{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T18:57:11Z","timestamp":1776452231876,"version":"3.51.2"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T00:00:00Z","timestamp":1431907200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["FIS2012-30820"],"award-info":[{"award-number":["FIS2012-30820"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Ophthalmic Physiologic Optic"],"published-print":{"date-parts":[[2015,7]]},"abstract":"Abstract<\/jats:title>\n \n Purpose<\/jats:title>\n To propose geodesic curvature as a metric to characterise how an optical surface locally differs from axial symmetry. To derive equations to evaluate geodesic curvatures of arbitrary surfaces expressed in polar coordinates.<\/jats:p>\n <\/jats:sec>\n \n Methods<\/jats:title>\n The concept of geodesic curvature is explained in detail as compared to other curvature\u2010based metrics. Starting with the formula representing a surface as function of polar coordinates, an equation for the geodesic curvature is obtained depending only on first and second radial and first order angular derivatives of the surface function. The potential of the geodesic curvature is illustrated using different surface tests.<\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n Geodesic curvature reveals local axial asymmetries more sharply than other types of curvatures such as normal curvatures.<\/jats:p>\n <\/jats:sec>\n \n Conclusion<\/jats:title>\n Geodesic curvature maps could be used to characterise local axial asymmetries for relevant optometry applications such as corneal topography anomalies (keratoconus) or ophthalmic lens metrology.<\/jats:p>\n <\/jats:sec>","DOI":"10.1111\/opo.12216","type":"journal-article","created":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T23:05:58Z","timestamp":1431990358000},"page":"388-393","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The concept of geodesic curvature applied to optical surfaces"],"prefix":"10.1007","volume":"35","author":[{"given":"Sergio","family":"Barbero","sequence":"first","affiliation":[{"name":"Instituto de \u00d3ptica (CSIC) Madrid Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,5,18]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Differential Geometry","author":"Stoker JJ","year":"1969"},{"key":"e_1_2_8_3_1","volume-title":"Introduction to Differential Geometry","author":"Goetz A","year":"1970"},{"key":"e_1_2_8_4_1","volume-title":"Irregular Astigmatism: Diagnosis and Treatment","author":"Wang M","year":"2008"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199711000-00025"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2004.843192"},{"key":"e_1_2_8_7_1","volume-title":"Differential Geometry","author":"Kreyszig E","year":"1991"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-198610000-00007"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199809000-00022"},{"key":"e_1_2_8_10_1","first-page":"33","volume-title":"Geometry for Analysis of Corneal Shape. Geometry for Analysis of Corneal Shape","author":"Barsky BA","year":"2003"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/3527608176"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2006.00382.x"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199711000-00029"},{"key":"e_1_2_8_14_1","volume-title":"1st World Meeting in Visual and Physiological Optics","author":"Kollbaum PS","year":"2014"}],"container-title":["Ophthalmic and Physiological Optics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fopo.12216","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/opo.12216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T11:24:02Z","timestamp":1767785042000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/opo.12216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,18]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["10.1111\/opo.12216"],"URL":"https:\/\/doi.org\/10.1111\/opo.12216","archive":["Portico"],"relation":{},"ISSN":["0275-5408","1475-1313"],"issn-type":[{"value":"0275-5408","type":"print"},{"value":"1475-1313","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,18]]},"assertion":[{"value":"2015-01-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-04-20","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-05-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}