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Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates
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摘要: 光栅干涉系统中的装配与角度调试误差是探测光发生几何错位、偏离探测器感光中心的直接原因。为厘清探测光综合姿态误差对干涉相位和位移测量结果的影响，本文基于狭义相对论波矢量的四维表达形式，将光频率和光波矢与光栅方程直接关联，构建了以任意角度入射、光栅沿任意方向运动的多普勒频移理论体系，论证了在不同光栅入射角度下，同级次衍射光频移关系具有一致性的物理特征。通过激光、光栅干涉系统之间物理图像的对比，阐明了即使系统光几何路径不随运动改变，也仍产生相位变化的原因是光栅表面的特殊波矢调制关系。结论表明，光栅干涉系统在探测光存在综合姿态误差情况下位移转化关系仍保持不变，光栅周期方向的偏转是系统几何测量误差的关键来源。最后，为初判某一系统的测量性能指标，文中给出了一种能够快速判断其位移测量原始分辨率的方法。由于本文的频移理论从物理底层逻辑出发，因此相关结论具有普适性，这不仅对所有光栅干涉系统的原理分析具有指导作用，同时还对各种先进系统中的几何测量误差分析具有重要参考价值。Abstract: The assembly and angular commissioning errors in the grating interference system are the direct causes of the geometric misalignment of the detection light and its deviation from the detector sensing center. To clarify the influence of the integrated attitude error of the detection light on the interferometric phase and displacement measurement results, based on the 4D expression of the wave vector of special relativity, this paper directly relates the optical frequency and optical wave vector to the grating equation, constructs a Doppler frequency shift theory system with any arbitrary angle of incidence and grating motion along any direction, and demonstrates the physical characteristics that the frequency shift relationship of diffraction light at the same level is consistent under different grating incidence angles. By comparing the physical images between laser and grating interference systems, it is clarified that even if the optical geometric path of the system does not change with the motion, the reason for the phase change is the special wave vector modulation relationship on the grating surface. The conclusion shows that the grating interference system maintains the displacement transformation relationship in the presence of integrated attitude error of the detection light, and the deflection of the grating period direction is the key source of the geometric measurement error of the system. To preliminarily determine the measurement performance index of a certain system, a method that can quickly determine the original resolution of displacement measurement is given in this paper. Since the frequency shift theory in this paper starts from the underlying logic of physics, the relevant conclusions are universal, which not only guides the principle analysis of all grating interference systems, but also has an important reference for the analysis of geometric measurement errors in various advanced systems.
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图 1 沿
${x}''$ 运动的坐标旋转示意图Figure 1. Schematic diagram of coordinate rotation along the
$x''$ axis
图 2 光栅与入射光源相对运动示意图
Figure 2. Schematic diagram of the relative motion between the grating and the incident light source
图 3 光栅衍射过程的矢量分解示意图
Figure 3. Schematic diagram of vector decomposition of the grating diffraction process
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[1] 李同保. 纳米计量与传递标准[J]. 上海计量测试, 2005(1): 8-13. doi: 10.3969/j.issn.1673-2235.2005.01.001 [2] 王芳, 施玉书, 张树, 等. 基于硅晶格常数的纳米线宽计量技术[J]. 计量科学与技术, 2022, 66(4): 13-18,47. [3] KUNZMANN H, PFEIFER T, SCHMITT R, et al. Productive Metrology - Adding Value to Manufacture[J]. CIRP Annals - Manufacturing Technology, 2005, 54(2): 155-168. doi: 10.1016/S0007-8506(07)60024-9 [4] GAO W, HAITJEMA H, FANG F Z, et al. On-machine and in-process surface metrology for precision manufacturing[J]. CIRP Annals - Manufacturing Technology, 2019, 68(2): 843-866. doi: 10.1016/j.cirp.2019.05.005 [5] MONOSTORI L, KáDáR B, BAUERNHANSL T, et al. Cyber-physical systems in manufacturing[J]. CIRP Annals - Manufacturing Technology, 2016, 65(2): 621-641. doi: 10.1016/j.cirp.2016.06.005 [6] LEE J, BAGHERI B, KAO H-A. A Cyber-Physical Systems architecture for Industry 4.0-based manufacturing systems[J]. Manufacturing Letters, 2015(3): 18-23. [7] GAO W, KIM S W, BOSSE H, et al. Measurement technologies for precision positioning[J]. CIRP Annals - Manufacturing Technology, 2015, 64(2): 773-796. doi: 10.1016/j.cirp.2015.05.009 [8] 李琪, 施玉书, 李伟, 等. 微纳米光学测量的严格耦合波分析方法[J]. 计量科学与技术, 2020(12): 3-6,11. doi: 10.3969/j.issn.2096-9015.2020.12.01 [9] KUNZMANN H, PFEIFER T, FLüGGE J. Scales vs. Laser Interferometers Performance and Comparison of Two Measuring Systems[J]. CIRP Annals - Manufacturing Technology, 1993, 42(2): 753-767. doi: 10.1016/S0007-8506(07)62538-4 [10] KUNZMANN H. Nanometrology at the PTB[J]. Metrologia, 1992, 28(6): 443-453. [11] SHIBAZAKI Y, KOHNO H, HAMATANI M. An innovative platform for high-throughput high-accuracy lithography using a single wafer stage[J]. Optical Microlithography XXII, 2009, 7274: 514-525. [12] CASTENMILLER T, VAN DE MAST F, DE KORT T, et al. Towards Ultimate Optical Lithography with NXT: 1950i Dual Stage Immersion Platform[C]//Optical Microlithography XXIII. International Society for Optics and Photonics, 2010: 76401N. [13] LEE C, LEE S-K. Multi-degree-of-freedom motion error measurement in an ultraprecision machine using laser encoder — Review[J]. Journal of Mechanical Science and Technology, 2013, 27(1): 141-152. doi: 10.1007/s12206-012-1217-6 [14] HIRANO K, SHIBAZAKI Y, HAMATANI M, et al. Latest results from the Nikon NSR-S620 double patterning immersion scanner[J]. Proceedings of SPIE - The International Society for Optical Engineering, 2009, 7520: 75200Z. [15] HU P C, CHANG D, TAN J B, et al. Displacement measuring grating interferometer: a review[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(5): 631-654. [16] HSIEH H L, LEE J Y, WU W T, et al. Quasi-common-optical-path heterodyne grating interferometer for displacement measurement[J]. Measurement Science and Technology, 2010, 21(11): 115304. doi: 10.1088/0957-0233/21/11/115304 [17] CHANG D, XING X, HU P, et al. Double-Diffracted Spatially Separated Heterodyne Grating Interferometer and Analysis on its Alignment Tolerance[J]. Applied Sciences, 2019, 9(2): 263. doi: 10.3390/app9020263 [18] WEI C, YAN S, LIN C, et al. Compact grating displacement measurement system with a 3×3 coupler[J]. Chin Opt Lett, 2015, 13(5): 051301. doi: 10.3788/COL201513.051301 [19] FAN K C, LAI Z F, WU P, et al. A displacement spindle in a micro/nano level[J]. Measurement Science and Technology, 2007, 18(6): 1710-1717. doi: 10.1088/0957-0233/18/6/S07 [20] KAO C F, LU S H, SHEN H M, et al. Diffractive Laser Encoder with a Grating in Littrow Configuration[J]. Japanese Journal of Applied Physics, 2008, 47(3): 1833-1837. doi: 10.1143/JJAP.47.1833 [21] WISE S, QUETSCHKE V, DESHPANDE A J, et al. Phase effects in the diffraction of light: Beyond the grating equation[J]. Physical Review Letters, 2005, 95(1): 031901. [22] JACKSON J D. Classical electrodynamics[J]. American Journal of Physics, 1999, 67(9): 841. [23] SHIMIZU Y, CHEN L C, KIM D W, et al. An insight into optical metrology in manufacturing[J]. Measurement Science and Technology, 2021, 32(4): 1-4. [24] CHEBEN P, HALIR R, SCHMID J H, et al. Subwavelength integrated photonics[J]. Nature, 2018, 560(7720): 565-572. doi: 10.1038/s41586-018-0421-7 -
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