{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T01:10:23Z","timestamp":1782522623437,"version":"3.54.5"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T00:00:00Z","timestamp":1559779200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Ophthalmic Physiologic Optic"],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>\n                      This report uses the principles of geometrical optics to compute the optical point\u2010spread function (\n                      <jats:styled-content style=\"fixed-case\">PSF<\/jats:styled-content>\n                      ) from the wavefront error function.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Method<\/jats:title>\n                    <jats:p>\n                      Step 1 uses Prentice's rule to determine the spatial form of the\n                      <jats:styled-content style=\"fixed-case\">PSF<\/jats:styled-content>\n                      established by tracing a field of rays from the eye's exit pupil to the retina. Ray vergence is related to the slope of the wavefront error function, which enables the mapping of light rays to produce a retinal \u2018spot diagram\u2019. Step 2 completes the\n                      <jats:styled-content style=\"fixed-case\">PSF<\/jats:styled-content>\n                      by assigning an irradiance value to each ray in the spot diagram.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results and Conclusions<\/jats:title>\n                    <jats:p>\n                      Spot irradiance is inversely proportional to the Gaussian curvature (i.e. the product of principal curvatures) of each local region of wavefront error surface centered on the corresponding ray. The Gaussian curvature, in turn, may be computed as the determinant of the vergence error matrix associated with each point on the wavefront error surface. Elements of the vergence error matrix consist of sums and differences of the local power vector components\n                      <jats:italic>M<\/jats:italic>\n                      ,\n                      <jats:italic>J<\/jats:italic>\n                      <jats:sub>0<\/jats:sub>\n                      and\n                      <jats:italic>J<\/jats:italic>\n                      <jats:sub>45<\/jats:sub>\n                      . This method is shown to be equivalent to published derivations of the geometric\n                      <jats:styled-content style=\"fixed-case\">PSF<\/jats:styled-content>\n                      using the Jacobian of the ray mapping function and equivalent also to the Hessian of the wavefront error function. Examples are presented for the familiar cases of spherical and astigmatic blur as well as for higher order aberrations and the formation of caustics in the retinal image.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.1111\/opo.12619","type":"journal-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:33:33Z","timestamp":1559867613000},"page":"232-244","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Calculation of the geometrical point\u2010spread function from wavefront aberrations"],"prefix":"10.1007","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3726-3344","authenticated-orcid":false,"given":"Larry N","family":"Thibos","sequence":"first","affiliation":[{"name":"School of Optometry Indiana University Bloomington USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,6,6]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1167\/4.4.9"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-012443760-9\/50003-9"},{"key":"e_1_2_6_4_1","volume-title":"Optical Lenses, Dioptric Formulae for Combined Cylindrical Lenses: The Prism\u2010Dioptry, and Other Optical Papers","author":"Prentice CF","year":"1907"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-198610000-00007"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199609000-00007"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199706000-00019"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-198110000-00006"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199706000-00018"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/opo.12420"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.36.000B97"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-198211000-00006"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/opo.12120"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.31.000964"},{"key":"e_1_2_6_15_1","unstructured":"ANSI (American National Standards Institute).American national standard Z80.28 for ophthalmics \u2010 methods for reporting optical aberrations of eyes.2010."},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2011.00860.x"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-197601000-00005"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.3928\/1081-597X-20000901-14"},{"key":"e_1_2_6_19_1","volume-title":"Advanced Calculus","author":"Buck RC","year":"1978"},{"key":"e_1_2_6_20_1","unstructured":"Wikipedia.Jacobian matrix. 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Available from:https:\/\/en.wikipedia.org\/wiki\/Hessian_matrix(Accessed May 2019)."},{"key":"e_1_2_6_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59887-6"},{"key":"e_1_2_6_24_1","first-page":"328","volume-title":"Natural Focusing and Fine Structure of Light","author":"Nye JF","year":"1999"},{"key":"e_1_2_6_25_1","doi-asserted-by":"publisher","DOI":"10.1364\/AO.49.000126"},{"key":"e_1_2_6_26_1","volume-title":"Physiologic Optics","author":"Tscherning M","year":"1904"},{"key":"e_1_2_6_27_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.67.001508"},{"key":"e_1_2_6_28_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.36.000B58"}],"container-title":["Ophthalmic and Physiological Optics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fopo.12619","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/opo.12619","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/opo.12619","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/opo.12619","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T11:25:13Z","timestamp":1767785113000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/opo.12619"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,6]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["10.1111\/opo.12619"],"URL":"https:\/\/doi.org\/10.1111\/opo.12619","archive":["Portico"],"relation":{},"ISSN":["0275-5408","1475-1313"],"issn-type":[{"value":"0275-5408","type":"print"},{"value":"1475-1313","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,6]]},"assertion":[{"value":"2019-01-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-04-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-06-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}