{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T05:23:51Z","timestamp":1782537831609,"version":"3.54.5"},"reference-count":76,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:00:00Z","timestamp":1664323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Science Foundation","award":["22-14-00041"],"award-info":[{"award-number":["22-14-00041"]}]},{"name":"Russian Science Foundation","award":["007-GZ\/Ch3363\/26"],"award-info":[{"award-number":["007-GZ\/Ch3363\/26"]}]},{"name":"Government of the Samara Region","award":["22-14-00041"],"award-info":[{"award-number":["22-14-00041"]}]},{"name":"Government of the Samara Region","award":["007-GZ\/Ch3363\/26"],"award-info":[{"award-number":["007-GZ\/Ch3363\/26"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["22-14-00041"],"award-info":[{"award-number":["22-14-00041"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["007-GZ\/Ch3363\/26"],"award-info":[{"award-number":["007-GZ\/Ch3363\/26"]}]},{"DOI":"10.13039\/501100012190","name":"Federal Research Center \u201cCrystallography and Photonics\u201d RAS","doi-asserted-by":"publisher","award":["22-14-00041"],"award-info":[{"award-number":["22-14-00041"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Federal Research Center \u201cCrystallography and Photonics\u201d RAS","doi-asserted-by":"publisher","award":["007-GZ\/Ch3363\/26"],"award-info":[{"award-number":["007-GZ\/Ch3363\/26"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and\/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach.<\/jats:p>","DOI":"10.3390\/s22197365","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T22:53:19Z","timestamp":1664405599000},"page":"7365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Simplifying the Experimental Detection of the Vortex Topological Charge Based on the Simultaneous Astigmatic Transformation of Several Types and Levels in the Same Focal Plane"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2248-614X","authenticated-orcid":false,"given":"Pavel A.","family":"Khorin","sequence":"first","affiliation":[{"name":"Department of Technical Cybernetics, Samara National Research University, 443086 Samara, Russia"},{"name":"Image Processing Systems Institute of RAS\u2014Branch of the FSRC \u201cCrystallography and Photonics\u201d RAS, 443001 Samara, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6765-4373","authenticated-orcid":false,"given":"Svetlana N.","family":"Khonina","sequence":"additional","affiliation":[{"name":"Department of Technical Cybernetics, Samara National Research University, 443086 Samara, Russia"},{"name":"Image Processing Systems Institute of RAS\u2014Branch of the FSRC \u201cCrystallography and Photonics\u201d RAS, 443001 Samara, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexey P.","family":"Porfirev","sequence":"additional","affiliation":[{"name":"Department of Technical Cybernetics, Samara National Research University, 443086 Samara, Russia"},{"name":"Image Processing Systems Institute of RAS\u2014Branch of the FSRC \u201cCrystallography and Photonics\u201d RAS, 443001 Samara, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0180-7522","authenticated-orcid":false,"given":"Nikolay L.","family":"Kazanskiy","sequence":"additional","affiliation":[{"name":"Department of Technical Cybernetics, Samara National Research University, 443086 Samara, Russia"},{"name":"Image Processing Systems Institute of RAS\u2014Branch of the FSRC \u201cCrystallography and Photonics\u201d RAS, 443001 Samara, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"ref_1","first-page":"165","article-title":"Dislocations in Wave Trains","volume":"336","author":"Nye","year":"1974","journal-title":"Proc. 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