{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:39:37Z","timestamp":1773232777786,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T00:00:00Z","timestamp":1674604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Romanian Ministry of Research, Innovation and Digitization","award":["PN-III-P4-ID-PCE-2020-2600"],"award-info":[{"award-number":["PN-III-P4-ID-PCE-2020-2600"]}]},{"name":"Romanian Ministry of Research, Innovation and Digitization","award":["POCU\/993\/6\/13\/153437"],"award-info":[{"award-number":["POCU\/993\/6\/13\/153437"]}]},{"name":"Project ork of excellence in applied research and innovation for doctoral and postdoctoral programs \/ InoHub project co-funded by the European Social Fund financing agreement","award":["PN-III-P4-ID-PCE-2020-2600"],"award-info":[{"award-number":["PN-III-P4-ID-PCE-2020-2600"]}]},{"name":"Project ork of excellence in applied research and innovation for doctoral and postdoctoral programs \/ InoHub project co-funded by the European Social Fund financing agreement","award":["POCU\/993\/6\/13\/153437"],"award-info":[{"award-number":["POCU\/993\/6\/13\/153437"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Laser scanners with rotational Risley prisms produce scan patterns that can be classified as a type of rhodonea curve, because of their symmetry. The present study builds upon the novel, graphical method that we have developed to simulate and analyze such patterns using a commercially available mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France). This graphical method has both the advantage of simplicity (regarding analytical methods) and of generating exact scan patterns (in contrast to approximate methods). The aim of this work is to utilize this method to study symmetry properties of scan patterns produced by a pair of rotational Risley prisms. A multi-parameter analysis is performed, considering the characteristic parameters of the approached scanner: refractive indexes and angles of the prisms, as well as their rotational velocities. Furthermore, Marshall\u2019s parameters are considered: ratios of the rotational velocities and of the prism angles. Because the symmetries are identical for scan patterns generated by all the four possible configurations of a pair of prisms (and only their dimensions are different), the shape of these patterns is studied only for one of these configurations. Therefore, without losing generality, the symmetries of the patterns produced by such scanners are determined, as well as some of their characteristic dimensions. Rules-of-thumb were obtained to be able to generate patterns that are appropriate for a specific application. Moreover, we demonstrated that the existing symmetries simplify the process of obtaining the scan patterns by identifying repetitive parts (defined as structures of symmetry) of a pattern.<\/jats:p>","DOI":"10.3390\/sym15020336","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T04:54:41Z","timestamp":1674622481000},"page":"336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Symmetries of Scan Patterns of Laser Scanners with Rotational Risley Prisms"],"prefix":"10.3390","volume":"15","author":[{"given":"Alexandru-Lucian","family":"Dimb","sequence":"first","affiliation":[{"name":"Doctoral School, Polytechnic University of Timisoara, 1 Mihai Viteazu Ave., 300222 Timisoara, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5558-4777","authenticated-orcid":false,"given":"Virgil-Florin","family":"Duma","sequence":"additional","affiliation":[{"name":"Doctoral School, Polytechnic University of Timisoara, 1 Mihai Viteazu Ave., 300222 Timisoara, Romania"},{"name":"3OM Optomechatronics Group, Faculty of Engineering, Aurel Vlaicu University of Arad, Str. Elena Dragoi No. 2, 310177 Arad, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,25]]},"reference":[{"key":"ref_1","unstructured":"Bass, M. (2009). Handbook of Optics, Mc. Graw-Hill Inc.. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Marshall, G.F., and Stutz, G.E. (2011). Handbook of Optical and Laser Scanning, CRC Press. [2nd ed.].","DOI":"10.1201\/b11090"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1366\/0003702011954206","article-title":"Small Fourier transform spectroscope using an integrated prism-scanning interferometer","volume":"55","author":"Kiyokura","year":"2001","journal-title":"Appl. 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