Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates

LIN Zichao; YAO Yulin; ZHOU Tong; XUE Dongbai; GU Zhenjie; DENG Xiao; CHENG Xinbin; LI Tongbao

doi:10.12338/j.issn.2096-9015.2022.0248

Volume 66 Issue 11

Jan. 2023

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Article Navigation > Metrology Science and Technology > 2022 > 66(11): 3-11, 26

LIN Zichao, YAO Yulin, ZHOU Tong, XUE Dongbai, GU Zhenjie, DENG Xiao, CHENG Xinbin, LI Tongbao. Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates[J]. Metrology Science and Technology, 2022, 66(11): 3-11, 26. doi: 10.12338/j.issn.2096-9015.2022.0248

Citation:

LIN Zichao, YAO Yulin, ZHOU Tong, XUE Dongbai, GU Zhenjie, DENG Xiao, CHENG Xinbin, LI Tongbao. Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates[J]. Metrology Science and Technology, 2022, 66(11): 3-11, 26. doi: 10.12338/j.issn.2096-9015.2022.0248

Citation:

LIN Zichao, YAO Yulin, ZHOU Tong, XUE Dongbai, GU Zhenjie, DENG Xiao, CHENG Xinbin, LI Tongbao. Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates[J]. Metrology Science and Technology, 2022, 66(11): 3-11, 26. doi: 10.12338/j.issn.2096-9015.2022.0248

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Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates

doi: 10.12338/j.issn.2096-9015.2022.0248

LIN Zichao^{1, 2, 3, 4, 5
,},
YAO Yulin^{1, 2, 3, 4, 5},
ZHOU Tong^{1, 2, 3, 4, 5},
XUE Dongbai^{1, 2, 3, 4, 5},
GU Zhenjie^{1, 2, 3, 4, 5},
DENG Xiao^{1, 2, 3, 4, 5
,
,},
CHENG Xinbin^{1, 2, 3, 4, 5},
LI Tongbao^{1, 2, 3, 4, 5}

1.
Institute of Precision Optical Engineering, Shanghai 200092, China
2.
MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai 200092, China
3.
Shanghai Frontiers Science Center of Digital Optics, Shanghai 200092, China
4.
Shanghai Professional Technical Service Platform for Full-Spectrum and High-Performance Optical Thin Film Devices and Applications, Shanghai 200092, China
5.
School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

Available Online: 2022-12-01
Publish Date: 2023-01-17

Abstract

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.
- grating interference system,
- 4D covariates,
- grating Doppler effect,
- attitude error,
- measurement resolution

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References(24)

References

[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