基于光强自标定移相算法检测光学面形
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摘要
考虑菲佐型波长移相干涉仪中波长可调谐激光器光强与调节电压之间的关系会对相位计算精度造成影响,本文提出了一种基于光强自标定的波长移相算法。首先,分析了波长可调谐激光器调节电压与输出光强之间的关系,建立了数学模型;然后,依据最小二乘判据,推导出了波长移相干涉仪的光强自标定移相算法。最后,实施了仿真实验,通过计算机生成背景光强具有一定变化的12幅干涉图,利用所提出的算法进行了相位恢复。结果表明,提出的算法可以很好地免疫激光器的光强变化,实现高精度的相位恢复。对口径为100mm的平面镜的测量结果显示RMS为0.005λ,PV为0.073λ。与ZYGO干涉仪测量结果的比较显示,两次测量面形的偏差RMS为0.0014λ,PV为0.022λ。得到的结果证明了算法的可行性及在菲佐型波长移相干涉仪中的实用性。
As the relationship between output intensity and modulation voltage of a modulation laser in Fizeau interferometer will effect the accuracy of phase calculation,this paper proposes an intensity self-calibration phase-shifting algorithm.Firstly,the relationship between output intensity and modulation voltage of the modulation laser was analyzed,and a mathematical model was established.Then,on the basis of least square estimation,the intensity self-calibration phase-shifting algorithm was deduced.Finally,a simulation experiment was performed.The 12 interferograms with changed backgrounds were generated by computers,and their phases were retrieved.The experiment indicates that the algorithm immunes the intensity change well,and retrieves the phase accurately.The measuring results for a flat mirror with a caliber of 100 mm show that the calculated phase precision is RMS of 0.005λ,and PV of 0.073λ.As a comparison with a ZYGO interferometer for the same flat mirror,the deviations are RMS of 0.0014λ,and PV of 0.022λ.Both simulation and experiment results show that the proposed intensity self-calibration phase-shifting algorithm is feasible and practical in the Fizeau interferometer with wavelength tunning.
As the relationship between output intensity and modulation voltage of a modulation laser in Fizeau interferometer will effect the accuracy of phase calculation,this paper proposes an intensity self-calibration phase-shifting algorithm.Firstly,the relationship between output intensity and modulation voltage of the modulation laser was analyzed,and a mathematical model was established.Then,on the basis of least square estimation,the intensity self-calibration phase-shifting algorithm was deduced.Finally,a simulation experiment was performed.The 12 interferograms with changed backgrounds were generated by computers,and their phases were retrieved.The experiment indicates that the algorithm immunes the intensity change well,and retrieves the phase accurately.The measuring results for a flat mirror with a caliber of 100 mm show that the calculated phase precision is RMS of 0.005λ,and PV of 0.073λ.As a comparison with a ZYGO interferometer for the same flat mirror,the deviations are RMS of 0.0014λ,and PV of 0.022λ.Both simulation and experiment results show that the proposed intensity self-calibration phase-shifting algorithm is feasible and practical in the Fizeau interferometer with wavelength tunning.
引文
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[11]郭仁慧,李建欣,朱日宏,等.长干涉腔波长移相计算的自适应相位筛选法[J].光学学报,2013,33(1):0112004.GUO R H,LI J X,ZHU R H,et al..An adaptive phase selecting method of wavelength tuning at long interference cavity length[J].Acta Optica Sinica,2013,33(1):0112004.(in Chinese)
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[13]苏志德,史振广,彭吉,等.菲索干涉仪中精确移相的实现[J].中国光学,2013,6(2):244-250.SU ZH D,SHI ZH G,PENG J,et al..Implementation of accurate phase shift in Fizeau interferometer[J].Chinese Optics,2013,6(2):244-250.(in Chinese)
[2]GREIVENKAMP J E,BRUNING J H.Phase Shifting Interferometry in Optical Shop Testing[M].2nd Edition.New York:Wiley,1992.
[3]任寰,马力,刘旭,等.多表面干涉下的光学元件面形检测[J].光学精密工程,2013,21(5):1144-1150.REN H,MA L,LIU X,et al..Optical element test with multiple surface interference[J].Opt.Precision Eng.,2013,21(5):1144-1150.(in Chinese)
[4]de GROOT P J,DECK L L.Numerical simulation of vibration in phase-shifting interferometry[J].Appl.Opt.,1996,35(13):2172-2178.
[5]de GROOT P J.Vibration in phase shifting interferometry[J].JOSA A,1995,12:354-365.
[6]王平,王汝东,田伟,等.Fizeau干涉仪主机的热稳定性设计与分析[J].光学精密工程,2011,19(9):2100-2107.WANG P,WANG R D,TIAN W,et al..Design and analysis of the thermal stability for main frame in Fizeau interferometer[J].Opt.Precision Eng.,2011,19(9):2100-2107.(in Chinese)
[7]赵智亮,夏伯才,陈立华,等.相移干涉测量中相移误差的自修正[J].光学精密工程,2013,21(5):1117-1121.ZHAO ZH L,XIA B C,CHEN L H,et al..Selfcorrection of phase step error in phase shifting interferometric measurement[J].Opt.Precision Eng.,2013,21(5):1117-1121.(in Chinese)
[8]ISHII Y,ONODERA R.Phase-shift-locked interferometer with a wavelength-modulated laser diode[J].Appl.Opt.,2003,42:91-96.
[9]于瀛洁,张本好,焦云芳.基于时域傅里叶变换的波长移相算法[J].计量学报,2004,25(4):301-313.YU Y J,ZHANG B H,JIAO Y F.Algorithm of phase-shifting by wavelength tunning based on temporal DFT[J].Acta Metrologica Sinica,2004,25(4):310-313.(in Chinese)
[10]苏志德,史振广,苏东奇,等.在随机和倾斜移相下光强归一化的迭代移相算法[J].光学学报,2013,33(1):0112001.SU ZH D,SHI ZH G,SU D Q,et al..Iterative phase shifting algorithm with normalized intersity in the presence of random and tilt phase shifts[J].Acta Optica Sinica,2013,33(1):0112001.(in Chinese)
[11]郭仁慧,李建欣,朱日宏,等.长干涉腔波长移相计算的自适应相位筛选法[J].光学学报,2013,33(1):0112004.GUO R H,LI J X,ZHU R H,et al..An adaptive phase selecting method of wavelength tuning at long interference cavity length[J].Acta Optica Sinica,2013,33(1):0112004.(in Chinese)
[12]郭仁慧,李建欣,朱日宏,等.波长调谐随机移相算法的研究[J].中国激光,2012,39(5):0508002.GUO R H,LI J X,ZHU R H,et al..Research on the randomly phase shifting algorithm with wavelength tuning[J].Chinese Journal of Laser,2012,39(5):0508002.(in Chinese)
[13]苏志德,史振广,彭吉,等.菲索干涉仪中精确移相的实现[J].中国光学,2013,6(2):244-250.SU ZH D,SHI ZH G,PENG J,et al..Implementation of accurate phase shift in Fizeau interferometer[J].Chinese Optics,2013,6(2):244-250.(in Chinese)