{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T05:27:49Z","timestamp":1785302869074,"version":"3.55.0"},"reference-count":149,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,12,1]],"date-time":"2019-12-01T00:00:00Z","timestamp":1575158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["15H05957"],"award-info":[{"award-number":["15H05957"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In dimensional metrology it is necessary to carry out multi-axis angle and displacement measurement for high-precision positioning. Although the state-of-the-art linear displacement sensors have sub-nanometric measurement resolution, it is not easy to suppress the increase of measurement uncertainty when being applied for multi-axis angle and displacement measurement due to the Abbe errors and the influences of sensor misalignment. In this review article, the state-of-the-art multi-axis optical sensors, such as the three-axis autocollimator, the three-axis planar encoder, and the six-degree-of-freedom planar encoder based on a planar scale grating are introduced. With the employment of grating reflectors, measurement of multi-axis translational and angular displacement can be carried out while employing a single laser beam. Fabrication methods of a large-area planar scale grating based on a single-point diamond cutting with the fast tool servo technique and the interference lithography are also presented, followed by the description of the evaluation method of the large-area planar scale grating based on the Fizeau interferometer.<\/jats:p>","DOI":"10.3390\/s19235289","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T10:50:45Z","timestamp":1575283845000},"page":"5289","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":73,"title":["Optical Sensors for Multi-Axis Angle and Displacement Measurement Using Grating Reflectors"],"prefix":"10.3390","volume":"19","author":[{"given":"Yuki","family":"Shimizu","sequence":"first","affiliation":[{"name":"Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiraku","family":"Matsukuma","sequence":"additional","affiliation":[{"name":"Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9336-2729","authenticated-orcid":false,"given":"Wei","family":"Gao","sequence":"additional","affiliation":[{"name":"Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.cirp.2019.05.005","article-title":"On-machine and in-process surface metrology for precision manufacturing","volume":"68","author":"Gao","year":"2019","journal-title":"Cirp Ann.-Manuf. 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