{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:31:26Z","timestamp":1778711486723,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,9]],"date-time":"2016-07-09T00:00:00Z","timestamp":1468022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Ministry of Science and Technology of Taiwan","award":["MOST 103-2221-E-194-006 -MY3"],"award-info":[{"award-number":["MOST 103-2221-E-194-006 -MY3"]}]},{"name":"the Ministry of Science and Technology of Taiwan","award":["MOST 105-2218-E-194 -004"],"award-info":[{"award-number":["MOST 105-2218-E-194 -004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Automated optical inspection is a very important technique. For this reason, this study proposes an optical non-contact slanting surface measuring system. The essential features of the measurement system are obtained through simulations using the optical design software Zemax. The actual propagation of laser beams within the measurement system is traced by using a homogeneous transformation matrix (HTM), the skew-ray tracing method, and a first-order Taylor series expansion. Additionally, a complete mathematical model that describes the variations in light spots on photoelectric sensors and the corresponding changes in the sample orientation and distance was established. Finally, a laboratory prototype system was constructed on an optical bench to verify experimentally the proposed system. This measurement system can simultaneously detect the slanting angles (x, z) in the x and z directions of the sample and the distance (y) between the biconvex lens and the flat sample surface.<\/jats:p>","DOI":"10.3390\/s16071061","type":"journal-article","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T09:47:19Z","timestamp":1468230439000},"page":"1061","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["An Optical Sensor for Measuring the Position and Slanting Direction of Flat Surfaces"],"prefix":"10.3390","volume":"16","author":[{"given":"Yu-Ta","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations, National Chung Cheng University, Chiayi County 62102, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yen-Sheng","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations, National Chung Cheng University, Chiayi County 62102, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chien-Sheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations, National Chung Cheng University, Chiayi County 62102, Taiwan"},{"name":"Graduate Institute of Opto-Mechatronics, National Chung Cheng University, Chiayi County 62102, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"714","DOI":"10.3390\/s16050714","article-title":"Error ellipsoid analysis for the diameter measurement of cylindroid components using a laser radar measurement system","volume":"16","author":"Du","year":"2016","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"130","DOI":"10.3390\/s16010130","article-title":"Interferometric laser scanner for direction determination","volume":"16","author":"Kaloshin","year":"2016","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105101","DOI":"10.1088\/0957-0233\/24\/10\/105101","article-title":"A novel laser displacement sensor with improved robustness toward geometrical fluctuations of the laser beam","volume":"24","author":"Liu","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10714","DOI":"10.1364\/OE.23.010714","article-title":"Imaging properties of extended depth of field microscopy through single-shot focus scanning","volume":"23","author":"Lu","year":"2015","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.optlaseng.2014.10.004","article-title":"Precise autofocusing microscope with rapid response","volume":"66","author":"Liu","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1007\/s00340-014-5940-9","article-title":"Design and experimental validation of novel enhanced-performance autofocusing microscope","volume":"117","author":"Liu","year":"2014","journal-title":"Appl. Phys. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s00340-015-6202-1","article-title":"Design and characterization of high-performance autofocusing microscope with zoom in\/out functions","volume":"121","author":"Liu","year":"2015","journal-title":"Appl. Phys. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.optlaseng.2015.08.005","article-title":"Simultaneous spatial and angular positioning of plane specular samples by a novel double beam triangulation probe with full auto-compensation","volume":"77","author":"Makai","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1007\/s00170-005-0294-4","article-title":"A laser sensor with multiple detectors for freeform surface digitization","volume":"31","author":"Lee","year":"2007","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_10","unstructured":"Shiou, F.J., and Lee, R.T. (2006). Opto-Electronic Detector for Distance and Slanting Direction Measurement of a Surface. (I246585), TW Patent."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/S0141-6359(02)00121-6","article-title":"A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers","volume":"26","author":"Gao","year":"2002","journal-title":"Precis. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.ijleo.2005.10.004","article-title":"Matrix-based paraxial skew ray-tracing in 3D systems with non-coplanar optical axis","volume":"117","author":"Lin","year":"2006","journal-title":"Opt. Int. J. Light Electron Opt."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14601","DOI":"10.1364\/OE.15.014601","article-title":"An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts","volume":"15","author":"Chen","year":"2007","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3085","DOI":"10.1364\/AO.53.003085","article-title":"Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design","volume":"53","author":"Lin","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lin, P.D. (2013). New Computation Methods for Geometrical Optics, Springer.","DOI":"10.1007\/978-981-4451-79-6"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"23887","DOI":"10.1364\/OE.23.023887","article-title":"Real-time adaptive drift correction for super-resolution localization microscopy","volume":"23","author":"Grover","year":"2015","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"619","DOI":"10.3390\/s16050619","article-title":"Analysis and calibration of sources of electronic error in PSD sensor response","volume":"16","author":"Tsirigotis","year":"2016","journal-title":"Sensors"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1061\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:48Z","timestamp":1760210748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,9]]},"references-count":17,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["s16071061"],"URL":"https:\/\/doi.org\/10.3390\/s16071061","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,9]]}}}