{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:17:43Z","timestamp":1760235463089,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T00:00:00Z","timestamp":1630022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 109-2221-E-415-024"],"award-info":[{"award-number":["MOST 109-2221-E-415-024"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This investigation develops a laser encoder system based on a heterodyne laser interferometer. For eliminating geometric errors, the optical structure of the proposed encoder system was carried out with the internal zero-point method. The designed structure can eliminate the geometric errors, including positioning error, straightness error, squareness error, and Abbe error of the positioning stage. The signal processing system is composed of commercial integrated circuits (ICs). The signal type of the proposed encoding system is a differential signal that is compatible with most motion control systems. The proposed encoder system is embedded in a two-dimensional positioning stage. By the experimental results of the positioning test in the measuring range of 27 mm \u00d7 27 mm, with a resolution of 15.8 nm, the maximum values of the positioning error and standard deviation are 12.64 nm and 126.4 nm, respectively, in the positioning experiments. The result shows that the proposed encoder system can fit the positioning requirements of the optoelectronic and semiconductor industries.<\/jats:p>","DOI":"10.3390\/s21175775","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T22:58:15Z","timestamp":1630450695000},"page":"5775","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Development of the Heterodyne Laser Encoder System for the X\u2013Y Positioning Stage"],"prefix":"10.3390","volume":"21","author":[{"given":"Chung-Ping","family":"Chang","sequence":"first","affiliation":[{"name":"Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi 600, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tsung-Chun","family":"Tu","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi 600, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siang-Ruei","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi 600, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yung-Cheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Syuan-Cheng","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,27]]},"reference":[{"key":"ref_1","unstructured":"Wu, M.-H., and Fang, Y.-H. 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