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Opt."],"published-print":{"date-parts":[[2023,6,20]]},"abstract":"<jats:p>A new digital coherent holographic system that works as a spatial-frequency shifter for measuring three-dimensional (3D) vibration of an object is proposed. The spatial-frequency shifter is constructed by a system of three mirrors inclined with different small angles to shift the object wave to three different frequencies in the spatial-frequency domain. By applying the Fourier transform method and appropriate filters to the hologram recorded by the camera of the system, a three-phase set of object waves corresponding to three shifted frequencies was obtained. From the relation between the phases and the relative position of the object, the position of each point on the surface of the object along the <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>, and <jats:italic>z<\/jats:italic> directions was extracted from each hologram. The same process was repeatedly applied to a series of holograms recorded by a fast camera, allowing the 3D vibration of the object to be precisely observed.<\/jats:p>","DOI":"10.1364\/ao.488986","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T15:00:07Z","timestamp":1685545207000},"page":"4921","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Noncontact vibration measurement using three spatial-frequency shifting coherent digital holography"],"prefix":"10.1364","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8556-2325","authenticated-orcid":true,"given":"Quang Duc","family":"Pham","sequence":"first","affiliation":[{"name":"Vietnam National University Hanoi"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tuan Duc","family":"Pham","sequence":"additional","affiliation":[{"name":"Hanoi University of Science and Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6826-9995","authenticated-orcid":true,"given":"Yoshio","family":"Hayasaki","sequence":"additional","affiliation":[{"name":"Utsunomiya University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"285","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"ao-62-18-4921-R1","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1007\/s00170-021-06873-2","volume":"114","author":"de S\u00e1 S\u00f3 Martins","year":"2021","journal-title":"Int. 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