{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T06:19:18Z","timestamp":1785392358934,"version":"3.55.0"},"reference-count":26,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T00:00:00Z","timestamp":1568851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Wenhao li","award":["2018YFF01011000"],"award-info":[{"award-number":["2018YFF01011000"]}]},{"name":"Wenhao Li","award":["20170519019JH"],"award-info":[{"award-number":["20170519019JH"]}]},{"name":"Wenhao Li","award":["2017SYHZ0025"],"award-info":[{"award-number":["2017SYHZ0025"]}]},{"name":"Shuo Yang","award":["61805233"],"award-info":[{"award-number":["61805233"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A third-order aberration theory has been developed for the Offner imaging spectrometer comprising an extended source; two concave mirrors; a convex diffraction grating; and an image plane. Analytic formulas of the spot diagram are derived for tracing rays through the system based on Fermat\u2019s principle. The proposed theory can be used to discuss in detail individual aberrations of the system such as coma, spherical aberration and astigmatism, and distortion together with the focal conditions. It has been critically evaluated as well in a comparison with exact ray tracing constructed using the commercial software ZEMAX. In regard to the analytic formulas, the results show a high degree of practicality.<\/jats:p>","DOI":"10.3390\/s19184046","type":"journal-article","created":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T10:55:21Z","timestamp":1568890521000},"page":"4046","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Geometric Aberration Theory of Offner Imaging Spectrometers"],"prefix":"10.3390","volume":"19","author":[{"given":"Meihong","family":"Zhao","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanxiu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuo","family":"Yang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhao","family":"Li","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,19]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Optical system design for a shortwave infrared imaging spectrometer","volume":"Volume 85570R","author":"Huang","year":"2012","journal-title":"Optical Design and Testing V"},{"key":"ref_2","first-page":"10","article-title":"Freeform spectrometer enabling increased compactness","volume":"6","author":"Jacob","year":"2017","journal-title":"Light Sci. 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