{"id":32578,"date":"2024-10-02T12:26:38","date_gmt":"2024-10-02T16:26:38","guid":{"rendered":"https:\/\/www.iridian.ca\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements\/"},"modified":"2024-10-02T12:26:40","modified_gmt":"2024-10-02T16:26:40","slug":"effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements","status":"publish","type":"post","link":"https:\/\/www.iridian.ca\/zh-hans\/cn-learning-center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements\/","title":{"rendered":"Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;4.16&#8243; custom_margin=&#8221;0px|0px||0px|false|true&#8221; custom_padding=&#8221;0px|0px||0px|false|true&#8221; da_disable_devices=&#8221;off|off|off&#8221; global_colors_info=&#8221;{}&#8221; da_is_popup=&#8221;off&#8221; da_exit_intent=&#8221;off&#8221; da_has_close=&#8221;on&#8221; da_alt_close=&#8221;off&#8221; da_dark_close=&#8221;off&#8221; da_not_modal=&#8221;on&#8221; da_is_singular=&#8221;off&#8221; da_with_loader=&#8221;off&#8221; da_has_shadow=&#8221;on&#8221;][et_pb_row _builder_version=&#8221;4.16&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; width=&#8221;100%&#8221; custom_margin=&#8221;0px|0px||0px|false|true&#8221; custom_padding=&#8221;0px|0px||0px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;4.27.0&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; custom_padding=&#8221;||10px||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p>Graham Carlow,* Brian T. Sullivan, Claude Montcalm, AND Alexander Miles<br \/><em>Iridian Spectral Technologies Ltd., 2700 Swansea Crescent, Ottawa, Ontario K1G 6R8, Canada<\/em><br \/><em>*Corresponding author: <a href=\"mailto:gcarlow@idexcorp.com\" data-linkindex=\"4\">gcarlow@idexcorp.com<\/a><\/em><\/p>\n<p>&nbsp;<\/p>\n<h4 id=\"Abstract\" class=\"article-heading\"><strong>Abstract<\/strong><\/h4>\n<p>The wavefront error (WE) of a surface with an optical coating (\u201cfilter\u201d) is ideally measured at the in-band wavelength of the filter. However, quite often this is not possible, requiring that the filter be measured at an out-of-band wavelength (typically 633 nm), assuming that the filter transmits (for transmitted WE, or TWE) or reflects (for reflected WE, or RWE) at this wavelength. This out-of-band TWE\/RWE is generally assumed to provide a good estimation of the desired in-band TWE\/RWE. It will be shown in this paper that this is not the case for a large class of filters (i.e., bandpass) where the group delay is significantly different at the in-band and out-of-band wavelengths and where the optical filter exhibits a thickness non-uniformity across the surface. A theoretical explanation will be given along with an approach to predict the in-band TWE\/RWE based on the coating non-uniformity, the measured out-of-band TWE\/RWE, and the theoretical properties of the optical filter at the in-band and out-of-band wavelengths. A reasonable agreement between theory and measurement was demonstrated by measuring the TWE of an 11 nm wide bandpass filter (centered at 1048 nm) at both in-band (lambda <span class=\"inline-formula\"><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BB;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;1048&lt;\/mn&gt;&lt;\/mrow&gt;&lt;mspace width=&quot;thickmathspace&quot; \/&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;n&lt;\/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;m&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mi\"><\/span><span id=\"MathJax-Span-4\" class=\"mo\">= <\/span><span id=\"MathJax-Span-5\" class=\"texatom\"><span id=\"MathJax-Span-6\" class=\"mrow\"><span id=\"MathJax-Span-7\" class=\"mn\">1048<\/span><\/span><\/span><span id=\"MathJax-Span-8\" class=\"mspace\"><\/span><span id=\"MathJax-Span-9\" class=\"texatom\"><span id=\"MathJax-Span-10\" class=\"mrow\"><span id=\"MathJax-Span-11\" class=\"mi\">n<\/span><span id=\"MathJax-Span-12\" class=\"mi\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) and out-of-band (lambda <span class=\"inline-formula\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BB;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;625&lt;\/mn&gt;&lt;\/mrow&gt;&lt;mspace width=&quot;thickmathspace&quot; \/&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;n&lt;\/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;m&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-13\" class=\"math\"><span id=\"MathJax-Span-14\" class=\"mrow\"><span id=\"MathJax-Span-15\" class=\"mi\"><\/span><span id=\"MathJax-Span-16\" class=\"mo\">= <\/span><span id=\"MathJax-Span-17\" class=\"texatom\"><span id=\"MathJax-Span-18\" class=\"mrow\"><span id=\"MathJax-Span-19\" class=\"mn\">625<\/span><\/span><\/span><span id=\"MathJax-Span-20\" class=\"mspace\"><\/span><span id=\"MathJax-Span-21\" class=\"texatom\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mi\">n<\/span><span id=\"MathJax-Span-24\" class=\"mi\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) wavelengths. A similar treatment is provided for RWE.<\/p>\n<p>\u00a9 2020 Optical Society of America<\/p>\n<p>&nbsp;<\/p>\n<p>[\/et_pb_text][et_pb_button button_url=&#8221;https:\/\/www.osapublishing.org\/ao\/abstract.cfm?uri=ao-59-5-A135&#8243; url_new_window=&#8221;on&#8221; button_text=&#8221;Full Article&#8221; _builder_version=&#8221;4.16&#8243; custom_margin=&#8221;||50px||false|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_button][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The wavefront error (WE) of a surface with an optical coating (\u201cfilter\u201d) is ideally measured at the in-band wavelength of the filter. However, quite often this is not possible, requiring that the filter be measured at an out-of-band wavelength (typically 633\u00a0nm), assuming that the filter transmits (for transmitted WE, or TWE) or reflects (for reflected WE, or RWE) at this wavelength. This out-of-band TWE\/RWE is generally assumed to provide a good estimation of the desired in-band TWE\/RWE. It will be shown in this paper that this is not the case for a large class of filters (i.e., bandpass) where the group delay is significantly different at the in-band and out-of-band wavelengths and where the optical filter exhibits a thickness non-uniformity across the surface. <\/p>\n","protected":false},"author":159,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[2234,2230],"tags":[],"class_list":["post-32578","post","type-post","status-publish","format-standard","hentry","category-cn-technical-notes","category-cn-learning-center"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.0) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Effect optical coating on in-band and out-of-band WE<\/title>\n<meta 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