{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T08:14:46Z","timestamp":1776327286406,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T00:00:00Z","timestamp":1563753600000},"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3\u03c3 value respectively within 30 s.<\/jats:p>","DOI":"10.3390\/s19143219","type":"journal-article","created":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T11:07:28Z","timestamp":1563793648000},"page":"3219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Two Degree-of-Freedom Fiber-Coupled Heterodyne Grating Interferometer with Milli-Radian Operating Range of Rotation"],"prefix":"10.3390","volume":"19","author":[{"given":"Fuzhong","family":"Yang","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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weinan","family":"Ye","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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yizhou","family":"Xia","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":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.1088\/0957-0233\/16\/11\/005","article-title":"Developments at PTB in nanometrology for support of the semiconductor industry","volume":"16","author":"Bosse","year":"2005","journal-title":"Meas. 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