基于单光弹调制器的米勒矩阵测量技术
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摘要
针对已有米勒矩阵测量方法的不足,提出了一种基于单光弹调制器的米勒矩阵测量技术,给出了米勒矩阵测量优化算法及系统参数两步校准法。该技术通过两步校准法对系统参数进行校准测量,利用优化算法计算得到待测样品的米勒矩阵。实验结果表明,待测1/4波片相位延迟量测量值为90.4185°,误差在标称偏差λ/300以内,快轴方位角测量值为0.2348°,误差在最大旋转误差0.4°以内。同快轴方位角为0°的1/4波片标准米勒矩阵相比,待测1/4波片米勒矩阵各元素最大相对误差的直接测量值和间接测量值分别为1.97%和0.83%,均小于最大相对误差的模拟仿真值2.11%。通过提高旋转台的读数精度和减小相位延迟量的标称偏差,可以进一步减小米勒矩阵各元素的最大相对误差。
A measurement technique for the Mueller matrix based on a single photo-elastic modulator is proposed to improve the current measurement methods.An optimization algorithm and a two-step procedure of system parameter calibration are also presented.System parameters are calibrated by the two-step calibration procedure.Then,the Mueller matrix of the measured sample is obtained with the optimization algorithm.The experimental results show that the retardation and the fast axis angle of the measured quarter-wave plate are 90.4185° and 0.2348°,respectively.The corresponding errors are less than the retardation tolerance λ/300 and the maximum rotation error 0.4°,respectively.Compared to the standard Mueller matrix of a quarter-wave plate whose fast axis angle is set at 0°,the maximum relative errors of each element of the Mueller matrix of the measured quarter-wave plate are 1.97% and 0.83% with direct and indirect measurement method,respectively.Both errors are less than 2.11%,which is the simulation value of the maximum relative error.Decreasing the retardation tolerance or improving the precision of the rotation stage can diminish the maximum relative error of each element of the Mueller matrix.
A measurement technique for the Mueller matrix based on a single photo-elastic modulator is proposed to improve the current measurement methods.An optimization algorithm and a two-step procedure of system parameter calibration are also presented.System parameters are calibrated by the two-step calibration procedure.Then,the Mueller matrix of the measured sample is obtained with the optimization algorithm.The experimental results show that the retardation and the fast axis angle of the measured quarter-wave plate are 90.4185° and 0.2348°,respectively.The corresponding errors are less than the retardation tolerance λ/300 and the maximum rotation error 0.4°,respectively.Compared to the standard Mueller matrix of a quarter-wave plate whose fast axis angle is set at 0°,the maximum relative errors of each element of the Mueller matrix of the measured quarter-wave plate are 1.97% and 0.83% with direct and indirect measurement method,respectively.Both errors are less than 2.11%,which is the simulation value of the maximum relative error.Decreasing the retardation tolerance or improving the precision of the rotation stage can diminish the maximum relative error of each element of the Mueller matrix.
引文
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12Y.W.Liu,G.A.Jones,Y.Peng et al..Generalized theoryand application of Stokes parameter measurements made with asingle photoelastic modulator[J].Appl.Phys.,2006,100(6):063537
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18Hu Jianming,Zeng Aijun,Wang Xiangzhao.Method to measurephase retardation of wave plate based on photoelastic modulation[J].Acta Optica Sinica,2006,26(11):1681～1686胡建明,曾爱军,王向朝.基于光弹调制技术的波片相位延迟量测量方法[J].光学学报,2006,26(11):1681～1686
19Zeng Aijun,Wang Xiangzhao,Dong Zuoren et al..Applicationof photoelastic modulator in modulation of polarization direction[J].Chinese J.Lasers,2005,32(8):1063～1067曾爱军,王向朝,董作人等.光弹调制器在偏振方向调制中的应用[J].中国激光,2005,32(8):1063～1067
20Zeng Aijun,Wang Xiangzhao,Li Dailinet al..A new method tocalibrate accurately aphotoelastic modulator[J].Acta OpticaSinica,2005,25(6):799～802曾爱军,王向朝,李代林等.精确标定光弹调制器的新方法[J].光学学报,2005,25(6):799～802
21Baoliang Wang,T.C.Oakberg.A new instrument formeasuring both the magnitude and angle of low level linearbirefringence[J].Rev.Sci.Instrum.,1999,70(10):3847～3854
22Li Fanyue,Han Jie,Zeng Aijun et al..Method for measuringretardation by swinging quarter-wave plate with phase modulator[J].Chinese J.Lasers,2011,38(2):0208003李凡月,韩杰,曾爱军等.基于相位调制和样品摆动的1/4波片相位延迟量测量方法[J].中国激光,2011,38(2):0208003
2M.Losurdo,M.Bergmair,G.Bruno.Spectroscopicellipsometry and polarimetry for materials and systems analysis atthe nanometer scale:state-of-the-art,potential,and perspectives[J].J.Nanopart.Res.,2009,11(7):1521～1554
3G.R.McIntyre,J.Kye,H.Levinson et al..Polarizationaberrations in hyper-numerical-aperture projection printing:acomparison of various representations[J].Microlith.,Microfab.Microsyst.,2006,5(3):033001
4S.B.Hatit,M.Foldyna,A.D.Martinoet al..Angle-resolvedMueller polarimeter using a microscope objective[J].Phys.Stat.Sol.(A).,2008,205(4):743～747
5R.A.Chipman.Handbook of Optics[M].New York:McGrawHill,Inc.,1995
6D.H.Goldstein.Mueller matrix dual-rotating retarderpolarimeter[J].Appl.Opt.,1992,31(31):6676～6683
7R.W.Collins,J.Koh.Dual rotating-compensator multichannelellipsometer:instrument design for real-time Mueller matrixspectroscopy of surfaces and films[J].J.Opt.Soc.Am.A,1999,16(8):1997～2006
8I.J.Vaughn,B.G.Hoover.Noise reduction in a laserpolarimeter based on discrete waveplate rotations[J].Opt.Express,2008,16(3):2091～2108
9A.D.Martino,Y.K.Kim,E.Garcia-Caurel et al..OptimizedMueller polarimeter with liquid crystals[J].Opt.Lett.,2003,28(8):616～618
10D.Goldstein.Polarized Light[M].New York:Marcel Dekker,Inc.,2003
11Aijun Zeng,Fanyue Li,Linglin Zhu et al..Simultaneousmeasurement of retardance and fast axis angle of a quarter-waveplate using one photoelastic modulator[J].Appl.Opt.,2011,50(22):4347～4352
12Y.W.Liu,G.A.Jones,Y.Peng et al..Generalized theoryand application of Stokes parameter measurements made with asingle photoelastic modulator[J].Appl.Phys.,2006,100(6):063537
13B.Wang,T.C.Oakberg.A new instrument for measuring boththe magnitude and angle of low level linear birefringence[J].Rev.Sci.Instrum.,1999,70(10):3847～3854
14W.Guan,G.A.Jones,Y.W.Liuet al..The measurement ofthe Stokes parameters:ageneralized methodology using a dualphotoelastic modulator system[J].Appl.Phys.,2008,49(14):2644～2652
15Y.Takakura,J.E.Ahmad.Noise distribution of Muellermatrices retrieved with active rotating polarimeters[J].Appl.Opt.,2007,46(30):7354～7364
16A.Ambirajan,D.C.Look.Optimum angles for a polarimeter:part 1[J].Opt.Eng.,1995,34(6):1651～1655
17Yang Kun,Zeng Aijun,Wang Xiangzhao et al..Fast axiscalibration of quarter-wave plate by fundamental componentextinction[J].Chinese J.Lasers,2007,34(11):1554～1556杨坤,曾爱军,王向朝等.基于基频分量消光的1/4波片快轴标定方法[J].中国激光,2007,34(11):1554～1556
18Hu Jianming,Zeng Aijun,Wang Xiangzhao.Method to measurephase retardation of wave plate based on photoelastic modulation[J].Acta Optica Sinica,2006,26(11):1681～1686胡建明,曾爱军,王向朝.基于光弹调制技术的波片相位延迟量测量方法[J].光学学报,2006,26(11):1681～1686
19Zeng Aijun,Wang Xiangzhao,Dong Zuoren et al..Applicationof photoelastic modulator in modulation of polarization direction[J].Chinese J.Lasers,2005,32(8):1063～1067曾爱军,王向朝,董作人等.光弹调制器在偏振方向调制中的应用[J].中国激光,2005,32(8):1063～1067
20Zeng Aijun,Wang Xiangzhao,Li Dailinet al..A new method tocalibrate accurately aphotoelastic modulator[J].Acta OpticaSinica,2005,25(6):799～802曾爱军,王向朝,李代林等.精确标定光弹调制器的新方法[J].光学学报,2005,25(6):799～802
21Baoliang Wang,T.C.Oakberg.A new instrument formeasuring both the magnitude and angle of low level linearbirefringence[J].Rev.Sci.Instrum.,1999,70(10):3847～3854
22Li Fanyue,Han Jie,Zeng Aijun et al..Method for measuringretardation by swinging quarter-wave plate with phase modulator[J].Chinese J.Lasers,2011,38(2):0208003李凡月,韩杰,曾爱军等.基于相位调制和样品摆动的1/4波片相位延迟量测量方法[J].中国激光,2011,38(2):0208003