位移测量光栅干涉仪综述

胡鹏程; 常笛; 谭久彬; 杨睿韬; 杨宏兴; 付海金

doi:10.1631/FITEE.1800708

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位移测量光栅干涉仪综述

精密测量与仪器技术专题 | Updated：2022-05-19

- 位移测量光栅干涉仪综述
  Enhanced Publication
- Displacement measuring grating interferometer: a review
- 信息与电子工程前沿（英文） 2019年20卷第5期页码：631-654
- Affiliations：
  
  Center of Ultra-precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China
  Key Lab of Ultra-precision Intelligent Instrumentation, Ministry of Industry and Information Technology, Harbin 150080, China
- Author bio：
  
  Jiu-bin TAN, E-mail: jbtan@hit.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 51605120, 51675138, and 61675058) and the National Science and Technology Major Project, China (No. 2017ZX02101006-005)
- DOI：10.1631/FITEE.1800708
  中图分类号： TH744.3;TH822
- 纸质出版日期：2019-05，
  
  收稿日期：2018-11-07，
  
  修回日期：2019-05-08，
- Accepted：
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胡鹏程, 常笛, 谭久彬, 等. 位移测量光栅干涉仪综述[J]. 信息与电子工程前沿（英文）, 2019,20(5):631-654.

PENG-CHENG HU, DI CHANG, JIU-BIN TAN, et al. Displacement measuring grating interferometer: a review. [J]. Frontiers of information technology & electronic engineering, 2019, 20(5): 631-654.
胡鹏程, 常笛, 谭久彬, 等. 位移测量光栅干涉仪综述[J]. 信息与电子工程前沿（英文）, 2019,20(5):631-654. DOI： 10.1631/FITEE.1800708.

PENG-CHENG HU, DI CHANG, JIU-BIN TAN, et al. Displacement measuring grating interferometer: a review. [J]. Frontiers of information technology & electronic engineering, 2019, 20(5): 631-654. DOI： 10.1631/FITEE.1800708.

摘要

Abstract

A grating interferometer

called the "optical encoder

" is a commonly used tool for precise displacement measurements. In contrast to a laser interferometer

a grating interferometer is insensitive to the air refractive index and can be easily applied to multi-degree-of-freedom measurements

which has made it an extensively researched and widely used device. Classified based on the measuring principle and optical configuration

a grating interferometer experiences three distinct stages of development: homodyne

heterodyne

and spatially separated heterodyne. Compared with the former two

the spatially separated heterodyne grating interferometer could achieve a better resolution with a feature of eliminating periodic nonlinear errors. Meanwhile

numerous structures of grating interferometers with a high optical fold factor

a large measurement range

good usability

and multi- degree-of-freedom measurements have been investigated. The development of incremental displacement measuring grating interferometers achieved in recent years is summarized in detail

and studies on error analysis of a grating interferometer are briefly introduced.

关键词

Keywords

Grating interferometerOptical encoderDisplacement measurementPrecision measurement

references

K Akiyama, , , H Iwaoka. . High Resolution Digital Diffraction Grating Scale Encoder. . US Patent US4629886A, , 1986. ..

S Asano, , , T Goto, , , H Tanimura, , , 等. . Development of a new measurement system for straightness error by a heterodyne interferometer with a grating. . Proc 10th Initiatives of Precision Engineering at the Beginning of a Millennium, , 2001. . p.799--803. . DOI:10.1007/0-306-47000-4_157http://doi.org/10.1007/0-306-47000-4_157..

VG Badami, , , PJ de Groot. . Displacement measuring interferometry. . In: Harding K (Ed.), Handbook of Optical Dimensional Metrology. CRC Press, Boca Raton, USA, , 2013. . p.157--238. . ..

M Badaroglu, , , K Ng, , , M Salmani, , , 等. . More Moore landscape for system readiness—ITRS2.0 requirements. . IEEE 32nd Int Conf on Computer Design, , 2014. . p.147--152. . DOI:10.1109/ICCD.2014.6974674http://doi.org/10.1109/ICCD.2014.6974674..

EW Bae, , , JA Kim, , , SH Kim. . Multi-degree-of-freedom displacement measurement system for milli-structures. . Meas Sci Technol, , 2011. . 121495--1502. . DOI:10.1088/0957-0233/12/9/316http://doi.org/10.1088/0957-0233/12/9/316..

Y Bai, , , PC Hu, , , YF Lu, , , 等. . A six-axis heterodyne interferometer system for Joule balance. . IEEE Trans Instrum Meas, , 2017. . 66((6):):1579--1585. . DOI:10.1109/TIM.2016.2634758http://doi.org/10.1109/TIM.2016.2634758..

JL Bi, , , SB Liu. . Precision measurement of displacement with two quasi-orthogonal signals for linear diffraction grating interferometric sensors. . Proc 6th Int Conf on Machinery, Materials, Environment, Biotechnology and Computer, , 2016. . p.25--29. . DOI:10.2991/mmebc-16.2016.5http://doi.org/10.2991/mmebc-16.2016.5..

HJ Cai. . Research on Picometer Resolution Phase Subdivision for Heterodyne Laser Interferometer Signals. . MS Thesis, Harbin Institute of Technology, Harbin, China, , 2015. ..

D Chang, , , X Xing, , , P Hu, , , 等. . Double-diffracted spatially separated heterodyne grating interferometer and analysis on its alignment tolerance. . Appl Sci, , 2019. . 9((2):):Article 263DOI:10.3390/app9020263http://doi.org/10.3390/app9020263..

F Cheng, , , KC Fan. . Linear diffraction grating interferometer with high alignment tolerance and high accuracy. . Appl Opt, , 2011. . 50((22):):4550--4556. . DOI:10.1364/AO.50.004550http://doi.org/10.1364/AO.50.004550..

F Cheng, , , KC Fan, , , YT Fei. . An improved design of the linear diffraction grating interferometer. . Proc Asian Symp on Precision Engineering and Nanotechnology, , 2009a. . p.146--149. . ..

F Cheng, , , YT Fei, , , KC Fan. . New method on real-time signal correction and subdivision for grating-based nanometrology. . Proc 4th Int Symp on Advanced Optical Manufacturing and Testing Technologies: Design, Manufacturing, and Testing of Micro- and Nano-Optical Devices and Systems, , 2009b. . No. 728403DOI:10.1117/12.832061http://doi.org/10.1117/12.832061..

A Cho. . The long road to LIGO. . Science, , 2016. . 353((6299):):534--535. . DOI:10.1126/science.353.6299.534http://doi.org/10.1126/science.353.6299.534..

XC Chu, , , HB Lü, , , SH Zhao. . Research on long-range grating interferometry with nanometer resolution. . Meas Sci Technol, , 2008. . 19((1):):017001DOI:10.1088/0957-0233/19/1/017001http://doi.org/10.1088/0957-0233/19/1/017001..

YC Chung, , , KC Fan, , , BC Lee. . Development of a novel planar encoder for 2D displacement measurement in nanometer resolution and accuracy. . Proc 9th World Congress on Intelligent Control and Automation, , 2011. . p.449--453. . DOI:10.1109/WCICA.2011.5970554http://doi.org/10.1109/WCICA.2011.5970554..

G Cloud. . Optical methods in experimental mechanics, part 16: the optical Doppler effect. . Exp Tech, , 2005. . 29((2):):17--19. . DOI:10.1111/j.1747-1567.2005.tb00207.xhttp://doi.org/10.1111/j.1747-1567.2005.tb00207.x..

SJAG Cosijns, , , MJ Jansen. . Advanced optical incremental sensors: encoders and interferometers. . In: Nihtianov S, Luque A (Eds.), Smart Sensors and MEMS: Intelligent Devices and Microsystems for Industrial Applications. Woodhead Publishing, Oxford, UK, , 2014. . p.230--277. . DOI:10.1533/9780857099297.1.230http://doi.org/10.1533/9780857099297.1.230..

C Damm, , , T Peschel, , , S Risse, , , 等. . Wafer stage assembly for ion projection lithography. . Microelectron Eng, , 2001. . 57-58181--185. . DOI:10.1016/S0167-9317(01)00513-5http://doi.org/10.1016/S0167-9317(01)00513-5..

LL Deck, , , PJ de Groot, , , M Schroeder. . Interferometric Encoder Systems. . US Patent US898 869 0B2, , 2015. ..

PJ de Groot, , , M Schroeder. . Interferometric Heterodyne Optical Encoder System. . US Patent US2012/0194824, , 2012. ..

PJ de Groot, , , VG Badami, , , J Liesener. . Concepts and geometries for the next generation of precision heterodyne optical encoders. . Proc 31st Annual Meeting of the American Society for Precision Engineering, , 2016. . p.146--149. . ..

JJ Deng, , , XN Yan, , , CL Wei, , , 等. . Eightfold optical encoder with high-density grating. . Appl Opt, , 2018. . 57((10):):2366--2375. . DOI:10.1364/AO.57.002366http://doi.org/10.1364/AO.57.002366..

M Dobosz. . High-resolution laser linear encoder with numerical error compensation. . Opt Eng, , 1999. . 38((6):):968--973. . DOI:10.1117/1.602137http://doi.org/10.1117/1.602137..

Dr. Johannes Heidenhain GmbH. . Exposed linear encoders, , https://www.heidenhain.com/fileadmin/pdb/media/img/208960-2E_Exposed_Linear_Encoders_en.pdfhttps://www.heidenhain.com/fileadmin/pdb/media/img/208960-2E_Exposed_Linear_Encoders_en.pdf, , [Accessed on Aug. 15, 2018]2018. ..

JD Ellis. . Field Guide to Displacement Measuring Interferometry, , ::Bellingham, UKSPIE Press, , 2014. ..

KC Fan, , , F Cheng. . LDGI signal subdivision by soft computing for nanomeasurement. . Proc 6th Int Symp on Precision Engineering Measurements and Instrumentation, , 2010. . No. 75440IDOI:10.1117/12.885413http://doi.org/10.1117/12.885413..

KC Fan, , , YS Liu, , , YJ Chen, , , 等. . A linear diffraction grating interferometer with high accuracy. . Proc 3rd Int Symp on Precision Mechanical Measurements, , 2006. . No. 628008DOI:10.1117/12.715260http://doi.org/10.1117/12.715260..

KC Fan, , , ZF Lai, , , P Wu, , , 等. . A displacement spindle in a micro/nano level. . Meas Sci Technol, , 2007. . 18((6):):1710--1717. . DOI:10.1088/0957-0233/18/6/S07http://doi.org/10.1088/0957-0233/18/6/S07..

KC Fan, , , JW Miao, , , W Gong, , , 等. . High precision measurement system based on coplanar XY-stage. . Proc 7th Int Symp on Precision Engineering Measurement and Instrumentation, , 2011a. . No. 832119DOI:10.1117/12.904072http://doi.org/10.1117/12.904072..

KC Fan, , , BC Lee, , , YC Chung. . A planar laser diffraction encoder in Littrow configuration for 2D nanometric positioning. . Int J Autom Smart Technol, , 2011b. . 1((2):):93--99. . DOI:10.5875/ausmt.v1i2.53http://doi.org/10.5875/ausmt.v1i2.53..

KC Fan, , , BH Liao, , , YC Chung, , , 等. . Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution. . Proc IEEE Int Instrumentation and Measurement Technology Conf, , 2012a. . p.894--897. . DOI:10.1109/I2MTC.2012.6229209http://doi.org/10.1109/I2MTC.2012.6229209..

KC Fan, , , YL Zhang, , , JW Miao, , , 等. . Error compensation of grating interferometer due to angular error of linear stage. . Proc IEEE/ASME Int Conf on advanced Intelligent Mechatronics, , 2012b. . p.428--431. . DOI:10.1109/AIM.2012.6265886http://doi.org/10.1109/AIM.2012.6265886..

KC Fan, , , HY Wang, , , HW Yang, , , 等. . Techniques of multi-degree-of-freedom measurement on the linear motion errors of precision machines. . Adv Opt Technol, , 2014. . 3((4):):375--386. . DOI:10.1515/aot-2014-0038http://doi.org/10.1515/aot-2014-0038..

C Feng, , , M Kajima, , , S Gonda, , , 等. . Accurate measurement of orthogonality of equal-period, two-dimensional gratings by an interferometric method. . Metrologia, , 2012. . 49236--244. . DOI:10.1088/0026-1394/49/3/236http://doi.org/10.1088/0026-1394/49/3/236..

C Feng, , , LJ Zeng, , , SW Wang. . Heterodyne planar grating encoder with high alignment tolerance, especially insensitivity to grating tilts. . Proc 8th Int Symp on Precision Engineering Measurement and Instrumentation, , 2013. . No. 87593LDOI:10.1117/12.2012649http://doi.org/10.1117/12.2012649..

HJ Fu, , , RD Ji, , , PC Hu, , , 等. . Measurement method for nonlinearity in heterodyne laser interferometers based on double-channel quadrature demodulation. . Sensors, , 2018a. . 18((9):):Article 2768DOI:10.3390/s18092768http://doi.org/10.3390/s18092768..

HJ Fu, , , Y Wang, , , PC Hu, , , 等. . Nonlinear errors resulting from ghost reflection and its coupling with optical mixing in heterodyne laser interferometers. . Sensors, , 2018b. . 18((3):):Article 758DOI:10.3390/s18030758http://doi.org/10.3390/s18030758..

W Gao. . Precision Nanometrology. . Springer-Verlag London Limited, London, UK, , 2010. . p.69--140. . ..

W Gao, , , A Kimura. . A three-axis displacement sensor with nanometric resolution. . CIRP Ann, , 2007. . 56((1):):529--532. . DOI:10.1016/j.cirp.2007.05.126http://doi.org/10.1016/j.cirp.2007.05.126..

W Gao, , , A Kimura. . A fast evaluation method for pitch deviation and out-of-flatness of a planar scale grating. . CIRP Ann, , 2010. . 59505--508. . DOI:10.1016/j.cirp.2010.03.035http://doi.org/10.1016/j.cirp.2010.03.035..

W Gao, , , Y Saito, , , H Muto, , , 等. . A three-axis autocollimator for detection of angular error motions of a precision stage. . CIRP Ann, , 2011. . 60515--518. . DOI:10.1016/j.cirp.2011.03.052http://doi.org/10.1016/j.cirp.2011.03.052..

ZY Gao, , , JC Hu, , , Y Zhu, , , 等. . A new 6-degree-of- freedom measurement method of X-Y stages based on additional information. . Prec Eng, , 2013. . 37((3):):606--620. . DOI:10.1016/j.precisioneng.2013.01.006http://doi.org/10.1016/j.precisioneng.2013.01.006..

W Gao, , , SW Kim, , , H Bosse, , , 等. . Measurement technologies for precision positioning. . CIRP Ann, , 2015. . 64((2):):773--796. . DOI:10.1016/j.cirp.2015.05.009http://doi.org/10.1016/j.cirp.2015.05.009..

S Goler, , , A Bertolini, , , M Born, , , 等. . The AEI 10m prototype interferometer. . Class Quant Grav, , 2010. . 27((8):):Article 080423DOI:10.1088/0264-9381/27/8/084023http://doi.org/10.1088/0264-9381/27/8/084023..

J Guan, , , P Kchert, , , C Weichert, , , 等. . A differential interferometric heterodyne encoder with 30 picometer periodic nonlinearity and sub-nanometer stability. . Prec Eng, , 2017. . 50114--118. . DOI:10.1016/j.precisioneng.2017.04.019http://doi.org/10.1016/j.precisioneng.2017.04.019..

DM Guo, , , M Wang. . Note: design of a laser feedback interferometer with double diffraction system. . Rev Sci Instrum, , 2015. . 86((9):):096111DOI:10.1063/1.4931781http://doi.org/10.1063/1.4931781..

DM Guo, , , M Wang, , , H Hao. . Displacement measurement using a laser feedback grating interferometer. . Appl Opt, , 2015. . 54((31):):9320--9325. . DOI:10.1364/AO.54.009320http://doi.org/10.1364/AO.54.009320..

DM Guo, , , M Wang, , , H Hao. . Self-mixing grating interferometer: theoretical analysis and experimental observations. . Proc Interferometry XVIII, , 2016. . No. 996019DOI:10.1117/12.2239519http://doi.org/10.1117/12.2239519..

DM Guo, , , L Shi, , , YG Yu, , , 等. . Micro-displacement reconstruction using a laser self-mixing grating interferometer with multiple-diffraction. . Opt Exp, , 2017. . 25((25):):31394--31406. . DOI:10.1364/OE.25.031394http://doi.org/10.1364/OE.25.031394..

RK Heilmann, , , CG Chen, , , PT Konkola, , , 等. . Dimensional metrology for nanometer-scale science and engineering: towards sub-nanometer accurate encoders. . Nanotechnology, , 2004. . 15((10):):S504--S511. . DOI:10.1088/0957-4484/15/10/002http://doi.org/10.1088/0957-4484/15/10/002..

W Holzapfel. . Advancements in displacement metrology based on encoder systems. . Proc 23rd Annual Meeting of the American Society for Precision Engineering, , 2008. . p.1--4. . ..

Y Hori, , , S Gonda, , , Y Bitou, , , 等. . Periodic error evaluation system for linear encoders using a homodyne laser interferometer with 10 picometer uncertainty. . Prec Eng, , 2018. . 51388--392. . DOI:10.1016/j.precisioneng.2017.09.009http://doi.org/10.1016/j.precisioneng.2017.09.009..

K Hosono, , , W Kim, , , A Kimura, , , 等. . Surface encoders for a mosaic scale grating. . Int J Autom Technol, , 2011. . 5((2):):91--96. . DOI:10.20965/ijat.2011.p0091http://doi.org/10.20965/ijat.2011.p0091..

GM Hossein, , , MJ Lin, , , JB Horng, , , 等. . Critical femtosecond laser parameters for the fabrication of optimal reflecting diffraction grating on Invar36. . Opt Laser Eng, , 2016. . 8197--102. . DOI:10.1016/j.optlaseng.2016.01.004http://doi.org/10.1016/j.optlaseng.2016.01.004..

WM Hou, , , YB Zhang, , , HJ Hu. . A simple technique for eliminating the nonlinearity of a heterodyne interferometer. . Meas Sci Technol, , 2009. . 20((10):):105303DOI:10.1088/0957-0233/20/10/105303http://doi.org/10.1088/0957-0233/20/10/105303..

HL Hsieh, , , W Chen. . Heterodyne Wollaston laser encoder for measurement of in-plane displacement. . Opt Exp, , 2016. . 24((8):):8693--8707. . DOI:10.1364/OE.24.008693http://doi.org/10.1364/OE.24.008693..

HL Hsieh, , , SW Pan. . Three-degree-of-freedom displacement measurement using grating-based heterodyne interferometry. . Appl Opt, , 2013. . 52((27):):6840--6848. . DOI:10.1364/AO.52.006840http://doi.org/10.1364/AO.52.006840..

HL Hsieh, , , SW Pan. . Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements. . Opt Exp, , 2015. . 23((3):):2451--2465. . DOI:10.1364/OE.23.002451http://doi.org/10.1364/OE.23.002451..

HL Hsieh, , , JY Lee, , , WT Wu, , , 等. . Quasi-common- optical-path heterodyne grating interferometer for displacement measurement. . Meas Sci Technol, , 2010. . 21((11):):115304DOI:10.1088/0957-0233/21/11/115304http://doi.org/10.1088/0957-0233/21/11/115304..

HL Hsieh, , , JC Chen, , , G Lerondel, , , 等. . Two- dimensional displacement measurement by quasi- common-optical-path heterodyne grating interferometer. . Opt Exp, , 2011. . 19((10):):9770--9782. . DOI:10.1364/OE.19.009770http://doi.org/10.1364/OE.19.009770..

HL Hsieh, , , JY Lee, , , YC Chung. . Wavelength-modulated heterodyne grating shearing interferometry for precise displacement measurement. . Adv Opt Technol, , 2014. . 3((4):):395--400. . DOI:10.1515/aot-2014-0027http://doi.org/10.1515/aot-2014-0027..

CC Hsu, , , CC Wu, , , JY Lee, , , 等. . Reflection type heterodyne grating interferometry for in-plane displacement measurement. . Opt Commun, , 2008. . 281((9):):2582--2589. . DOI:10.1016/j.optcom.2007.12.098http://doi.org/10.1016/j.optcom.2007.12.098..

CC Hsu, , , JY Lee, , , CC Wu. . Compensated laser encoder with symmetric and quasi-common-path heterodyne interferometry. . Optical Measurement Systems for Industrial Inspection, , 2009. . No. 73891MDOI:10.1117/12.827453http://doi.org/10.1117/12.827453..

CC Hsu, , , PP Sung, , , ZR Lin, , , 等. . Prototype of a compact displacement sensor with a holographic diffraction grating. . Opt Laser Technol, , 2013. . 48200--205. . DOI:10.1016/j.optlastec.2012.10.003http://doi.org/10.1016/j.optlastec.2012.10.003..

CC Hsu, , , H Chen, , , CW Chiang, , , 等. . Dual displacement resolution encoder by integrating single holographic grating sensor and heterodyne interferometry. . Opt Exp, , 2017. . 25((24):):30189--30202. . DOI:10.1364/OE.25.030189http://doi.org/10.1364/OE.25.030189..

CC Hsu, , , H Chen, , , HY Tseng, , , 等. . High displacement resolution encoder by using triple grating combination interferometer. . Opt Laser Technol, , 2018. . 105221--228. . DOI:10.1016/j.optlastec.2018.03.005http://doi.org/10.1016/j.optlastec.2018.03.005..

PC Hu, , , F Pollinger, , , K Meiners-Hagen, , , 等. . Fine correction of nonlinearity in homodyne interferometry. . 6th Int Symp on Precision Engineering Measurements and Instrumentation, , 2010. . No. 75444EDOI:10.1117/12.885392http://doi.org/10.1117/12.885392..

PC Hu, , , JB Tan, , , P Chen. . Double Frequency Laser Grating Interference Three-dimensional Measurement Method and System with Optical Aliasing Resistance. . CN Patent CN103 604 376A, , 2014. ..

PC Hu, , , JH Zhu, , , XB Guo, , , 等. . Compensation for the variable cyclic error in homodyne laser interferometers. . Sensors, , 2015. . 153090--3106. . DOI:10.3390/s150203090http://doi.org/10.3390/s150203090..

HL Huang, , , CH Liu, , , WY Jywe, , , 等. . Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage. . Rev Sci Instrum, , 2007. . 78((6):):066103DOI:10.1063/1.2743165http://doi.org/10.1063/1.2743165..

S Ito, , , R Aihara, , , WJ Kim, , , 等. . Three-axis vibration measurement by using a grating-interferometric vibrometer. . Adv Opt Technol, , 2014. . 3((4):):435--440. . DOI:10.1515/aot-2014-0028http://doi.org/10.1515/aot-2014-0028..

A Jaktas, , , S Kauinis, , , J Flügge. . Investigation of calibration facilities of precision line scales. . Mechanika, , 2005. . 53((3):):62--67. . ..

YS Jang, , , SW Kim. . Compensation of the refractive index of air in laser interferometer for distance measurement: a review. . Int J Prec Eng Manuf, , 2017. . 18((12):):1881--1890. . DOI:10.1007/s12541-017-0217-yhttp://doi.org/10.1007/s12541-017-0217-y..

ML Jiang, , , FP Li, , , XD Wang. . Mini-nano-displacement measurement with double diffraction grating. . Adv Mater Res, , 2011. . 230-2321159DOI:10.4028/www.scientific.net/AMR.230-232.1159http://doi.org/10.4028/www.scientific.net/AMR.230-232.1159..

ML Jiang, , , FP Li, , , XD Wang. . Nano-displacement measurement with grating interference. . Appl Mech Mater, , 2012. . 10335--40. . DOI:10.4028/www.scientific.net/AMM.103.35http://doi.org/10.4028/www.scientific.net/AMM.103.35..

ML Jiang, , , HF Li, , , XD Wang, , , 等. . Research status and developing trends of grating nanometer measuring technology. . 6th Int Symp on Precision Mechanical Measurements, , 2013. . No. 891631DOI:10.1117/12.2035685http://doi.org/10.1117/12.2035685..

Y Jourlin, , , J Jay, , , O Parriaux. . Compact diffractive interferometric displacement sensor in reflection. . Prec Eng, , 2002. . 261--6. . DOI:10.1016/S0141-6359(01)00081-2http://doi.org/10.1016/S0141-6359(01)00081-2..

CF Kao, , , CC Chang, , , MH Lu. . Double-diffraction planar encoder by conjugate optics. . Opt Eng, , 2005a. . 44((2):):023603DOI:10.1117/1.1839227http://doi.org/10.1117/1.1839227..

CF Kao, , , SH Lu, , , MH Lu. . High resolution planar encoder by retro-reflection. . Rev Sci Instrum, , 2005b. . 76((8):):085110DOI:10.1063/1.2006368http://doi.org/10.1063/1.2006368..

CF Kao, , , SH Lu, , , HM Shen, , , 等. . Diffractive laser encoder with a grating in Littrow configuration. . Jpn J Appl Phys, , 2008. . 47((3):):1833--1837. . DOI:10.1143/JJAP.47.1833http://doi.org/10.1143/JJAP.47.1833..

OG Karhade, , , FL Degertekin, , , TR Kurfess. . SOI-based micro scanning grating interferometers: device characterization, control and demonstration of parallel operation. . J Microm Micr, , 2008. . 18((4):):045007DOI:10.1088/0960-1317/18/4/045007http://doi.org/10.1088/0960-1317/18/4/045007..

J Kilby. . The integrated circuit's early history. . Proc IEEE, , 2000. . 88((1):):109--111. . DOI:10.1109/5.811607http://doi.org/10.1109/5.811607..

JA Kim, , , KC Kim, , , EW Bae, , , 等. . Six-degree-of- freedom displacement measurement system using a diffraction grating. . Rev Sci Instrum, , 2000. . 71((8):):3214--3219. . DOI:10.1063/1.1305816http://doi.org/10.1063/1.1305816..

JA Kim, , , EW Bae, , , SH Kim, , , 等. . Design methods for six-degree-of-freedom displacement measurement systems using cooperative targets. . Prec Eng, , 2002. . 26((1):):99--104. . DOI:10.1016/S0141-6359(01)00105-2http://doi.org/10.1016/S0141-6359(01)00105-2..

P Kim, , , D Kim, , , K You. . Adaptive compensation for the nonlinearity error in a heterodyne interferometer. . J Korean Phys Soc, , 2012. . 61((11):):1759--1765. . DOI:10.3938/jkps.61.1759http://doi.org/10.3938/jkps.61.1759..

A Kimura, , , W Gao, , , Y Arai, , , 等. . Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness. . Prec Eng, , 2010a. . 34((1):):145--155. . DOI:10.1016/j.precisioneng.2009.05.008http://doi.org/10.1016/j.precisioneng.2009.05.008..

A Kimura, , , W Gao, , , LJ Zeng. . Position and out-of- straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder. . Meas Sci Technol, , 2010b. . 21054005DOI:10.1088/0957-0233/21/5/054005http://doi.org/10.1088/0957-0233/21/5/054005..

A Kimura, , , K Hosono, , , WJ Kim, , , 等. . A two-degree- of-freedom linear encoder with a mosaic scale grating. . Int J Nanomanuf, , 2011. . 7((1):):73--91. . DOI:10.1504/IJNM.2011.039964http://doi.org/10.1504/IJNM.2011.039964..

A Kimura, , , W Gao, , , WJ Kim, , , 等. . A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement. . Prec Eng, , 2012. . 36((4):):576--585. . DOI:10.1016/j.precisioneng.2012.04.005http://doi.org/10.1016/j.precisioneng.2012.04.005..

H Kunzmann, , , T Pfeifer, , , J Flügge. . Scales vs. . laser interferometers performance and comparison of two measuring systems. CIRP Ann, , 1993. . 42((2):):753--767. . DOI:10.1016/S0007-8506(07)62538-4http://doi.org/10.1016/S0007-8506(07)62538-4..

YBP Kwan. . Lithographic Apparatus, Device Manufacturing Method and Device Manufactured Thereby. . US Patent US794 039 2, , 2011. ..

HB Lan, , , YC Ding, , , HZ Liu, , , 等. . Review of the wafer stage for nanoimprint lithography. . Microelectron Eng, , 2007. . 84((4):):684--688. . DOI:10.1016/16/j.mee.200.2007.01.002http://doi.org/10.1016/16/j.mee.200.2007.01.002..

J Lazar, , , O p, , , M ek, , , 等. . Multiaxis interferometric system for positioning in nanometrology. . Proc 9th WSEAS Int Conf on Microelectronics, Nanoelectronics, Optoelectronics, , 2010. . p.92--95. . ..

CB Lee, , , SK Lee. . Multi-degree-of-freedom motion error measurement in an ultraprecision machine using laser encoder. . Rev J Mech Sci Technol, , 2013. . 27((1):):141--152. . DOI:10.1007/s12206-012-1217-6http://doi.org/10.1007/s12206-012-1217-6..

CB Lee, , , GH Kim, , , SK Lee. . Design and construction of a single unit multi-function optical encoder for a six- degree-of-freedom motion error measurement in an ultraprecision linear stage. . Meas Sci Technol, , 2011. . 22((10):):105901DOI:10.1088/0957-0233/22/10/105901http://doi.org/10.1088/0957-0233/22/10/105901..

CB Lee, , , GH Kim, , , SK Lee. . Uncertainty investigation of grating interferometry in six degree-of-freedom motion error measurements. . Int J Prec Eng Manuf, , 2012. . 13((9):):1509--1515. . DOI:10.1007/s12541-012-0199-8http://doi.org/10.1007/s12541-012-0199-8..

CK Lee, , , CC Wu, , , SJ Chen, , , 等. . Design and construction of linear laser encoders that possess high tolerance of mechanical runout. . Appl Opt, , 2004. . 43((31):):5754--5762. . DOI:10.1364/AO.43.005754http://doi.org/10.1364/AO.43.005754..

JY Lee, , , MP Lu. . Optical heterodyne grating shearing interferometry for long-range positioning applications. . Opt Commun, , 2011. . 284((1):):857--862. . DOI:10.1016/j.optcom.2010.09.079http://doi.org/10.1016/j.optcom.2010.09.079..

JY Lee, , , GA Jiang. . Displacement measurement using a wavelength phase-shifting grating interferometer. . Opt Exp, , 2013. . 21((21):):25553--25564. . DOI:10.1364/OE.21.025553http://doi.org/10.1364/OE.21.025553..

JY Lee, , , HY Chen, , , CC Hsu, , , 等. . Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution. . Sensor Actuat A, , 2007. . 137((1):):185--191. . DOI:10.1016/j.sna.2007.02.017http://doi.org/10.1016/j.sna.2007.02.017..

JY Lee, , , HL Hsieh, , , C Lerondel, , , 等. . Heterodyne grating interferometer based on a quasi-common-optical path configuration for a two-degrees-of-freedom straightness measurement. . Appl Opt, , 2011. . 50((9):):1272--1279. . DOI:10.1364/AO.50.001272http://doi.org/10.1364/AO.50.001272..

TH Lee. . The (pre-) history of the integrated circuit: a random walk. . IEEE SSCS News, , 2007. . 12((2):):16--22. . DOI:10.1109/N-SSC.2007.4785573http://doi.org/10.1109/N-SSC.2007.4785573..

XH Li, , , W Gao, , , H Muto, , , 等. . A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage. . Prec Eng, , 2013. . 37((3):):771--781. . DOI:10.1016/j.precisioneng.2013.03.005http://doi.org/10.1016/j.precisioneng.2013.03.005..

XH Li, , , Y Shimizu, , , T Ito, , , 等. . Measurement of six- degree-of-freedom planar motions by using a multiprobe surface encoder. . Opt Eng, , 2014. . 53((12):):122405..

Q Li, , , X Liu, , , L Zhao, , , 等. . A novel vibration sensor based on phase grating interferometry. . Appl Phys B, , 2017. . 123((5):):Article 162DOI:10.1007/s00340-017-6724-9http://doi.org/10.1007/s00340-017-6724-9..

J Liesener. . Compact Encoder for Interferometric Encoder System. . US Patent US201 311 406 2A1, , 2013. ..

CB Lin, , , SH Yan, , , C Wei, , , 等. . Optimized design and error analysis of optical system for heterodyne grating interferometry. . Int Conf on Optical Instruments and Technology: Optoelectronic Measurement Technology and Systems, , 2013. . No. 90460CDOI:10.1117/12.2037576http://doi.org/10.1117/12.2037576..

CB Lin, , , SH Yan, , , ZG Du, , , 等. . High-efficiency gold-coated cross-grating for heterodyne grating interferometer with improved signal contrast and optical subdivision. . Opt Commun, , 2015a. . 33986--93. . DOI:10.1016/j.optcom.2014.11.059http://doi.org/10.1016/j.optcom.2014.11.059..

CB Lin, , , SH Yan, , , ZG Du, , , 等. . Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer. . Chin Opt Lett, , 2015b. . 13((10):):100501DOI:10.3788/COL201513.100501http://doi.org/10.3788/COL201513.100501..

CB Lin, , , SH Yan, , , D Ding, , , 等. . Two-dimensional diagonal-based heterodyne grating interferometer with enhanced signal-to-noise ratio and optical subdivision. . Opt Eng, , 2018. . 57((6):):064102DOI:10.1117/1.OE.57.6.064102http://doi.org/10.1117/1.OE.57.6.064102..

DJ Lin, , , H Jiang, , , C Yin. . Analysis of nonlinearity in a high-resolution grating interferometer. . Opt Laser Technol, , 2000. . 32((2):):95--99. . DOI:10.1016/S0030-3992(00)00022-0http://doi.org/10.1016/S0030-3992(00)00022-0..

J Lin, , , J Guan, , , F Wen, , , 等. . Grating encoder for wide range three-axis displacement measurement. . 9th Int Symp on Precision Engineering Measurement and Instrumentation, , 2015. . No. 944602DOI:10.1117/12.2082475http://doi.org/10.1117/12.2082475..

J Lin, , , J Guan, , , F Wen, , , 等. . High-resolution and wide range displacement measurement based on planar grating. . Opt Commun, , 2017. . 404132--138. . DOI:10.1016/j.optcom.2017.03.012http://doi.org/10.1016/j.optcom.2017.03.012..

CH Liu, , , CH Cheng. . Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light. . Sens Actuat A, , 2012. . 18187--93. . DOI:10.1016/j.sna.2012.05.004http://doi.org/10.1016/j.sna.2012.05.004..

CH Liu, , , WY Jywe, , , SC Tzeng. . Simple three-dimensional laser angle sensor for three-dimensional small-angle measurement. . Appl Opt, , 2004. . 43((14):):2840--2845. . DOI:10.1364/AO.43.002840http://doi.org/10.1364/AO.43.002840..

CH Liu, , , HL Huang, , , HW Lee. . Five-degrees-of-freedom diffractive laser encoder. . Appl Opt, , 2009. . 48((14):):2767--2777. . DOI:10.1364/AO.48.002767http://doi.org/10.1364/AO.48.002767..

YC Lu, , , CH Zhou, , , S Li, , , 等. . Study of a grating interferometer with high optical subdivision technique. . Holography, Diffractive Optics, and Applications Ⅶ, , 2016a. . No. 1002214DOI:10.1117/12.2246091http://doi.org/10.1117/12.2246091..

YC Lu, , , CL Wei, , , W Jia, , , 等. . Two-degree-freedom displacement measurement based on a short period grating in symmetric Littrow configuration. . Opt Commun, , 2016b. . 380382--386. . DOI:10.1016/j.optcom.2016.06.016http://doi.org/10.1016/j.optcom.2016.06.016..

YX Lu, , , XD Qi, , , XT Li, , , 等. . Removal of all mosaic grating errors in a single-interferometer system by a phase-difference reference window. . Appl Opt, , 2016. . 55((28):):7997--8002. . DOI:10.1364/AO.55.007997http://doi.org/10.1364/AO.55.007997..

ZG Lu, , , PP Wei, , , CQ Wang, , , 等. . Two-degree-of- freedom displacement measurement system based on double diffraction gratings. . Meas Sci Technol, , 2016. . 27((7):):074012DOI:10.1088/0957-0233/27/7/074012http://doi.org/10.1088/0957-0233/27/7/074012..

Q Lv, , , ZW Liu, , , W Wang, , , 等. . Simple and compact grating-based heterodyne interferometer with the Littrow configuration for high-accuracy and long-range measurement of two-dimensional displacement. . Appl Opt, , 2018. . 57((31):):9455--9463. . DOI:10.1364/AO.57.009455http://doi.org/10.1364/AO.57.009455..

S Makinouchi, , , A Watanabe, , , M Takasaki, , , 等. . An evaluation of a modulated laser encoder. . Prec Eng, , 2011. . 35((2):):302--308. . DOI:10.1016/j.precisioneng.2010.11.008http://doi.org/10.1016/j.precisioneng.2010.11.008..

S Olayee, , , AG Firoozjah. . Modeling the nonlinearity of polarizing beam splitters in nano-displacement measurement of laser encoder using Jones matrix analysis. . Proc 13th Int Conf on Telecommunications, , 2015. . p.1--6. . DOI:10.1109/ConTEL.2015.7231188http://doi.org/10.1109/ConTEL.2015.7231188..

S Olayee, , , AG Firoozjah, , , A Naraghi. . Mathematically modeling of imperfect polarized laser beam in laser encoders for automotive applications. . Proc 5th Int Conf on Control, Instrumentation, and Automation, , 2017. . p.44--48. . DOI:10.1109/ICCIAutom.2017.8258651http://doi.org/10.1109/ICCIAutom.2017.8258651..

SW Pan, , , HL Hsieh, , , WC Wang. . 6-DOF displacement and angle measurements using heterodyne laser encoder. . Instrumentation, Metrology, and Standards for Nanomanufacturing, Optics, and Semiconductors Ⅶ, , 2013. . No. 881909DOI:10.1117/12.2024082http://doi.org/10.1117/12.2024082..

D Post. . Moiré fringe multiplication with a nonsymmetrical doubly blazed reference grating. . Appl Opt, , 1971. . 10((4):):901--907. . DOI:10.1364/AO.10.000901http://doi.org/10.1364/AO.10.000901..

J Prince. . Compact Littrow Encoder. . US Patent US786 433 6, , 2011. ..

P Ramm, , , A Klumpp, , , J Weber, , , 等. . 3D system-on-chip technologies for more than Moore systems. . Michrosyst Technol, , 2010. . 16((7):):1051--1055. . DOI:10.1007/s00542-009-0976-1http://doi.org/10.1007/s00542-009-0976-1..

MJM Renkens, , , AM Struycken, , , RJ Kok, , , 等. . Lithographic Apparatus, Measurement System, and Device Manufacturing Method. . US Patent US710 272 9, , 2006. ..

C Richardson, , , M Tsuriya, , , H Fu. . Technology roadmap overviews and future direction through technology gaps. . Int Conf on Electronics Packaging, , 2017. . p.35--40. . DOI:10.1109/ICEP-IAAC.2015.7111028http://doi.org/10.1109/ICEP-IAAC.2015.7111028..

O Riemer. . Advances in ultra precision manufacturing. . Proc Int Symp on Ultraprecision Engineering and Nanotechnology, , 2011. . p.1--6. . ..

V Ronchi. . Forty years of history of a grating interferometer. . Appl Opt, , 1964. . 3((4):):437--451. . DOI:10.1364/AO.3.000437http://doi.org/10.1364/AO.3.000437..

Y Saito, , , Y Arai, , , W Gao. . Detection of three-axis angles by an optical sensor. . Sensors Actuat A, , 2009. . 150((2):):175--183. . DOI:10.1016/j.sna.2008.12.019http://doi.org/10.1016/j.sna.2008.12.019..

RHM Schmidt. . Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry. . Phil Trans R Soc A, , 2012. . 370((1973):):3950--3972. . DOI:10.1098/rsta.2011.0054http://doi.org/10.1098/rsta.2011.0054..

H Schwenke, , , U Neuschaefer-Rube, , , T Pfeifer, , , 等. . Optical methods for dimensional metrology in production engineering. . CIRP Ann, , 2002. . 51((2):):685--699. . DOI:10.1016/S0007-8506(07)61707-7http://doi.org/10.1016/S0007-8506(07)61707-7..

P Shang, , , HJ Xia, , , YT Fei. . High-resolution diffraction grating interferometric transducer of linear displacements. . 7th Int Symp on Precision Mechanical Measurements, , 2016. . No. 99031IDOI:10.1117/12.2212280http://doi.org/10.1117/12.2212280..

A Shankar, , , LS Tanwar, , , RS Sirohi. . High resolution and low run-out errors in displacement measuring grating interferometer using natural interference zone. . J Opt, , 2007. . 36((3):):111--122. . DOI:10.1007/BF03354822http://doi.org/10.1007/BF03354822..

Y Shibazaki, , , H Kohno, , , M Hamatani. . An innovative platform for high-throughput, high-accuracy lithography using a single wafer stage. . Proc SPIE, Optical Microlithography XXII, , 2009. . No. 72741IDOI:10.1117/12.813386http://doi.org/10.1117/12.813386..

Y Shimizu, , , WJ Kim, , , S Ito, , , 等. . Form error characterization of reflective-type gratings. . Key Eng Mater, , 2012. . 523-524859--864. . DOI:10.4028/www.scientific.net/KEM.523-524.859http://doi.org/10.4028/www.scientific.net/KEM.523-524.859..

Y Shimizu, , , T Ito, , , X Li, , , 等. . Design and testing of a four-probe optical sensor head for three-axis surface encoder with a mosaic scale grating. . Meas Sci Technol, , 2014. . 25((9):):094002DOI:10.1088/0957-0233/25/9/094002http://doi.org/10.1088/0957-0233/25/9/094002..

D Shin, , , B Kim. . An optical encoder using micromachined two gratings with phase. . Proc ASME Int Mechanical Engineering Congress & Exposition, , 2010. . p.479--483. . DOI:10.1115/IMECE2010-40392http://doi.org/10.1115/IMECE2010-40392..

D Shin, , , B Kim. . A laser interferometer encoder with two micromachined gratings generating phase-shifted quadrature. . J Micromech Microeng, , 2011. . 21((8):):085036DOI:10.1088/0960-1317/21/8/085036http://doi.org/10.1088/0960-1317/21/8/085036..

MV Shishova, , , SB Odinokov, , , DS Lushnikov, , , 等. . Mathematical modeling of signal transfer process into optical system of a linear displacement encoder. . Proc Eng, , 2017. . 201623--629. . DOI:10.1016/j.proeng.2017.09.676http://doi.org/10.1016/j.proeng.2017.09.676..

XM Shu, , , Y Zuo, , , XB Xu. . Error correction technology of the length grating measuring system. . Proc 6th Int Symp on Precision Engineering Measurements and Instrumentation, , 2010. . No. 75442GDOI:10.1117/12.885868http://doi.org/10.1117/12.885868..

L iaudinyt, , , G Molnar, , , R Kning, , , 等. . Multi- dimensional grating interferometer based on fibre-fed measurement heads arranged in Littrow configuration. . Meas Sci Technol, , 2018. . 29((5):):054007DOI:10.1088/1361-6501/aaa8b4http://doi.org/10.1088/1361-6501/aaa8b4..

JB Tan, , , PC Hu, , , X Xing. . Double Frequency Laser Grating Interference Two-dimensional Measurement Method. . CN Patent CN103 604 375A, , 2014. ..

Z Tao, , , JB Tan, , , JW Cui. . Linear response, multi-order grating interferometry using a reversal shearing imaging system. . Opt Lett, , 2015. . 40((19):):4552--4555. . DOI:10.1364/OL.40.004552http://doi.org/10.1364/OL.40.004552..

A Teimel. . Technology and application of grating interferometers in high-precision measurement. . Progress in Precision Engineering. Springer-Verlag, Berlin, Germany, , 1991. . p.15--30. . DOI:10.1016/0141-6359(92)90003-Fhttp://doi.org/10.1016/0141-6359(92)90003-F..

GC Wang, , , XD Xie, , , SH Yan. . Influence of non-ideal performance of lasers on displacement precision in single grating heterodyne interferometry. . Proc 5th Int Symp on Advanced Optical Manufacturing and Testing Technologies, , 2010. . No. 76562XDOI:10.1117/12.864195http://doi.org/10.1117/12.864195..

GC Wang, , , SH Yan, , , DX Yang, , , 等. . An interference signal processing method for displacement measurement by dual wavelength and single grating. . 7th Int Symp on Precision Engineering Measurement and Instrumentation, , 2011. . No. 83211ADOI:10.1117/12.904076http://doi.org/10.1117/12.904076..

GC Wang, , , SH Yan, , , WH Zhou, , , 等. . Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer. . Opt Eng, , 2012. . 51((8):):081512DOI:10.1117/1.OE.51.8.081512http://doi.org/10.1117/1.OE.51.8.081512..

J Wang. . Research on 3-DOF Grating Interference Measurement Model of Mask Table. . MS Thesis, Harbin Institute of Technology, Harbin, China, , 2017. ..

LJ Wang, , , M Zhang, , , Y Zhu, , , 等. . A novel heterodyne grating interferometer system for in-plane and out-of- plane displacement measurement with nanometer resolution. . Proc 29th Annual Meeting of the American Society for Precision Engineering, , 2014. . p.173--177. . ..

XZ Wang, , , XH Dong, , , J Guo, , , 等. . Two-dimensional displacement sensing using a cross diffraction grating scheme. . J Opt A Pure Appl Opt, , 2004. . 6((1):):106--111. . DOI:10.1088/1464-4258/6/1/019http://doi.org/10.1088/1464-4258/6/1/019..

CH Wei, , , SH Yan, , , CB Lin, , , 等. . Compact grating displacement measurement system with a 3×3 coupler. . Chin Opt Lett, , 2015a. . 13((5):):051301DOI:10.3788/COL201513.051301http://doi.org/10.3788/COL201513.051301..

CH Wei, , , SH Yan, , , CB Lin, , , 等. . Signal processing for single grating displacement measurement based on 3×3 coupler. . Proc 9th Int Symp on Precision Engineering Measurement and Instrumentation, , 2015b. . No. 944625DOI:10.1117/12.2180922http://doi.org/10.1117/12.2180922..

PP Wei, , , X Lu, , , DC Qiao, , , 等. . Two-dimensional displacement measurement based on two parallel gratings. . Rev Sci Instrum, , 2018. . 89((6):):065105DOI:10.1063/1.5024637http://doi.org/10.1063/1.5024637..

RP Williams, , , SK Hord, , , NA Hall. . Optically read displacement detection using phase-modulated diffraction gratings with reduced zeroth-order reflections. . Appl Phys Lett, , 2017. . 110((15):):151104DOI:10.1063/1.4979541http://doi.org/10.1063/1.4979541..

S Wise, , , V Quetschke, , , AJ Deshpande, , , 等. . Phase effects in the diffraction of light: beyond the grating equation. . Phys Rev Lett, , 2005. . 95((1):):013901DOI:10.1103/PhysRevLett.95.013901http://doi.org/10.1103/PhysRevLett.95.013901..

CC Wu, , , YC Chen, , , CK Lee, , , 等. . Design verifications of a linear laser encoder with high head-to-scale tolerance. . Current Developments in Optical Design and Optical Engineering Ⅷ, , 1999. . p.73--82. . DOI:10.1117/12.368194http://doi.org/10.1117/12.368194..

CC Wu, , , CC Chang, , , CF Kao, , , 等. . Novel planar laser encoder system for two-dimensional positioning with ultra high head-to-scale alignment tolerance. . Current Developments in Lens Design and Optical Engineering Ⅳ, , 2003. . p.55--63. . DOI:10.1117/12.504442http://doi.org/10.1117/12.504442..

CC Wu, , , WJ Wu, , , ZS Pan, , , 等. . Laser linear encoder with both high fabrication and head-to-scale tolerances. . Appl Opt, , 2007. . 46((16):):3169--3176. . DOI:10.1364/AO.46.003169http://doi.org/10.1364/AO.46.003169..

CC Wu, , , CC Hsu, , , JY Lee, , , 等. . Optical heterodyne laser encoder for in-plane nanopositioning. . Interferometry XIV: Techniques and Analysis, , 2008. . No. 70631ADOI:10.1117/12.793710http://doi.org/10.1117/12.793710..

CC Wu, , , CY Cheng, , , ZY Yang. . Optical homodyne common-path grating interferometer with subnanometer displacement resolution. . Interferometry XV: Applications, , 2010. . No. 779105DOI:10.1117/12.860513http://doi.org/10.1117/12.860513..

CC Wu, , , CC Hsu, , , JY Lee, , , 等. . Common-path laser encoder for nanopositioning in long travel range. . Proc SICE Annual Conf, , 2011. . p.817--820. . ..

CC Wu, , , JS Yang, , , CY Cheng, , , 等. . Common-path laser encoder. . Sens Actuat A, , 2013a. . 18986--92. . DOI:10.1016/j.sna.2012.08.034http://doi.org/10.1016/j.sna.2012.08.034..

CC Wu, , , YZ Chen, , , CH Liao. . Common-path laser planar encoder. . Opt Exp, , 2013b. . 21((16):):18872--18883. . DOI:10.1364/OE.21.018872http://doi.org/10.1364/OE.21.018872..

CC Wu, , , CC Hsu, , , JY Lee, , , 等. . Heterodyne common-path grating interferometer with Littrow configuration. . Opt Exp, , 2013c. . 21((11):):13322--13332. . DOI:10.1364/OE.21.013322http://doi.org/10.1364/OE.21.013322..

CC Wu, , , CC Hsu, , , JY Lee, , , 等. . Littrow-type self-aligned laser encoder with high tolerance using double diffractions. . Opt Commun, , 2013d. . 29789--97. . DOI:10.1016/j.optcom.2013.01.048http://doi.org/10.1016/j.optcom.2013.01.048..

HJ Xia, , , YT Fei. . Precise stage design with planar diffraction grating interferometer. . Proc 6th Int Symp on Precision Engineering Measurements and Instrumentation, , 2010. . No. 754411DOI:10.1117/12.885215http://doi.org/10.1117/12.885215..

JD Xie, , , LP Yan, , , BY Chen, , , 等. . Iterative compensation of nonlinear error of heterodyne interferometer. . Opt Exp, , 2017. . 25((4):):4470--4482. . DOI:10.1364/OE.25.004470http://doi.org/10.1364/OE.25.004470..

X Xing, , , D Chang, , , PC Hu, , , 等. . Spatially separated heterodyne grating interferometer for eliminating periodic nonlinear errors. . Opt Exp, , 2017. . 25((25):):31384--31393. . DOI:10.1364/OE.25.031384http://doi.org/10.1364/OE.25.031384..

SH Yan, , , GC Wang, , , CB Lin, , , 等. . Displacement measurement by single-grating heterodyne interferometry. . Proc 11th Conf on Lasers and Electro-Optics Pacific Rim, , 2015. . p.1--2. . ..

GY Ye, , , SJ Fan, , , HZ Liu, , , 等. . Design of a precise and robust linearized converter for optical encoders using a ratiometric technique. . Meas Sci Technol, , 2014. . 25((12):):125003DOI:10.1088/0957-0233/25/12/125003http://doi.org/10.1088/0957-0233/25/12/125003..

HY Yu, , , HZ Liu, , , X Li, , , 等. . Calibration of non-contact incremental linear encoders using a macro–micro dual- drive high-precision comparator. . Meas Sci Technol, , 2015. . 26((9):):Article 095103DOI:10.1088/0957-0233/26/9/095103http://doi.org/10.1088/0957-0233/26/9/095103..

JL Yuan, , , BH Lyu, , , W Hang, , , 等. . Review on the progress of ultra-precision machining technologies. . Front Mech Eng, , 2017. . 12((2):):158--180. . DOI:10.1007/s11465-017-0455-9http://doi.org/10.1007/s11465-017-0455-9..

M Zhang, , , Y Zhu, , , LJ Wang, , , 等. . Two-DOF Heterodyne Grating Interferometer Displacement Measurement System. . US Patent US013 890 3A1, , 2016. ..

M Zhang, , , Y Zhu, , , C Ni, , , 等. . Two-DOF Heterodyne Grating Interferometer Displacement Measurement System. . CN Patent CN106 289 068A, , 2017. ..

B Zhao, , , L Wang, , , ME Xu, , , 等. . A displacement measuring system based on grating double diffraction. . Proc 9th Int Symp on Precision Engineering Measurement and Instrumentation, , 2015. . No. 94464JDOI:10.1117/12.2182024http://doi.org/10.1117/12.2182024..

JL Zhao. . Key Technology of Signal Processing in Heterodyne Laser Interferometry with Pico Meter Resolution. . MS Thesis, Harbin Institute of Technology, Harbin, China, , 2016. ..

SS Zhao, , , CL Hou, , , J Bai, , , 等. . Nanometer-scale displacement sensor based on phase-sensitive diffraction grating. . Appl Opt, , 2011. . 50((10):):1413--1416. . DOI:10.1364/AO.50.001413http://doi.org/10.1364/AO.50.001413..

AY Zherdev, , , SB Odinokov, , , DS Lushnikov, , , 等. . Optical position encoder on four-section diffraction grating. . roc SPIE, Holography: Advances and Modern Trends, , 2017. . No. 102331IDOI:10.1117/12.2264801http://doi.org/10.1117/12.2264801..

Y Zhu, , , M Zhang, , , LJ Wang, , , 等. . Dual-Frequency Grating Interferometer Displacement Measurement System. . WO Patent WO201 407 180 6A1, , 2014. ..

Y Zhu, , , M Zhang, , , LJ Wang, , , 等. . Dual-frequency Grating Interferometer Displacement Measurement System. . US Patent US988 556 B2, , 2018. ..

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