{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T23:24:43Z","timestamp":1768001083881,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T00:00:00Z","timestamp":1593043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We report a technique to measure in-plane and out-of-plane motions of MEMS using typical out-of-plane (single-axis) Laser Doppler Vibrometers (LDVs). The efficacy of the technique is demonstrated by evaluating the in-plane and out-of-plane modal response and frequency response of an interdigitated comb-drive actuator. We also investigate the validity of observing planar modes of vibration outside their dominant plane of motion and find that it leads to erroneous results. Planar modes must be evaluated in their plan of motion.<\/jats:p>","DOI":"10.3390\/s20123594","type":"journal-article","created":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T10:36:54Z","timestamp":1593081414000},"page":"3594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Measurement of In-Plane Motions in MEMS"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3945-6104","authenticated-orcid":false,"given":"Mohamed","family":"Arabi","sequence":"first","affiliation":[{"name":"Department of Systems Design Engineering, University of Waterloo, Waterloo N2L 3G1, ON, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mary","family":"Gopanchuk","sequence":"additional","affiliation":[{"name":"Design &amp; Engineering, Polytechnic University of Milan, Piazza Leonardo Da Vinci, 32, 20133 Milano MI, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3709-7593","authenticated-orcid":false,"given":"Eihab","family":"Abdel-Rahman","sequence":"additional","affiliation":[{"name":"Department of Systems Design Engineering, University of Waterloo, Waterloo N2L 3G1, ON, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustafa","family":"Yavuz","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo N2L 3G1, ON, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1088\/0960-1317\/17\/4\/021","article-title":"A sensitive electronic capacitance measurement system to measure the comb drive motion of surface micromachined MEMS devices","volume":"17","author":"Oosterkamp","year":"2007","journal-title":"J. Micromech. Microeng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"085007","DOI":"10.1088\/1361-6439\/aa77bd","article-title":"Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current","volume":"27","author":"Park","year":"2017","journal-title":"J. Micromech. Microeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1117\/12.478195","article-title":"MEMS characterization using laser Doppler vibrometry","volume":"Volume 4980","author":"Lawrence","year":"2003","journal-title":"Reliability, Testing, and Characterization of MEMS\/MOEMS II"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Osten, W. (2018). Optical Inspection of Microsystems, CRC Press.","DOI":"10.1201\/9781420019162"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1590\/S1678-58782003000300001","article-title":"In-plane strain measurement by digital image correlation","volume":"25","author":"Hung","year":"2003","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_6","first-page":"127","article-title":"Optical measurement methods to study dynamic behavior in MEMS","volume":"Volume 4400","author":"Rembe","year":"2001","journal-title":"Microsystems Engineering: Metrology and Inspection"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/JMEMS.2009.2031698","article-title":"Fiber-optic laser Doppler vibrometer to dynamically measure MEMS actuator with in-plane motion","volume":"18","author":"Kim","year":"2009","journal-title":"J. Microelectromech. Syst."},{"key":"ref_8","first-page":"144","article-title":"Multi-dimensional MEMS motion characterization using laser vibrometry","volume":"21","author":"Turner","year":"1999","journal-title":"Dig. Tech. Pap. Transducers\u2019 99"},{"key":"ref_9","unstructured":"(2020, February 12). MSA-100-3D Micro System Analyzer. Available online: https:\/\/www.polytec.com\/eu\/vibrometry\/products\/microscope-based-vibrometers\/msa-100-3d-micro-system-analyzer\/."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Herth, E., Lardet-Vieudrin, F., Deux, F., Valbin, L., Algr\u00e9, E., Schell, J., and Steger, H. (June, January 30). Detection of out-of-plane and in-plane (XYZ) motions of piezoelectric microcantilever by 3D-Laser Doppler Vibrometry. Proceedings of the IEEE 2016 Symposium on Design, Test, Integration and Packaging of MEMS\/MOEMS (DTIP), Budapest, Hungary.","DOI":"10.1109\/DTIP.2016.7514876"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"84300C","DOI":"10.1117\/12.922184","article-title":"Real-time 3D vibration measurements in microstructures","volume":"Volume 8430","author":"Kowarsch","year":"2012","journal-title":"Optical Micro-and Nanometrology IV"},{"key":"ref_12","unstructured":"(2020, February 17). PSV-500-3D Scanning Vibrometer. 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Characterization of a Non-Interdigitated Comb Drive. ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers.","DOI":"10.1115\/DETC2018-86271"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1109\/84.825787","article-title":"Electrostatic model for an asymmetric combdrive","volume":"9","author":"Yeh","year":"2000","journal-title":"J. Microelectromech. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/12\/3594\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:42:50Z","timestamp":1760175770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/12\/3594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,25]]},"references-count":16,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["s20123594"],"URL":"https:\/\/doi.org\/10.3390\/s20123594","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,25]]}}}