Displacement measuring grating interferometer: a review

Peng-cheng HU; Di CHANG; Jiu-bin TAN; Rui-tao YANG; Hong-xing YANG; Hai-jin FU

doi:10.1631/FITEE.1800708

Your Location：

Home >

Browse articles >

Displacement measuring grating interferometer: a review

Special Feature on Precision Measurement and Instrumentation Technology | Updated：2022-05-19

- Displacement measuring grating interferometer: a review
- 位移测量光栅干涉仪综述
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 5, Pages: 631-654(2019)
- 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：
- DOI：10.1631/FITEE.1800708
  CLC： TH744.3;TH822
- Received：07 November 2018，
  
  Revised：2019-;5-;8，
  
  Published：2019-05
- Accepted：
Scan QR Code
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：

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

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 10 th Initiatives of Precision Engineering at the Beginning of a Millennium , , 2001 . . p.799 - - 803 . . DOI: 10.1007/0-306-47000-4_157 http://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 32 nd Int Conf on Computer Design , , 2014 . . p.147 - - 152 . . DOI: 10.1109/ICCD.2014.6974674 http://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 . . 12 1495 - - 1502 . . DOI: 10.1088/0957-0233/12/9/316 http://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.2016.2634758 http://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 6 th Int Conf on Machinery, Materials, Environment, Biotechnology and Computer , , 2016 . . p.25 - - 29 . . DOI: 10.2991/mmebc-16.2016.5 http://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 263 DOI: 10.3390/app9020263 http://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.50.004550 http://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 4 th Int Symp on Advanced Optical Manufacturing and Testing Technologies: Design, Manufacturing, and Testing of Micro- and Nano-Optical Devices and Systems , , 2009b . . No. 728403 DOI: 10.1117/12.832061 http://doi.org/10.1117/12.832061 . .

A Cho . . The long road to LIGO . . Science , , 2016 . . 353 ( ( 6299 ): ): 534 - - 535 . . DOI: 10.1126/science.353.6299.534 http://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 ): ): 017001 DOI: 10.1088/0957-0233/19/1/017001 http://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 9 th World Congress on Intelligent Control and Automation , , 2011 . . p.449 - - 453 . . DOI: 10.1109/WCICA.2011.5970554 http://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.x http://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: 10.1533/9780857099297.1.230 http://doi.org/10.1533/9780857099297.1.230 . .

C Damm , , , T Peschel , , , S Risse , , , 等 . . Wafer stage assembly for ion projection lithography . . Microelectron Eng , , 2001 . . 57-58 181 - - 185 . . DOI: 10.1016/S0167-9317(01)00513-5 http://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 31 st 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.57.002366 http://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: 10.1117/1.602137 http://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.pdf https://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, UK SPIE Press , , 2014 . . .

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

KC Fan , , , YS Liu , , , YJ Chen , , , 等 . . A linear diffraction grating interferometer with high accuracy . . Proc 3 rd Int Symp on Precision Mechanical Measurements , , 2006 . . No. 628008 DOI: 10.1117/12.715260 http://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/S07 http://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 7 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2011a . . No. 832119 DOI: 10.1117/12.904072 http://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.v1i2.53 http://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.2012.6229209 http://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.2012.6265886 http://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-2014-0038 http://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 . . 49 236 - - 244 . . DOI: 10.1088/0026-1394/49/3/236 http://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 8 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2013 . . No. 87593L DOI: 10.1117/12.2012649 http://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 2768 DOI: 10.3390/s18092768 http://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 758 DOI: 10.3390/s18030758 http://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.2007.05.126 http://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 . . 59 505 - - 508 . . DOI: 10.1016/j.cirp.2010.03.035 http://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 . . 60 515 - - 518 . . DOI: 10.1016/j.cirp.2011.03.052 http://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.2013.01.006 http://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.2015.05.009 http://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 080423 DOI: 10.1088/0264-9381/27/8/084023 http://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 . . 50 114 - - 118 . . DOI: 10.1016/j.precisioneng.2017.04.019 http://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 ): ): 096111 DOI: 10.1063/1.4931781 http://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.54.009320 http://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. 996019 DOI: 10.1117/12.2239519 http://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.25.031394 http://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: 10.1088/0957-4484/15/10/002 http://doi.org/10.1088/0957-4484/15/10/002 . .

W Holzapfel . . Advancements in displacement metrology based on encoder systems . . Proc 23 rd 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 . . 51 388 - - 392 . . DOI: 10.1016/j.precisioneng.2017.09.009 http://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.p0091 http://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 . . 81 97 - - 102 . . DOI: 10.1016/j.optlaseng.2016.01.004 http://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 ): ): 105303 DOI: 10.1088/0957-0233/20/10/105303 http://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.24.008693 http://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.52.006840 http://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.23.002451 http://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 ): ): 115304 DOI: 10.1088/0957-0233/21/11/115304 http://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.19.009770 http://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-2014-0027 http://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.2007.12.098 http://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. 73891M DOI: 10.1117/12.827453 http://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 . . 48 200 - - 205 . . DOI: 10.1016/j.optlastec.2012.10.003 http://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.25.030189 http://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 . . 105 221 - - 228 . . DOI: 10.1016/j.optlastec.2018.03.005 http://doi.org/10.1016/j.optlastec.2018.03.005 . .

PC Hu , , , F Pollinger , , , K Meiners-Hagen , , , 等 . . Fine correction of nonlinearity in homodyne interferometry . . 6 th Int Symp on Precision Engineering Measurements and Instrumentation , , 2010 . . No. 75444E DOI: 10.1117/12.885392 http://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 . . 15 3090 - - 3106 . . DOI: 10.3390/s150203090 http://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 ): ): 066103 DOI: 10.1063/1.2743165 http://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-2014-0028 http://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-y http://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 . . 230-232 1159 DOI: 10.4028/www.scientific.net/AMR.230-232.1159 http://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 . . 103 35 - - 40 . . DOI: 10.4028/www.scientific.net/AMM.103.35 http://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 . . 6 th Int Symp on Precision Mechanical Measurements , , 2013 . . No. 891631 DOI: 10.1117/12.2035685 http://doi.org/10.1117/12.2035685 . .

Y Jourlin , , , J Jay , , , O Parriaux . . Compact diffractive interferometric displacement sensor in reflection . . Prec Eng , , 2002 . . 26 1 - - 6 . . DOI: 10.1016/S0141-6359(01)00081-2 http://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 ): ): 023603 DOI: 10.1117/1.1839227 http://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 ): ): 085110 DOI: 10.1063/1.2006368 http://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.47.1833 http://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 ): ): 045007 DOI: 10.1088/0960-1317/18/4/045007 http://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: 10.1109/5.811607 http://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: 10.1063/1.1305816 http://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)00105-2 http://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.61.1759 http://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.2009.05.008 http://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 . . 21 054005 DOI: 10.1088/0957-0233/21/5/054005 http://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.2011.039964 http://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.2012.04.005 http://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)62538-4 http://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.200.2007.01.002 http://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 9 th 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/s12206-012-1217-6 http://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 ): ): 105901 DOI: 10.1088/0957-0233/22/10/105901 http://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/s12541-012-0199-8 http://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.43.005754 http://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.2010.09.079 http://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.21.025553 http://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.2007.02.017 http://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.50.001272 http://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.2007.4785573 http://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.2013.03.005 http://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 162 DOI: 10.1007/s00340-017-6724-9 http://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. 90460C DOI: 10.1117/12.2037576 http://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 . . 339 86 - - 93 . . DOI: 10.1016/j.optcom.2014.11.059 http://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 ): ): 100501 DOI: 10.3788/COL201513.100501 http://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 ): ): 064102 DOI: 10.1117/1.OE.57.6.064102 http://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)00022-0 http://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 . . 9 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2015 . . No. 944602 DOI: 10.1117/12.2082475 http://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 . . 404 132 - - 138 . . DOI: 10.1016/j.optcom.2017.03.012 http://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 . . 181 87 - - 93 . . DOI: 10.1016/j.sna.2012.05.004 http://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.43.002840 http://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.48.002767 http://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. 1002214 DOI: 10.1117/12.2246091 http://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 . . 380 382 - - 386 . . DOI: 10.1016/j.optcom.2016.06.016 http://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.55.007997 http://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 ): ): 074012 DOI: 10.1088/0957-0233/27/7/074012 http://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.57.009455 http://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.2010.11.008 http://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 13 th Int Conf on Telecommunications , , 2015 . . p.1 - - 6 . . DOI: 10.1109/ConTEL.2015.7231188 http://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 5 th Int Conf on Control, Instrumentation, and Automation , , 2017 . . p.44 - - 48 . . DOI: 10.1109/ICCIAutom.2017.8258651 http://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. 881909 DOI: 10.1117/12.2024082 http://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.10.000901 http://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/s00542-009-0976-1 http://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.2015.7111028 http://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.3.000437 http://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.2008.12.019 http://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.2011.0054 http://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)61707-7 http://doi.org/10.1016/S0007-8506(07)61707-7 . .

P Shang , , , HJ Xia , , , YT Fei . . High-resolution diffraction grating interferometric transducer of linear displacements . . 7 th Int Symp on Precision Mechanical Measurements , , 2016 . . No. 99031I DOI: 10.1117/12.2212280 http://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/BF03354822 http://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. 72741I DOI: 10.1117/12.813386 http://doi.org/10.1117/12.813386 . .

Y Shimizu , , , WJ Kim , , , S Ito , , , 等 . . Form error characterization of reflective-type gratings . . Key Eng Mater , , 2012 . . 523-524 859 - - 864 . . DOI: 10.4028/www.scientific.net/KEM.523-524.859 http://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 ): ): 094002 DOI: 10.1088/0957-0233/25/9/094002 http://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/IMECE2010-40392 http://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 ): ): 085036 DOI: 10.1088/0960-1317/21/8/085036 http://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 . . 201 623 - - 629 . . DOI: 10.1016/j.proeng.2017.09.676 http://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 6 th Int Symp on Precision Engineering Measurements and Instrumentation , , 2010 . . No. 75442G DOI: 10.1117/12.885868 http://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 ): ): 054007 DOI: 10.1088/1361-6501/aaa8b4 http://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.40.004552 http://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-F http://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 5 th Int Symp on Advanced Optical Manufacturing and Testing Technologies , , 2010 . . No. 76562X DOI: 10.1117/12.864195 http://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 . . 7 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2011 . . No. 83211A DOI: 10.1117/12.904076 http://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 ): ): 081512 DOI: 10.1117/1.OE.51.8.081512 http://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 29 th 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: 10.1088/1464-4258/6/1/019 http://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 ): ): 051301 DOI: 10.3788/COL201513.051301 http://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 9 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2015b . . No. 944625 DOI: 10.1117/12.2180922 http://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 ): ): 065105 DOI: 10.1063/1.5024637 http://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 ): ): 151104 DOI: 10.1063/1.4979541 http://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 ): ): 013901 DOI: 10.1103/PhysRevLett.95.013901 http://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: 10.1117/12.368194 http://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: 10.1117/12.504442 http://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.46.003169 http://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. 70631A DOI: 10.1117/12.793710 http://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. 779105 DOI: 10.1117/12.860513 http://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 . . 189 86 - - 92 . . DOI: 10.1016/j.sna.2012.08.034 http://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.21.018872 http://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.21.013322 http://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 . . 297 89 - - 97 . . DOI: 10.1016/j.optcom.2013.01.048 http://doi.org/10.1016/j.optcom.2013.01.048 . .

HJ Xia , , , YT Fei . . Precise stage design with planar diffraction grating interferometer . . Proc 6 th Int Symp on Precision Engineering Measurements and Instrumentation , , 2010 . . No. 754411 DOI: 10.1117/12.885215 http://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.25.004470 http://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.25.031384 http://doi.org/10.1364/OE.25.031384 . .

SH Yan , , , GC Wang , , , CB Lin , , , 等 . . Displacement measurement by single-grating heterodyne interferometry . . Proc 11 th 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 ): ): 125003 DOI: 10.1088/0957-0233/25/12/125003 http://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 095103 DOI: 10.1088/0957-0233/26/9/095103 http://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/s11465-017-0455-9 http://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 9 th Int Symp on Precision Engineering Measurement and Instrumentation , , 2015 . . No. 94464J DOI: 10.1117/12.2182024 http://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.50.001413 http://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. 102331I DOI: 10.1117/12.2264801 http://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 . . .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

A planar capacitive sensor for 2D long-range displacement measurement

Related Author

Jian-ping YU

Wen WANG

Ke-qing LU

De-qing MEI

Zi-chen CHEN

Related Institution

Department of Mechanical Engineering, Zhejiang University

School of Mechanical Engineering, Hangzhou Dianzi University

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰