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Opt."],"published-print":{"date-parts":[[2024,5,1]]},"abstract":"<jats:p>The paper presents a method for a rough estimation of the aberrations and of the MTF of an optical system by means of the Helmholtz-Lagrange invariant. The method allows for a rough understanding of an optical design and can find application in those cases where approximated performance predictions are needed, for example, before running complex and time-consuming analyses. The simple approach presented here is a rough approximation and should always be followed by the usual tolerance analyses.<\/jats:p>","DOI":"10.1364\/ao.520107","type":"journal-article","created":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T09:00:06Z","timestamp":1712048406000},"page":"3390","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optical MTF and aberration predictions with the Helmholtz-Lagrange invariant"],"prefix":"10.1364","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4401-7205","authenticated-orcid":true,"given":"P.","family":"Sandri","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0586wsk08","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2024,4,19]]},"reference":[{"key":"ao-63-13-3390-R1","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1038\/s41377-018-0058-1","volume":"7","author":"Neshev","year":"2018","journal-title":"Light Sci. 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