{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T01:42:15Z","timestamp":1780969335958,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"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":["62275142"],"award-info":[{"award-number":["62275142"]}],"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":["2021B1515120007"],"award-info":[{"award-number":["2021B1515120007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic and Applied Basic Research Foundation of Guangdong Province","award":["62275142"],"award-info":[{"award-number":["62275142"]}]},{"name":"Basic and Applied Basic Research Foundation of Guangdong Province","award":["2021B1515120007"],"award-info":[{"award-number":["2021B1515120007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>An absolute-type four-degree-of-freedom (four-DOF) grating encoder that can simultaneously measure the three-axis pose (\u03b8x, \u03b8y, \u03b8z) and one-axis out-of-plane position (Z) of an object with high accuracy is demonstrated for the first time in this research. This grating encoder is composed of a stationary reading head and a movable grating reflector. A light beam from the reading head is projected onto the grating, and three diffracted beams (0th-, +1st-, and \u22121st-order) are generated, collimated, and received by three separate quadrant photodetectors (QPDs). The information of \u03b8x, \u03b8y, \u03b8z, and Z is coded into spot positions of these three diffracted beams on the QPDs. Thus, the modeling and decoupling algorithms were investigated, and an independent calculation of these four-DOF absolute positions was theoretically guaranteed. A prototype was then designed, constructed, and evaluated. Experimental results verified that the proposed grating encoder could achieve the absolute measurement of four-DOF \u03b8x, \u03b8y, \u03b8z, and Z with an accuracy of sub-arcseconds and sub-micrometers. To the best of our knowledge, the proposed encoder in this research is the first one to achieve absolute simultaneous measurements of four-DOF position and pose with a large measurement range. The success of this new grating encoder can benefit various multi-DOF positioning applications, especially for large-scale synthetic aperture optics (SAO), including stitching off-axis parabolic mirrors and pulse compression grating.<\/jats:p>","DOI":"10.3390\/s22239047","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T08:29:58Z","timestamp":1669105798000},"page":"9047","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["An Ultra-Precision Absolute-Type Multi-Degree-of-Freedom Grating Encoder"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5888-9864","authenticated-orcid":false,"given":"Shengtong","family":"Wang","sequence":"first","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linbin","family":"Luo","sequence":"additional","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junhao","family":"Zhu","sequence":"additional","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ningning","family":"Shi","sequence":"additional","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinghui","family":"Li","sequence":"additional","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"},{"name":"Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,22]]},"reference":[{"key":"ref_1","first-page":"12","article-title":"System Analysis of Ground-based Inverse Synthetic Aperture Lidar for Geosynchronous Orbit Object Imaging","volume":"47","author":"Xuan","year":"2018","journal-title":"Acta Photonica Sin."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1088\/1674-4527\/12\/9\/003","article-title":"The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)","volume":"12","author":"Cui","year":"2012","journal-title":"Res. 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