{"id":142,"date":"2024-04-10T16:28:27","date_gmt":"2024-04-10T14:28:27","guid":{"rendered":"https:\/\/logbooks.ifosim.org\/oscar\/?p=142"},"modified":"2024-04-10T16:34:14","modified_gmt":"2024-04-10T14:34:14","slug":"astigmatic-surface-generation","status":"publish","type":"post","link":"https:\/\/logbooks.ifosim.org\/oscar\/2024\/04\/10\/astigmatic-surface-generation\/","title":{"rendered":"Astigmatic surface generation"},"content":{"rendered":"\n

While in OSCAR, the function Add_Astigmatism() <\/em>can add an extra sagitta distortion with a Zernike polynomial over a certain diameter, it is not always practical. Sometimes, it is simpler to define a surface with two perpendicular radii of curvature R_x and R_Y.<\/p>\n\n\n\n

The solution described here was given to me by Jean-Yves Vinet (a big thank from all the OSCAR users). A 3D ellipsoid in a general manner could be defined as the surface following this equation:<\/p>\n\n\n\n

\\frac{x^2}{a^2} + \\frac{y}{b^2} + \\frac{z^2}{R^2} = 1<\/div>\n\n\n\n

Isolating the z coordinate, the above equation could be written as:<\/p>\n\n\n\n

z = \\pm R \\sqrt{1 – \\frac{x^2}{a^2} – \\frac{y^2}{b^2} }<\/div>\n\n\n\n

For a surface tangential to the plan z = 0, we take:<\/p>\n\n\n\n

z = R – R \\sqrt{1 – \\frac{x^2}{a^2} – \\frac{y^2}{b^2} }<\/div>\n\n\n\n

In case of astigmatic mirror with R_x and R_y, we can set:<\/p>\n\n\n\n

R = \\frac{1}{2}(R_x + R_y), a^2 = R R_x, b^2 = R R_y<\/div>\n","protected":false},"excerpt":{"rendered":"

While in OSCAR, the function Add_Astigmatism() can add an extra sagitta distortion with a Zernike polynomial over a certain diameter, it is not always practical. Sometimes, it is simpler to define a surface with two perpendicular radii of curvature R_x and R_Y. The solution described here was given to me by Jean-Yves Vinet (a big […]<\/p>\n","protected":false},"author":67,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ssl_alp_hide_revisions":false,"footnotes":"","ssl_alp_hide_crossreferences_to":false},"categories":[25],"tags":[19],"ssl-alp-inventory-item":[],"ssl-alp-coauthor":[12],"class_list":["post-142","post","type-post","status-publish","format-standard","hentry","category-simulations","tag-howto","ssl-alp-unread-flag-ssl-alp-unread-flag-aaron-jonesligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-agreennikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-alexander-adamligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-andreas-freiseligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-anna-greenligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-antoine-amyligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-bas-swinkelsligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-camilla-derossiligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-catalina-ana-miritesculigo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-daniela-pascucciligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-davidgnikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-eleonora-capocasaligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-enzo-tapialigo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-hiro-yamamotoligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-jacques-dingligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-jonathan-perryligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-jperrynikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-kevin-kunsligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-maddalena-mantovaniligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-michele-valentiniligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-mischa-salleligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-mkolknikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-monica-seglar-arroyoligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-msalle","ssl-alp-unread-flag-ssl-alp-unread-flag-mvalentinikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-p70081609unimaas-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-paul-stevensligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-paulvalentin-hapkeligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-riccardo-maggioreligo-org","ssl-alp-unread-flag-ssl-alp-unread-flag-sebastslnikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-stopic","ssl-alp-unread-flag-ssl-alp-unread-flag-tschoonnikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-yuefangnikhef-nl","ssl-alp-unread-flag-ssl-alp-unread-flag-yuhang-zhao1ligo-org"],"_links":{"self":[{"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/posts\/142","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/users\/67"}],"replies":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/comments?post=142"}],"version-history":[{"count":2,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/posts\/142\/revisions"}],"predecessor-version":[{"id":144,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/posts\/142\/revisions\/144"}],"wp:attachment":[{"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/media?parent=142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/categories?post=142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/tags?post=142"},{"taxonomy":"ssl-alp-inventory-item","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/ssl-alp-inventory-item?post=142"},{"taxonomy":"ssl-alp-coauthor","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/oscar\/wp-json\/wp\/v2\/ssl-alp-coauthor?post=142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}