{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T22:01:12Z","timestamp":1785967272403,"version":"3.56.0"},"reference-count":39,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T00:00:00Z","timestamp":1636329600000},"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>An interferometric self-calibration method for the evaluation of the pitch deviation of scale grating has been extended to evaluate the pitch deviation of the long-range type linear scale by utilizing the stitching interferometry technique. Following the previous work, in which the interferometric self-calibration method was proposed to assess the pitch deviation of the scale grating by combing the first-order diffracted beams from the grating, a stitching calibration method is proposed to enlarge the measurement range. Theoretical analysis is performed to realize the X-directional pitch deviation calibration of the long-range linear scale while reducing the second-order accumulation effect by canceling the influence of the reference flat error in the sub-apertures\u2019 measurements. In this paper, the stitching interferometry theory is briefly reviewed, and theoretical equations of the X-directional pitch deviation stitching are derived for evaluation of the pitch deviation of the long-range linear scale. Followed by the simulation verification, some experiments with a linear scale of 105 mm length from a commercial interferential scanning-type optical encoder are conducted to verify the feasibility of the self-calibration stitching method for the calibration of the X-directional pitch deviation of the linear scale over its whole area.<\/jats:p>","DOI":"10.3390\/s21217412","type":"journal-article","created":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T22:08:41Z","timestamp":1636409321000},"page":"7412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Self-Calibration Stitching Method for Pitch Deviation Evaluation of a Long-Range Linear Scale by Using a Fizeau Interferometer"],"prefix":"10.3390","volume":"21","author":[{"given":"Xin","family":"Xiong","sequence":"first","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"},{"name":"The State Key Lab of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3527-2869","authenticated-orcid":false,"given":"Yuki","family":"Shimizu","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"},{"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":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5925-4951","authenticated-orcid":false,"given":"Wei","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,8]]},"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."},{"key":"ref_2","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."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.cirp.2009.03.007","article-title":"On-the-fly calibration of linear and rotary axes of machine tools and CMMs using a tracking interferometer","volume":"58","author":"Schwenke","year":"2009","journal-title":"CIRP Ann."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41871-018-0025-8","article-title":"Design and Verification of Micro\/Nano-Probes for Coordinate Measuring Machines","volume":"2","author":"Fan","year":"2018","journal-title":"Nanomanufacturing Metrol."},{"key":"ref_5","unstructured":"(2021, July 10). 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