{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:27:30Z","timestamp":1785432450039,"version":"3.56.0"},"reference-count":19,"publisher":"International Union of Crystallography (IUCr)","issue":"4","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}]}],"content-domain":{"domain":["iucr.org","wiley.com","iucrj.org"],"crossmark-restriction":true},"short-container-title":["J Synchrotron Rad","J Synchrotron Radiat"],"accepted":{"date-parts":[[2022,5,30]]},"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:p>\n                    Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems \u2014 a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the\n                    <jats:italic>xy<\/jats:italic>\n                    plane at the mirror's center \u2014 are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.\n                  <\/jats:p>","DOI":"10.1107\/s1600577522005793","type":"journal-article","created":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T05:38:29Z","timestamp":1655703509000},"page":"991-996","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":10,"title":["Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle"],"prefix":"10.1107","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9984-5780","authenticated-orcid":true,"given":"Kenneth A.","family":"Goldberg","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02jbv0t02","id-type":"ROR","asserted-by":"publisher"}],"department":["Advanced Light Source"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"329","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"yi5120_bb1","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1364\/JOSA.38.000766","volume":"38","author":"Baez","year":"1948","journal-title":"J. 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Proc."}],"container-title":["Journal of Synchrotron Radiation"],"original-title":[],"link":[{"URL":"https:\/\/journals.iucr.org\/s\/issues\/2022\/04\/00\/yi5120\/yi5120.pdf","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.iucr.org\/s\/issues\/2022\/04\/00\/yi5120\/yi5120.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T06:09:44Z","timestamp":1736748584000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.iucr.org\/paper?S1600577522005793"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,20]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["S1600577522005793"],"URL":"https:\/\/doi.org\/10.1107\/s1600577522005793","relation":{},"ISSN":["1600-5775"],"issn-type":[{"value":"1600-5775","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,20]]},"assertion":[{"value":"Journal of Synchrotron Radiation","order":0,"name":"journal","label":"Publication","explanation":{"URL":"https:\/\/journals.iucr.org\/s"},"group":{"name":"general","label":"General"}},{"value":"research papers","order":1,"name":"content_type","label":"Content type","explanation":{"URL":"https:\/\/journals.iucr.org\/s\/services\/notesforauthors.html"},"group":{"name":"general","label":"General"}},{"value":"Available","URL":"https:\/\/scripts.iucr.org\/cgi-bin\/citedin?yi5120","order":2,"name":"article_metrics","label":"Article metrics","group":{"name":"general","label":"General"}},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"23 December 2021","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication history"}},{"value":"30 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication history"}},{"value":"20 June 2022","order":2,"name":"published_online","label":"Published online","group":{"name":"publication_history","label":"Publication history"}},{"value":"\u00a9 2022 Kenneth A. Goldberg","order":0,"name":"copyright","label":"Copyright","explanation":{"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}},{"value":"Creative Commons Attribution (CC-BY)","order":1,"name":"license","label":"Licence","explanation":{"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}}]}}