{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:05:23Z","timestamp":1787029523928,"version":"3.56.0"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000},"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":["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>This paper proposes a new optical configuration for a two-axis surface encoder that can measure the in-plane (X-axis) and out-of-plane (Z-axis) displacements of a positioning stage. The two-axis surface encoder is composed of a scale grating and a sensor head. A transparent grating is employed in the sensor head for measurement of the Z-directional displacement of the scale grating based on the Fizeau-type measurement method; a reference beam reflected from the transparent grating and the zeroth-order diffracted beam from the scale grating are superimposed to generate an interference signal. A pair of prisms and a beam splitter are also employed in the sensor head, so that the positive and negative first-order diffracted beams can be superimposed over a long working distance to generate an interference signal for measurement of the X-directional displacement of the scale grating. Focusing on the new, extended Z-directional measurement mechanism, proof-of-principle experiments were carried out to verify the feasibility of the proposed optical configuration for the surface encoder that can measure the uni-directional displacements of a scale grating along the X- and Z-axis. Experimental results from the developed optical configuration demonstrated the achievement of a Z-directional measuring range of \u00b11.5 mm.<\/jats:p>","DOI":"10.3390\/s22083010","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T02:39:31Z","timestamp":1650335971000},"page":"3010","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A New Optical Configuration for the Surface Encoder with an Expanded 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, 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"}]},{"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":[[2022,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gao, W. 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