Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods
Around 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approa...
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Veröffentlicht in: | Applied optics (2004) 2021-07, Vol.60 (21), p.6226-6234 |
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description | Around 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approach and is analyzed here using analytic ray theory approaches appropriate to the paraxial regime. We demonstrate that the caustic assumes the standard astroid form when the maximum meniscus slope is small, and the shape starts to distort as the maximum meniscus slope increases. We show that competition between generalized coma and generalized astigmatism, with generalized coma dominating, is responsible for the cusp points of the astroid in the plane of the incident light being reversed with respect to their images in the exit plane of the optical system. We also show that Leonardo’s cross is the result of the twofold symmetry of the astigmatic focusing of the diagonally incident plane wave by the circularly symmetric meniscus. |
doi_str_mv | 10.1364/AO.426433 |
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This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approach and is analyzed here using analytic ray theory approaches appropriate to the paraxial regime. We demonstrate that the caustic assumes the standard astroid form when the maximum meniscus slope is small, and the shape starts to distort as the maximum meniscus slope increases. We show that competition between generalized coma and generalized astigmatism, with generalized coma dominating, is responsible for the cusp points of the astroid in the plane of the incident light being reversed with respect to their images in the exit plane of the optical system. We also show that Leonardo’s cross is the result of the twofold symmetry of the astigmatic focusing of the diagonally incident plane wave by the circularly symmetric meniscus.</description><identifier>ISSN: 1559-128X</identifier><identifier>EISSN: 2155-3165</identifier><identifier>EISSN: 1539-4522</identifier><identifier>DOI: 10.1364/AO.426433</identifier><language>eng</language><publisher>Washington: Optical Society of America</publisher><subject>Alkalies ; Astigmatism ; Incident light ; Plane waves ; Symmetry</subject><ispartof>Applied optics (2004), 2021-07, Vol.60 (21), p.6226-6234</ispartof><rights>Copyright Optical Society of America Jul 20, 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c290t-bec1dc71f247f38f892e436ce4ade05df45f71c84813024cb7bfd7c3d1f203ac3</citedby><cites>FETCH-LOGICAL-c290t-bec1dc71f247f38f892e436ce4ade05df45f71c84813024cb7bfd7c3d1f203ac3</cites><orcidid>0000-0002-3281-2527</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3258,27924,27925</link.rule.ids></links><search><creatorcontrib>Lock, James A.</creatorcontrib><creatorcontrib>Selmke, Markus</creatorcontrib><title>Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods</title><title>Applied optics (2004)</title><description>Around 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approach and is analyzed here using analytic ray theory approaches appropriate to the paraxial regime. We demonstrate that the caustic assumes the standard astroid form when the maximum meniscus slope is small, and the shape starts to distort as the maximum meniscus slope increases. We show that competition between generalized coma and generalized astigmatism, with generalized coma dominating, is responsible for the cusp points of the astroid in the plane of the incident light being reversed with respect to their images in the exit plane of the optical system. We also show that Leonardo’s cross is the result of the twofold symmetry of the astigmatic focusing of the diagonally incident plane wave by the circularly symmetric meniscus.</description><subject>Alkalies</subject><subject>Astigmatism</subject><subject>Incident light</subject><subject>Plane waves</subject><subject>Symmetry</subject><issn>1559-128X</issn><issn>2155-3165</issn><issn>1539-4522</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNpdkMtKAzEYhYMoWKsL32DAjYJTc8-Mu1q8QaEKCu5CJhecMm3GZEbsrg_hxtfrkxitK1fnLL7z858DwDGCI0Q4vRjPRhRzSsgOGGDEWE4QZ7tgkGyZI1y87IODGOcQEkZLMQCPV31VNTbzbVfreJlNrV-qYPxm_RUzHXyMWbDvdaw7azbrzwcVugyfZ60K6qNWTaaWqlmlaLIL2716Ew_BnlNNtEd_OgTPN9dPk7t8Oru9n4ynucYl7PLKamS0QA5T4UjhihJbSri2VBkLmXGUOYF0QQtEIKa6EpUzQhOTEpAoTYbgdHu3Df6tt7GTizpq2zRqaX0fJWai5JiXRCT05B86931In_9QjBcFJgwn6mxL_dYO1sk21AsVVhJB-TOuHM_kdlzyDQyTbbY</recordid><startdate>20210720</startdate><enddate>20210720</enddate><creator>Lock, James A.</creator><creator>Selmke, Markus</creator><general>Optical Society of America</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-3281-2527</orcidid></search><sort><creationdate>20210720</creationdate><title>Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods</title><author>Lock, James A. ; Selmke, Markus</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c290t-bec1dc71f247f38f892e436ce4ade05df45f71c84813024cb7bfd7c3d1f203ac3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Alkalies</topic><topic>Astigmatism</topic><topic>Incident light</topic><topic>Plane waves</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lock, James A.</creatorcontrib><creatorcontrib>Selmke, Markus</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Applied optics (2004)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lock, James A.</au><au>Selmke, Markus</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods</atitle><jtitle>Applied optics (2004)</jtitle><date>2021-07-20</date><risdate>2021</risdate><volume>60</volume><issue>21</issue><spage>6226</spage><epage>6234</epage><pages>6226-6234</pages><issn>1559-128X</issn><eissn>2155-3165</eissn><eissn>1539-4522</eissn><abstract>Around 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. 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subjects | Alkalies Astigmatism Incident light Plane waves Symmetry |
title | Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods |
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