{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T03:24:23Z","timestamp":1785554663893,"version":"3.56.0"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,15]],"date-time":"2023-04-15T00:00:00Z","timestamp":1681516800000},"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>A compact and high-precision three-degrees-of-freedom (DOF; X, Y, and Z directions) grating encoder based on the quadrangular frustum pyramid (QFP) prisms is proposed in this paper to solve the insufficient installation space problem of the reading head of the multi-DOF in high-precision displacement measurement applications. The encoder is based on the grating diffraction and interference principle, and a three-DOF measurement platform is built through the self-collimation function of the miniaturized QFP prism. The overall size of the reading head is 12.3 \u00d7 7.7 \u00d7 3 cm3 and has the potential for further miniaturization. The test results show that three-DOF measurements can be realized simultaneously in the range of X-250, Y-200, and Z-100 \u03bcm due to the limitations of the measurement grating size. The measurement accuracy of the main displacement is below 500 nm on average; the minimum and maximum errors are 0.0708% and 2.8422%, respectively. This design will help further popularize the research and applications of multi-DOF grating encoders in high-precision measurements.<\/jats:p>","DOI":"10.3390\/s23084022","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T02:26:02Z","timestamp":1681698362000},"page":"4022","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["A Compact and High-Precision Three-Degree-of-Freedom Grating Encoder Based on a Quadrangular Frustum Pyramid Prism"],"prefix":"10.3390","volume":"23","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":"Baiqi","family":"Liao","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-Berkerley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.cirp.2015.05.009","article-title":"Measurement technologies for precision positioning","volume":"64","author":"Gao","year":"2015","journal-title":"CIRP Ann.-Manuf. 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