{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T14:28:28Z","timestamp":1767796108272,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2011,8,23]],"date-time":"2011-08-23T00:00:00Z","timestamp":1314057600000},"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":[[2011,11]]},"abstract":"<jats:sec>\n                    <jats:label\/>\n                    <jats:p>\n                      <jats:bold>Citation information:<\/jats:bold>\n                      Harris WF. Aperture referral in heterocentric astigmatic systems.\n                      <jats:italic>Ophthalmic Physiol Opt<\/jats:italic>\n                      2011,\n                      <jats:bold>31<\/jats:bold>\n                      , 603\u2013614. doi: 10.1111\/j.1475\u20101313.2011.00860.x\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Abstract<\/jats:title>\n                    <jats:p>\n                      <jats:bold>Background:\u2002<\/jats:bold>\n                      Retinal blur patch, effective corneal patch, projective field, field of view and other concepts are usually regarded as disjoint concepts to be treated separately. However they have in common the fact that an aperture, often the pupil of the eye, has its effect at some other longitudinal position. Here the effect is termed aperture referral.\n                    <\/jats:p>\n                    <jats:p>\n                      <jats:bold>Purpose:\u2002<\/jats:bold>\n                      To develop a complete and general theory of aperture referral under which many ostensibly\u2010distinct aperture\u2010dependent concepts become unified and of which these concepts become particular applications. The theory allows for apertures to be elliptical and decentred and refracting surfaces in an eye or any other optical system to be astigmatic, heterocentric and tilted.\n                    <\/jats:p>\n                    <jats:p>\n                      <jats:bold>Methods:\u2002<\/jats:bold>\n                      The optical model used is linear optics, a three\u2010dimensional generalization of Gaussian optics. Positional and inclinational invariants are defined along a ray through an arbitrary optical system. A pencil of rays through a system is defined by an object or image point and an aperture defines a subset of the pencil called a restricted pencil.\n                    <\/jats:p>\n                    <jats:p>\n                      <jats:bold>Results:\u2002<\/jats:bold>\n                      Invariants are derived for four cases: an object and an image point at finite and at infinite distances. Formulae are obtained for the generalized magnification and transverse translation and for the geometry and location of an aperture referred to any other transverse plane.\n                    <\/jats:p>\n                    <jats:p>\n                      <jats:bold>Conclusions:\u2002<\/jats:bold>\n                      A restricted pencil is defined by an aperture and an object or image point. The intersection of the restricted pencil with a transverse plane is the aperture referred to that transverse plane. Many concepts, including effective corneal patch, retinal blur patch, projective field and visual field, can now be treated routinely as special cases of the general theory: having identified the aperture, the referred aperture and the referring point one applies the general formulae directly. The formulae are exact in linear optics, explicit and give insight into relationships.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.1111\/j.1475-1313.2011.00860.x","type":"journal-article","created":{"date-parts":[[2011,8,31]],"date-time":"2011-08-31T18:14:52Z","timestamp":1314814492000},"page":"603-614","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Aperture referral in heterocentric astigmatic systems"],"prefix":"10.1007","volume":"31","author":[{"given":"William F","family":"Harris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,8,23]]},"reference":[{"key":"e_1_2_14_2_2","volume-title":"Optics of the Human Eye","author":"Atchison DA","year":"2000"},{"key":"e_1_2_14_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511609541"},{"key":"e_1_2_14_4_2","volume-title":"Bennett and Rabbetts\u2019 Clinical Visual Optics","author":"Rabbetts RB","year":"2007"},{"key":"e_1_2_14_5_2","volume-title":"Geometric, Physical, and Visual Optics","author":"Keating MP","year":"2002"},{"key":"e_1_2_14_6_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2008.00602.x"},{"key":"e_1_2_14_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0886-3350(03)00214-1"},{"key":"e_1_2_14_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2005.05.026"},{"key":"e_1_2_14_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2008.07.033"},{"key":"e_1_2_14_10_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1444-0938.2008.00346.x"},{"key":"e_1_2_14_11_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2010.00793.x"},{"key":"e_1_2_14_12_2","volume-title":"Physiologic Optics","author":"Tscherning M","year":"1904"},{"key":"e_1_2_14_13_2","volume-title":"Dictionary of Visual Science and Related Clinical Terms","author":"Hofstetter HW","year":"2000"},{"key":"e_1_2_14_14_2","volume-title":"Introduction to Visual Optics","author":"Tunnacliffe AH","year":"1984"},{"key":"e_1_2_14_15_2","volume-title":"Optics","author":"Tunnacliffe AH","year":"1981"},{"key":"e_1_2_14_16_2","doi-asserted-by":"publisher","DOI":"10.1142\/5135"},{"key":"e_1_2_14_17_2","volume-title":"Introduction to the Optics of the Eye","author":"Goss DA","year":"2002"},{"key":"e_1_2_14_18_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2009.00690.x"},{"key":"e_1_2_14_19_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2010.00760.x"},{"key":"e_1_2_14_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2009.00708.x"},{"key":"e_1_2_14_21_2","doi-asserted-by":"publisher","DOI":"10.1097\/OPX.0b013e31819fa8d8"},{"key":"e_1_2_14_22_2","first-page":"1","volume-title":"Symplectic Techniques in Physics","author":"Guillemin V","year":"1984"},{"key":"e_1_2_14_23_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139171670"},{"key":"e_1_2_14_24_2","volume-title":"Linear Ray and Wave Optics in Phase Space","author":"Torre A","year":"2005"},{"key":"e_1_2_14_25_2","doi-asserted-by":"publisher","DOI":"10.1097\/00006324-199404000-00009"},{"key":"e_1_2_14_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/b105056"},{"key":"e_1_2_14_27_2","first-page":"3","article-title":"Symplecticity and relationships among the fundamental properties in linear optics","volume":"69","author":"Harris WF","year":"2010","journal-title":"S Afr Optom"},{"key":"e_1_2_14_28_2","first-page":"109","article-title":"Generalized magnification in visual optics. 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