{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:03:48Z","timestamp":1775869428511,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T00:00:00Z","timestamp":1654732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52075190"],"award-info":[{"award-number":["52075190"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020I0101"],"award-info":[{"award-number":["2020I0101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Program of Fujian, China","award":["52075190"],"award-info":[{"award-number":["52075190"]}]},{"name":"Science and Technology Program of Fujian, China","award":["2020I0101"],"award-info":[{"award-number":["2020I0101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To improve the accuracy of the current vision-based linear displacement measurement in a large range, a new type of linear displacement sensing system, namely, image grating, is proposed in this paper. The proposed system included a patterned glass plate attached to the moving object and an ultra-low distortion lens for high-accuracy image matching. A DFT local up-sampling phase correlation method was adopted to obtain the sub-pixel translation of the patterns onto the target plate. Multiple sets of stripe patterns with different designs were located on the glass plate to expand the measurement range, based on the principle of phase correlation. In order to improve the measurement accuracy, the main errors of the image grating system were analyzed, and the nonlinear error compensation was completed based on the dynamic calibration of the pixel equivalent. The measurement results, after the error compensation, showed that the total error of the proposed system was less than 2.5 \u03bcm in the range of 60 mm, and the repeatability was within 0.16 \u03bcm, as quantified by standard deviation.<\/jats:p>","DOI":"10.3390\/s22124361","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T02:01:44Z","timestamp":1655085704000},"page":"4361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A New Image Grating Sensor for Linear Displacement Measurement and Its Error Analysis"],"prefix":"10.3390","volume":"22","author":[{"given":"Fang","family":"Cheng","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongfang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8767-3889","authenticated-orcid":false,"given":"Qing","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tegoeh","family":"Tjahjowidodo","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, De Nayer Campus, KU Leuven, Jan Pieter de Nayerlaan 5, 2860 Sint-Katelijne-Waver, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18059","DOI":"10.1038\/s41598-019-54489-0","article-title":"Gate-tunable graphene-based Hall sensors on flexible substrates with increased sensitivity","volume":"9","author":"Uzlu","year":"2019","journal-title":"Sci. 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