动态干涉仪的位相光栅衍射效率研究
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摘要
为了解决普通二维光栅在动态干涉术中光能量利用不足的问题,使用标量衍射理论和傅里叶分析法对矩形正交位相光栅和棋盘型位相光栅的衍射效率进行推导,分别对两种光栅的最佳工作级次选择策略进行研究。分析结果表明,当分光器件为矩形正交位相光栅时,应选择(0,±1)级与(±1,0)级作为动态干涉仪的工作级次,光能量利用率达到54.4%;当分光器件为棋盘位相光栅时,应选择(±1,±1)级作为动态干涉仪的工作级次,光能量利用率达到65%。实验对比了两种光栅在动态干涉仪上的应用效果,当选用(±1,±1)级作为工作级次时,结果表明使用棋盘型位相光栅的应用效果优于矩形正交位相光栅。因此在动态干涉仪中使用棋盘位相光栅并选用(±1,±1)级作为工作级次能够消除光能量利用不足对测量造成的影响。
In order to overcome the insufficient of the light energy diffracted by common two dimension grating in dynamic interferometry, diffraction efficiency of the cross phase grating and phase chessboard were derived using scalar analysis and Fourier method, and selection scheme of optimum operation orders was studied. The analytical result of their diffraction efficiency demonstrates that if the cross phase grating is chosen, the(0, ±1)th and(±1,0)th orders should be selected as operation orders, and utilization rate can reach 54.4%; If the phase chessboard is chosen,( ±1,±1)th orders is selected as operation ones,and utilization rate can reach 65%. Application effect of these two phase grating are compared in dynamic interferometer. When( ±1,±1)th is selected as operation orders, the experimental results indicates that application effect of phase chessboard is better than that of cross phase grating. So influence of insufficient light energy on the measurement result can be eliminated by using phase chessboard and selecting(±1,±1)th as operation orders.
In order to overcome the insufficient of the light energy diffracted by common two dimension grating in dynamic interferometry, diffraction efficiency of the cross phase grating and phase chessboard were derived using scalar analysis and Fourier method, and selection scheme of optimum operation orders was studied. The analytical result of their diffraction efficiency demonstrates that if the cross phase grating is chosen, the(0, ±1)th and(±1,0)th orders should be selected as operation orders, and utilization rate can reach 54.4%; If the phase chessboard is chosen,( ±1,±1)th orders is selected as operation ones,and utilization rate can reach 65%. Application effect of these two phase grating are compared in dynamic interferometer. When( ±1,±1)th is selected as operation orders, the experimental results indicates that application effect of phase chessboard is better than that of cross phase grating. So influence of insufficient light energy on the measurement result can be eliminated by using phase chessboard and selecting(±1,±1)th as operation orders.
引文
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[2]Lu Heng,Chen Hao,He Yong.Alignment method for measurement of long focal length based on Talbot-Moiréeffect[J].Infrared and Laser Engineering,2013,42(10):2836-2841.(in Chinese)陆衡,陈好,何勇.基于泰伯莫尔法的长焦距测量系统的装调技术[J].红外与激光工程,2013,42(10):2836-2841.
[3]Zhiqiang Liu,Masashi Okada,Katsumi Sugisaki,et al.Double-grating lateral shearing interferometer for EUV optics at-wavelength measurement[C]//SPIE,2005,5752:663-672.
[4]Yucong Zhu,Satoru Odate,Ayako Sugaya,et al.Method for designing phase-calculation algorithms for two-dimensional grating phase-shifting interferometry[J].Appl Opt,2011,50(18):2815-2822.
[5]Zuo Fen,Chen Lei.Errors researching for a simultaneous phase shifting interferometer[J].Optical Technique,2009,35(4):536-540.(in Chinese)左芬,陈磊.一种同步移相干涉系统的误差研究[J].光学技术,2009,35(4):536-540.
[6]Li Bo,Chen Lei,Zhao Bing,et al.Spatial mismatch calibration using circular carrier technique in the simultaneous phase shifting interferometry[J].Appl Opt,2012,51(8):1037-10.
[7]Qian Kemao,Wu Xiaoping,Anand Asundi.Grating-based real-time polarization phase-shifting interferometry:error analysis[J].Appl Opt,2002,41(13):2448-2453.
[8]Neal Brock,John Hayes,Brad Kimbrough,et al.Dynamic Interferometry[C]//SPIE,2005,5875,1-10.
[9]Kevin G H,Steven L C.Phase grating use in moire interferometry[J].Appl Opt,1984,23(10):1517-1520.
[10]Vanusch Nercissian,Irina Harder,Klaus Mantel,et al.Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light[J].Appl Opt,2011,50(4):571-578.
[11]Jerome Primot,Nicolas Guerineau.Extended Hartmann test based on the pseudoguiding property of a Hartmann maskcompleted by a phase chessboard[J].Appl Opt,2000,39(31):5715-5720.
[12]Gustavo Rodriguez-Zurita,Cruz Meneses-Fabian,Noel-Ivan Toto-Arellano,et al.One-shot phase-shifting phase-grating interferometry with modulation of polarization:case of four interferograms[J].Optics Eexpress,2008,16(11):7806-7817.
[13]Rodriguez-Zurita G,Toto-Arellano N I,Meneses-Fabian C,et al.Lateral and rotational shearing phase-shifting interferometry with phase-grating multiplexing[C]//CLEO Pacific Rim,2009.
[14]Elias N Glytsis.Two-dimensionally-periodic diffractive optical elements:limitations of scalar analysis[J].J Opt Soc Am A,2002,19(4):702-715.
[15]Malacara D.Optical Shop Testing 3rd Edition[M].New York:Wiley,2007:501-598.