{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T15:45:14Z","timestamp":1780674314014,"version":"3.54.1"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:00:00Z","timestamp":1652486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51475262"],"award-info":[{"award-number":["51475262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021M701954"],"award-info":[{"award-number":["2021M701954"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["51475262"],"award-info":[{"award-number":["51475262"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2021M701954"],"award-info":[{"award-number":["2021M701954"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Grating interferometers that use large two-dimensional grating splice modules for performing wide-range measurements have significant advantages for identifying the position of the wafer stage. However, the manufacturing process of large two-dimensional grating splice modules is very difficult. In contrast to existing redundant designs in the grating line dimension, we propose a novel interferometric reading head with a redundant design for obtaining wide-range displacement measurements. This interferometric reading head uses a one-dimensional grating splice module, and it was observed to be compatible with two orthogonal gratings. We designed a grating interferometer system composed of four reading heads to achieve a wide range of measurements and verified it using ZEMAX simulation. By conducting experiments, we were able to verify the compatibility of the reading head with gratings possessing different grating line directions; the measurement noise was found to be less than 0.3 nm.<\/jats:p>","DOI":"10.3390\/s22103738","type":"journal-article","created":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T09:48:22Z","timestamp":1652608102000},"page":"3738","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Grating Interferometer with Redundant Design for Performing Wide-Range Displacement Measurements"],"prefix":"10.3390","volume":"22","author":[{"given":"Weinan","family":"Ye","sequence":"first","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rong","family":"Cheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Zhu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leijie","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinchun","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Lab of Precision\/Ultra-Precision Manufacture Equipment and Control, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"122405","DOI":"10.1117\/1.OE.53.12.122405","article-title":"Measurement of six-degree-of-freedom planar motions by using a multiprobe surface encoder","volume":"53","author":"Li","year":"2014","journal-title":"Opt. Eng."},{"key":"ref_2","first-page":"72741S","article-title":"Enabling the lithography roadmap: An immersion tool based on a novel stage positioning system","volume":"7274","author":"Castenmiller","year":"2009","journal-title":"Proc. SPIE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"87593L","DOI":"10.1117\/12.2012649","article-title":"Heterodyne planar grating encoder with high alignment tolerance, especially insensitivity to grating tilts","volume":"8759","author":"Feng","year":"2013","journal-title":"Proc. SPIE"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"942414","DOI":"10.1117\/12.2085645","article-title":"Improving full-wafer on-product overlay using computationally designed process-robust and device-like metrology targets","volume":"9424","author":"Kim","year":"2015","journal-title":"Proc. SPIE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2366","DOI":"10.1364\/AO.57.002366","article-title":"Eightfold optical encoder with high-density grating","volume":"57","author":"Deng","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1364\/OE.438490","article-title":"Polarization-modulated grating interferometer by conical diffraction","volume":"30","author":"Liu","year":"2022","journal-title":"Opt. Express"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9770","DOI":"10.1364\/OE.19.009770","article-title":"Two-dimensional displacement measurements by quasi-common-optical-path heterodyne grating interferometer","volume":"19","author":"Hsieh","year":"2011","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.precisioneng.2009.05.008","article-title":"Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness","volume":"34","author":"Kimura","year":"2010","journal-title":"Precis. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9455","DOI":"10.1364\/AO.57.009455","article-title":"Simple and compact grating-based heterodyne interferometer with the Littrow configuration for high-accuracy and long-range measurement of two-dimensional displacement","volume":"57","author":"Lv","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1364\/OE.23.002451","article-title":"Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements","volume":"23","author":"Hsieh","year":"2015","journal-title":"Opt. Express"},{"key":"ref_11","first-page":"288","article-title":"Latest performance of ArF immersion scanner NSR-S630D for high-volume manufacturing for 7 nm node","volume":"9426","author":"Funatsu","year":"2015","journal-title":"Proc. SPIE"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"76401N","DOI":"10.1117\/12.847025","article-title":"Towards ultimate optical lithography with NXT:1950i dual stage immersion platform","volume":"7640","author":"Castenmiller","year":"2010","journal-title":"Proc. SPIE"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"S504","DOI":"10.1088\/0957-4484\/15\/10\/002","article-title":"Dimensional metrology for nanometre-scale science and engineering: Towards sub-nanometre accurate encoders","volume":"15","author":"Heilmann","year":"2004","journal-title":"Nanotechnology"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ye, W., Zhang, M., Zhu, Y., Wang, L., Hu, J., Li, X., and Hu, C. (2019). Ultraprecision Real-Time Displacements Calculation Algorithm for the Grating Interferometer System. Sensors, 19.","DOI":"10.3390\/s19102409"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.precisioneng.2019.06.012","article-title":"Real-time displacement calculation and offline geometric calibration of the grating interferometer system for ultra-precision wafer stage measurement","volume":"60","author":"Ye","year":"2019","journal-title":"Precis. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"34734","DOI":"10.1364\/OE.26.034734","article-title":"Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner","volume":"26","author":"Ye","year":"2018","journal-title":"Opt. 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