{"id":17626,"date":"2021-04-13T23:33:38","date_gmt":"2021-04-14T03:33:38","guid":{"rendered":"https:\/\/iridian.jp\/?page_id=17626"},"modified":"2021-09-27T14:57:42","modified_gmt":"2021-09-27T18:57:42","slug":"effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup","status":"publish","type":"post","link":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/","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;4.9.4&#8243; hover_enabled=&#8221;0&#8243; custom_margin=&#8221;0px|0px||0px|false|true&#8221; custom_padding=&#8221;0px|0px||0px|false|true&#8221; sticky_enabled=&#8221;0&#8243;][et_pb_row _builder_version=&#8221;4.9.4&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; hover_enabled=&#8221;0&#8243; width=&#8221;100%&#8221; custom_margin=&#8221;0px|0px||0px|false|true&#8221; custom_padding=&#8221;0px|0px||0px|false|true&#8221; sticky_enabled=&#8221;0&#8243;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;3.25&#8243; custom_padding=&#8221;|||&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;4.9.4&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; custom_padding=&#8221;||10px||false|false&#8221; hover_enabled=&#8221;0&#8243; sticky_enabled=&#8221;0&#8243;]<\/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: gcarlow@idexcorp.com<\/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;4.2.2&#8243; custom_margin=&#8221;||50px||false|false&#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":"<h2 id=\"Abstract\" class=\"article-heading\">Abstract<\/h2><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. 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\u00a0nm wide bandpass filter (centered at 1048\u00a0nm) at both in-band (<span class=\"inline-formula\"><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\" role=\"presentation\" data-mathml=\"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mrow class=\"MJX-TeXAtom-ORD\"><mn>1048<\/mn><\/mrow><mspace width=\"thickmathspace\" \/><mrow class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math>\"><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 (<span class=\"inline-formula\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\" role=\"presentation\" data-mathml=\"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mrow class=\"MJX-TeXAtom-ORD\"><mn>625<\/mn><\/mrow><mspace width=\"thickmathspace\" \/><mrow class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math>\"><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><p>\u00a9 2020 Optical Society of America<\/p><p>\u00a0<\/p>","_et_gb_content_width":"","footnotes":""},"categories":[2205,2211],"tags":[],"class_list":["post-17626","post","type-post","status-publish","format-standard","hentry","category-learning_center","category-tech_notes"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v23.7 (Yoast SEO v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements - Iridian Spectral Technologies<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements\" \/>\n<meta property=\"og:description\" content=\"The wavefront error (WE) of a surface with an optical coating (\u201cfilter\u201d) is ideally measured at the in-band wavelength of the filter. 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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.","og_url":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/","og_site_name":"Iridian Spectral Technologies","article_published_time":"2021-04-14T03:33:38+00:00","article_modified_time":"2021-09-27T18:57:42+00:00","author":"Jeremy Liu","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Jeremy Liu","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/#article","isPartOf":{"@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/"},"author":{"name":"Jeremy Liu","@id":"https:\/\/iridian.jp\/en\/#\/schema\/person\/fb22ca7f20b82edc2caa1ca0d153e72b"},"headline":"Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements","datePublished":"2021-04-14T03:33:38+00:00","dateModified":"2021-09-27T18:57:42+00:00","mainEntityOfPage":{"@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/"},"wordCount":396,"articleSection":["Learning Center","Technical Notes"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/","url":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/","name":"Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements - Iridian Spectral Technologies","isPartOf":{"@id":"https:\/\/iridian.jp\/en\/#website"},"datePublished":"2021-04-14T03:33:38+00:00","dateModified":"2021-09-27T18:57:42+00:00","author":{"@id":"https:\/\/iridian.jp\/en\/#\/schema\/person\/fb22ca7f20b82edc2caa1ca0d153e72b"},"breadcrumb":{"@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/iridian.jp\/en\/learning_center\/effect-of-an-optical-coating-on-in-band-and-out-of-band-transmitted-and-reflected-wavefront-error-measurements-dup\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/iridian.jp\/en\/"},{"@type":"ListItem","position":2,"name":"Learning Center","item":"https:\/\/iridian.jp\/en\/technical-resources\/"},{"@type":"ListItem","position":3,"name":"Articles &#8211; 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