{"id":433,"date":"2016-08-22T18:45:44","date_gmt":"2016-08-22T18:45:44","guid":{"rendered":"https:\/\/live-optics-wp.pantheonsite.io\/jcwyant\/?page_id=433"},"modified":"2016-08-26T17:35:28","modified_gmt":"2016-08-26T17:35:28","slug":"zernike-polynomials","status":"publish","type":"page","link":"https:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/","title":{"rendered":"Zernike Polynomials"},"content":{"rendered":"<h2>Notes<\/h2>\n<ul>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/wp-content\/uploads\/sites\/13\/2016\/08\/Zernike-Equations.jpg\" target=\"_blank\">List of Zernike Polynomials<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/wp-content\/uploads\/sites\/13\/2016\/08\/Zernikes.pdf\">Notes on Zernike Polynomials<\/a> (Vol. XI, Applied Optics and Optical Engineering)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/wp-content\/uploads\/sites\/13\/2016\/08\/ZernikePolynomialsForTheWeb.pdf\">Notes on Zernike Polynomials<\/a> (Mathematica Notebook)<\/li>\n<li><a href=\"http:\/\/mathworld.wolfram.com\/ZernikePolynomial.html\" target=\"_blank\">Eric Weisstein&#8217;s world of Mathematics<\/a><\/li>\n<\/ul>\n<hr \/>\n<h2>Plots<\/h2>\n<p><strong>Two-Picture Stereograms<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n1-two-picture-stereograms\/\">n = 1<\/a> (Zernikes 1, 2, 3)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-2-two-picture-stereograms\/\">n = 2<\/a> (Zernikes 4, 5, 6, 7, 8)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-3-two-picture-stereograms\/\">n = 3<\/a> (Zernikes 9, 10, 11, 12, 13, 14, 15)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-4-two-picture-stereograms\/\">n = 4<\/a> (Zernikes 16, 17, 18, 19, 20, 21, 22, 23, 24)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-5-two-picture-stereograms\/\">n = 5<\/a> (Zernikes 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-6-two-picture-stereograms\/\">n = 6<\/a> (Zernikes 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/surface-of-revolution-stereogram\/\">n = 1 &#8211; 6, m = 0 Zernikes<\/a> (Animated gif)<\/li>\n<\/ul>\n<p><strong>Single-Picture Stereograms<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-5\/\">Zernike 5<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-6\/\">Zernike 6<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-8\/\">Zernike 8<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-25\/\">Zernike 25<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-35\/\">Zernike 35<\/a><\/li>\n<\/ul>\n<p>A good reference for using Mathematica to generate single-picture stereograms is &#8220;<a href=\"http:\/\/www.wolfram.com\/books\/profile.cgi?id=3789\" target=\"_blank\">The Mathematica Programmer II<\/a>&#8221; by <a href=\"http:\/\/www.mathconsult.ch\/en\/\" target=\"_blank\">Roman Maeder<\/a>.<\/p>\n<p><strong>Zernike Stereo Wallpaper<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/zernike-5-stereo-wallpaper\/\">Zernike 5<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-6-stereo-wallpaper\/\">Zernike 6<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-8-stereo-wallpaper\/\">Zernike 8<\/a> (My Favorite)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-24-stereo-wallpaper\/\">Zernike 24<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-25-stereo-wallpaper\/\">Zernike 25<\/a><\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/zernike-35-stereo-wallpaper\/\">Zernike 35<\/a><\/li>\n<\/ul>\n<p><strong>Density Plots<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-1-density-plot\/\">n = 1<\/a> (Zernikes 1, 2, 3)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-2-density-plot\/\">n = 2<\/a> (Zernikes 4, 5, 6, 7, 8)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-3-density-plot\/\">n = 3<\/a> (Zernikes 9, 10, 11, 12, 13, 14, 15)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-4-density-plot\/\">n = 4<\/a> (Zernikes 16, 17, 18, 19, 20, 21, 22, 23, 24)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-5-density-plot\/\">n = 5<\/a> (Zernikes 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35)<\/li>\n<li><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/zernike-polynomials\/n-6-density-plot\/\">n = 6<\/a> (Zernikes 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48)<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><a href=\"http:\/\/wp.optics.arizona.edu\/jcwyant\/miscellaneous\/neat-graphics\/\">&lt;&lt; Back to\u00a0Neat Graphics<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Notes List of Zernike Polynomials Notes on Zernike Polynomials (Vol. XI, Applied Optics and Optical Engineering) Notes on Zernike Polynomials (Mathematica Notebook) Eric Weisstein&#8217;s world of Mathematics Plots Two-Picture Stereograms n = 1 (Zernikes 1, 2, 3) n = 2 (Zernikes 4, 5, 6, 7, 8) n = 3 (Zernikes 9, 10, 11, 12, 13, 14, 15) n = 4<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1283,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-433","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/pages\/433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/comments?post=433"}],"version-history":[{"count":36,"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/pages\/433\/revisions"}],"predecessor-version":[{"id":1627,"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/pages\/433\/revisions\/1627"}],"up":[{"embeddable":true,"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/pages\/1283"}],"wp:attachment":[{"href":"https:\/\/wp.optics.arizona.edu\/jcwyant\/wp-json\/wp\/v2\/media?parent=433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}