C A, Price T R, Humphreys R A, et al. 1995Appl. Opt. 34 2081
[4]Lukin V P, Fortes B V 2002 Appl. Opt. 41 5616
[5]Steinbock M J, Hyde M W, Schmidt J D 2014 Appl. Opt. 533821
[6]Le B E, Wild W J, Kibblewhite E J 1998 Opt. Lett. 23 10
[7]Fried D L 2001 Opt. Commun. 200 43
[8]Barchers J D, Fried D L, Link D J 2002 Appl. Opt. 41 1012
[9]Aubailly M, Vorontsov M A 2012 JOSA A 29 1707
[10]Yazdani R,Fallah H 2017 Appl.Opt.56 1358
[11]Goodman J W(translated by Qin K C,L P S,Chen J B,Cao Q Z)2013 Introduction to Fourier Optics(3rd Ed.)(Beijing:Publishing House of Electronics Industry)p77
[12]Hudgin R H 1977 JOSA 67 378
[13]Hudgin R H 1977 JOSA 67 375
[14]Bornemann F A,Deuflhard P 1996 Numerische Mathematik75 135
[15]Venema T M,Schmidt J D 2008 Opt.Express 16 6985
[16]Steinbock M J,Schmidt J D,Hyde M W 2012 Aerospace Conference Big Sky,MT,USA,3-10 March,2012,pp1-13
[17]Roddier N A 1990 Opt.Eng.29 1174
[18]Southwell W H 1980 JOSA 70 998
[19]Jr J A F,Morris J R,Feit M D 1976 Appl.Phys.10 129
[20]Cai D M,Wang K,Jia P,Wang D,Liu J X 2014 Acta Phys.Sin.63 104217(in Chinese)[蔡冬梅,王昆,贾鹏,王东,刘建霞2014物理学报63 104217]
[21]Cheng Y C,Shan Q C,Dong L Z,Wang S,Yang P,Ao MW,Xu B 2015 Acta Phys.Sin.64 094207(in Chinese)[程生毅,陈善球,董理治,王帅,杨平,敖明武,许冰2015物理学报64 094207]
[22]Fan C,Wang Y,Gong Z 2004 Appl.Opt.43 4334
[2]Fried D L 1998 JOSA A 15 2759
[3]Primmerman C A, Price T R, Humphreys R A, et al. 1995Appl. Opt. 34 2081
[4]Lukin V P, Fortes B V 2002 Appl. Opt. 41 5616
[5]Steinbock M J, Hyde M W, Schmidt J D 2014 Appl. Opt. 533821
[6]Le B E, Wild W J, Kibblewhite E J 1998 Opt. Lett. 23 10
[7]Fried D L 2001 Opt. Commun. 200 43
[8]Barchers J D, Fried D L, Link D J 2002 Appl. Opt. 41 1012
[9]Aubailly M, Vorontsov M A 2012 JOSA A 29 1707
[10]Yazdani R,Fallah H 2017 Appl.Opt.56 1358
[11]Goodman J W(translated by Qin K C,L P S,Chen J B,Cao Q Z)2013 Introduction to Fourier Optics(3rd Ed.)(Beijing:Publishing House of Electronics Industry)p77
[12]Hudgin R H 1977 JOSA 67 378
[13]Hudgin R H 1977 JOSA 67 375
[14]Bornemann F A,Deuflhard P 1996 Numerische Mathematik75 135
[15]Venema T M,Schmidt J D 2008 Opt.Express 16 6985
[16]Steinbock M J,Schmidt J D,Hyde M W 2012 Aerospace Conference Big Sky,MT,USA,3-10 March,2012,pp1-13
[17]Roddier N A 1990 Opt.Eng.29 1174
[18]Southwell W H 1980 JOSA 70 998
[19]Jr J A F,Morris J R,Feit M D 1976 Appl.Phys.10 129
[20]Cai D M,Wang K,Jia P,Wang D,Liu J X 2014 Acta Phys.Sin.63 104217(in Chinese)[蔡冬梅,王昆,贾鹏,王东,刘建霞2014物理学报63 104217]
[21]Cheng Y C,Shan Q C,Dong L Z,Wang S,Yang P,Ao MW,Xu B 2015 Acta Phys.Sin.64 094207(in Chinese)[程生毅,陈善球,董理治,王帅,杨平,敖明武,许冰2015物理学报64 094207]
[22]Fan C,Wang Y,Gong Z 2004 Appl.Opt.43 4334