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Express"],"published-print":{"date-parts":[[2022,11,7]]},"abstract":"<jats:p>\n                    We propose a 3D measurement method based on 2D grating dual-channel and Littrow equal-optical path incidence to detect the 3D displacement of a 2D grating in the\n                    <jats:italic>X<\/jats:italic>\n                    -,\n                    <jats:italic>Y<\/jats:italic>\n                    -, and\n                    <jats:italic>Z<\/jats:italic>\n                    -directions. The 2D grating is combined with the Littrow incidence method and a turning element to cause the Littrow diffracted light with frequency\n                    <jats:italic>f<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    to interfere with the reference light at frequency\n                    <jats:italic>f<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    , and the displacement data in the\n                    <jats:italic>X<\/jats:italic>\n                    -,\n                    <jats:italic>Y<\/jats:italic>\n                    -, and\n                    <jats:italic>Z<\/jats:italic>\n                    -directions are obtained using the separation-dual-channel phase decoupling algorithm. A corresponding test experimental platform is constructed, and linear error evaluation and step error evaluation experiments are performed to determine the displacements in the\n                    <jats:italic>X<\/jats:italic>\n                    -,\n                    <jats:italic>Y<\/jats:italic>\n                    -, and\n                    <jats:italic>Z<\/jats:italic>\n                    -directions. The results obtained show that all linearity errors are within \u00b160 nm in the 10 mm measurement ranges in the\n                    <jats:italic>X<\/jats:italic>\n                    -,\n                    <jats:italic>Y<\/jats:italic>\n                    -, and\n                    <jats:italic>Z<\/jats:italic>\n                    -directions, and the test resolution is within \u00b15 nm. The proposed method can thus realize nanoscale synchronous measurement of\n                    <jats:italic>X<\/jats:italic>\n                    -,\n                    <jats:italic>Y<\/jats:italic>\n                    -, and\n                    <jats:italic>Z<\/jats:italic>\n                    -direction 3D displacements.\n                  <\/jats:p>","DOI":"10.1364\/oe.475830","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T13:00:48Z","timestamp":1666098048000},"page":"41671","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Littrow 3D measurement based on 2D grating dual-channel equal-optical path interference"],"prefix":"10.1364","volume":"30","author":[{"given":"Yunfei","family":"Yin","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Bai","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"Jirigalantu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongzhu","family":"Yu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"Bayanheshig","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8826-8017","authenticated-orcid":true,"given":"Zhaowu","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhao","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"oe-30-23-41671-R1","author":"EllisBellingham","year":"2014"},{"key":"oe-30-23-41671-R2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.37188\/lam.2022.033","volume":"3","author":"Hasegawa","year":"2022","journal-title":"Light: Adv. 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