{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:58:50Z","timestamp":1760144330464,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T00:00:00Z","timestamp":1712275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"publisher","award":["62205168","JAT220294","2020J01916"],"award-info":[{"award-number":["62205168","JAT220294","2020J01916"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young and Middle-Aged Teachers\u2019 Educational Research Projects of Fujian Province of China","award":["62205168","JAT220294","2020J01916"],"award-info":[{"award-number":["62205168","JAT220294","2020J01916"]}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["62205168","JAT220294","2020J01916"],"award-info":[{"award-number":["62205168","JAT220294","2020J01916"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient.<\/jats:p>","DOI":"10.3390\/sym16040439","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T08:27:52Z","timestamp":1712305672000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Third-Order Intrinsic Aberration Modification with Second-Order Accuracy Transfer of Pupil Coordinates and Extrinsic Aberration of Plane-Symmetric Optical System with a Two-Dimensional Field Light Source"],"prefix":"10.3390","volume":"16","author":[{"given":"Yiqing","family":"Cao","sequence":"first","affiliation":[{"name":"School of Mechanical, Electronic & Information Engineering, Putian University, Putian 351100, China"},{"name":"Fujian Laser Precision Machining Engineering Technology Research Center, Putian 351100, China"}]},{"given":"Lijun","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}]},{"given":"Zhijuan","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic & Information Engineering, Putian University, Putian 351100, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"034302","DOI":"10.1063\/4.0000096","article-title":"Highly efficient soft X-ray spectrometer for transient absorption spectroscopy with broadband table-top high harmonic sources","volume":"8","author":"Kleine","year":"2021","journal-title":"Struct. Dyn."},{"key":"ref_2","unstructured":"Born, M., and Wolf, E. (2005). Principle of Optics, Cambridge University Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1364\/JOSA.35.000311","article-title":"The Theory of the concave grating","volume":"35","author":"Beutler","year":"1945","journal-title":"J. Opt. Soc. Am."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1364\/JOSA.64.001031","article-title":"Geometrical theory of the grating","volume":"64","author":"Noda","year":"1974","journal-title":"J. Opt. Soc. Am."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0168-9002(92)90557-K","article-title":"Analytical representation of spot diagrams and its application to the design of monochromators","volume":"319","author":"Namioka","year":"1992","journal-title":"Nucl. Instrum. Meth. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2253","DOI":"10.1364\/JOSAA.16.002253","article-title":"Geometric aberration theory of double-element optical systems","volume":"16","author":"Masui","year":"1999","journal-title":"J. Opt. Soc. Am."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Palmer, C., Wheeler, B.S., and McKinney, W.R. (1998). Imaging Equations for Spectroscopic Systems Using Lie Transformations: II. Multielement Systems, SPIE.","DOI":"10.1117\/12.323410"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1364\/AO.22.001508","article-title":"Aberrations of holographic toroidal grating systems","volume":"22","author":"Chrisp","year":"1983","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kidger, M.J. (2004). Intermediate Optical Design, SPIE Press.","DOI":"10.1117\/3.540692"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"D69","DOI":"10.1364\/AO.49.000D69","article-title":"Theory of sixth-order wave aberrations","volume":"49","author":"Sasian","year":"2010","journal-title":"Appl. Opt."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1515\/aot-2012-0073","article-title":"Extrinsic aberrations in optical imaging systems","volume":"2","author":"Sasian","year":"2013","journal-title":"Adv. Opt. Technol."},{"key":"ref_12","unstructured":"Sasian, J. (2013). Introduction to Aberrations in Optical Imaging Systems, Cambridge University Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1364\/OE.22.000289","article-title":"Generation of spherical aberration with axially translating phase plates via extrinsic aberration","volume":"22","author":"Sasian","year":"2014","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1016\/j.ijleo.2009.01.016","article-title":"Aberrations of plane-symmetric multi-element optical systems","volume":"121","author":"Lu","year":"2010","journal-title":"Optik"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ijleo.2011.03.014","article-title":"Extension of aberration theory of grating systems from one- to two-dimension extended source","volume":"123","author":"Lu","year":"2012","journal-title":"Optik"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1107\/S0909049511026306","article-title":"SHADOW3: A new version of the synchrotron X-ray optics modeling package","volume":"18","author":"Canestrari","year":"2011","journal-title":"J. Synchrotron Radiat."},{"key":"ref_17","unstructured":"Peatman, W.B. (1997). Beamline Design for Soft X-ray Synchrotron Radiation Sources, Gordon and Beach Science Publisher."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7261","DOI":"10.1364\/AO.33.007261","article-title":"Geometric theory of the ellipsoidal grating","volume":"33","author":"Namioka","year":"1994","journal-title":"Appl. Opt."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/439\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:23:50Z","timestamp":1760106230000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,5]]},"references-count":18,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["sym16040439"],"URL":"https:\/\/doi.org\/10.3390\/sym16040439","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,4,5]]}}}