{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T03:24:42Z","timestamp":1785554682389,"version":"3.56.0"},"reference-count":40,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T00:00:00Z","timestamp":1670284800000},"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 (JSPS)","doi-asserted-by":"publisher","award":["20H00211"],"award-info":[{"award-number":["20H00211"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A modified two-axis surface encoder is proposed to separately measure both the in-plane displacement and the Z-directional out-of-plane displacement with minor crosstalk errors. The surface encoder is composed of a scale grating and a small-sized sensor head. In the modified surface encoder, the measurement laser beam from the sensor head is designed to be projected onto the scale grating at a right angle. For measurement of the X- and Y-directional in-plane scale displacement, the positive and negative first-order diffracted beams from the scale grating are superimposed on each other in the sensor head, producing interference signals. On the other hand, the Z-directional out-of-plane scale displacement is measured based on the principle of a Michelson-type interferometer. To avoid the influence of reflection from the middle area of the transparent grating, which causes periodic crosstalk errors in the previous research, a specially fabricated transparent grating with a hole in the middle is employed in the newly designed optical system. A prototype sensor head is constructed, and basic performances of the modified surface encoder are tested by experiments.<\/jats:p>","DOI":"10.3390\/s22239563","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T05:50:52Z","timestamp":1670392252000},"page":"9563","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Reduction of Crosstalk Errors in a Surface Encoder Having a Long Z-Directional Measuring Range"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0349-1058","authenticated-orcid":false,"given":"Yifan","family":"Hong","sequence":"first","affiliation":[{"name":"Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryo","family":"Sato","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\/0000-0003-3527-2869","authenticated-orcid":false,"given":"Yuki","family":"Shimizu","sequence":"additional","affiliation":[{"name":"Division of Mechanical and Space Engineering, Graduate School of Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo 060-8628, 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"}]},{"given":"Hiroki","family":"Shimizu","sequence":"additional","affiliation":[{"name":"Department of Engineering, Graduate School of Engineering, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu-shi, Fukuoka 804-8550, 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":[[2022,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gao, W. 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