{"id":51469,"date":"2026-03-26T16:05:14","date_gmt":"2026-03-26T16:05:14","guid":{"rendered":"https:\/\/www.bright-science.com\/2026\/03\/26\/application-of-monte-carlo-method-for-uncertainty-evaluation-in-photometric-measurements-using-type-c-goniophotometers\/"},"modified":"2026-06-16T15:16:37","modified_gmt":"2026-06-16T15:16:37","slug":"application-of-monte-carlo-method-for-uncertainty-evaluation-in-photometric-measurements-using-type-c-goniophotometers","status":"publish","type":"post","link":"https:\/\/www.bright-science.com\/en\/application-of-monte-carlo-method-for-uncertainty-evaluation-in-photometric-measurements-using-type-c-goniophotometers\/","title":{"rendered":"&#8220;Application of Monte Carlo method for uncertainty evaluation in photometric measurements using type C goniophotometers&#8221;"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><p>[vc_row type=&#8221;vc_default&#8221; margin_top=&#8221;0&#8243; margin_bottom=&#8221;5&#8243;][vc_column][vc_column_text css=&#8221;&#8221;]<\/p>\n<h3>Scientific paper submitted and accepted by the &#8220;Journal of Optics&#8221; in February 2026, as part of the final internship project of the Master&#8217;s in Applied Mathematics for Industry at ISEL.<\/h3>\n<p>The study evaluates the Monte Carlo method (MCM) for uncertainty propagation in photometric measurements using Type C goniophotometers, comparing it with the sum-of-squares method. Three MCM models were tested: one based on Type A\/B classifications, another on Shannon\u2019s information theory, and a third using random distributions. Sensitivity analysis (Pareto) identified key variables. The results showed lower uncertainties with the MCM (up to 2.3%) compared to the traditional method (3.4%). It is concluded that the MCM improves accuracy, with the Shannon model being the most efficient.<\/p>\n<p><strong>Authors of the article:<\/strong> Pedro B. Nogueira, Andr\u00e9 Carvalho, and Jos\u00e9 A. Rodrigues of ISEL, and Jo\u00e3o Ribeiro and Thomas Langhof of Bright Science.[\/vc_column_text]<style type=\"text\/css\" data-type=\"the7_shortcodes-inline-css\">#default-btn-ea2ae62737f538ce73b65f238c02f913.ico-right-side > i {\n  margin-right: 0px;\n  margin-left: 8px;\n}\n#default-btn-ea2ae62737f538ce73b65f238c02f913 > i {\n  margin-right: 8px;\n}<\/style><a href=\"\/wp-content\/uploads\/2016\/09\/Bright_Science-Artigos-MMC.pdf\" class=\"default-btn-shortcode dt-btn dt-btn-m link-hover-off ico-right-side btn-inline-left  vc_custom_1781622991280\" target=\"_blank\" id=\"default-btn-ea2ae62737f538ce73b65f238c02f913\" rel=\"noopener\"><span>Read the article<\/span><i class=\"Defaults-file-pdf-o\"><\/i><\/a>[vc_column_text css=&#8221;&#8221;]Also available in <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s12596-026-03088-0\" target=\"_blank\" rel=\"noopener\">Journal of Optics<\/a>.[\/vc_column_text][vc_row_inner css=&#8221;.vc_custom_1474099857231{padding-top: 30px !important;padding-bottom: 30px !important;}&#8221;][vc_column_inner width=&#8221;2\/3&#8243; offset=&#8221;vc_col-lg-offset-2 vc_col-lg-8 vc_col-md-offset-2 vc_col-md-8 vc_col-sm-offset-2&#8243;]<div class=\"hr-thin style-line accent-border-color\" style=\"width: 100%;border-top-width: 3px;\"><\/div>[vc_column_text css=&#8221;.vc_custom_1780502422942{padding-top: 20px !important;padding-bottom: 20px !important;}&#8221;]<\/p>\n<h5 style=\"text-align: center;\"><strong>ABSTRACT:<\/strong><\/h5>\n<h5 style=\"text-align: center;\">\u201cThe Monte Carlo Method is a powerful statistical technique for propagating uncertainty in photometric measurements, particularly when models are nonlinear or input variables deviate from Gaussian distributions. This study explores the application of MCM to luminous flux measurements using Type C goniophotometers, with comparisons to the conventional Root Sum of Squares Method. Three distinct Monte Carlo models were implemented. The first classified uncertainties as Type A or Type B, assigning corresponding probability distributions. The second employed Shannon information<br \/>\ntheory to derive distributions based on available knowledge, while the third exploratory model randomized distribution selection among normal, uniform, and triangular forms. Sensitivity analysis, guided by the Pareto principle, identified the key variables contributing to 80% of overall variability. Results showed that Root Sum of Squares Method yielded an expanded uncertainty of 3.4%, whereas the first, second, and third Monte Carlo models achieved 3.0%, 2.5%, and 2.3%, respectively. Importantly, the Pareto-based reduction strategy preserved accuracy while lowering computational complexity. These findings demonstrate that Monte Carlo Method provides a more effective framework for uncertainty evaluation in photometry than traditional approaches, with the information theory-based model offering the best balance between accuracy and efficiency. The proposed methodology enhances the reliability of luminaire characterization and supports practical adoption in industrial measurement contexts.\u201d<\/h5>\n<p>[\/vc_column_text]<div class=\"hr-thin style-line accent-border-color\" style=\"width: 100%;border-top-width: 3px;\"><\/div>[\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row]<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Scientific article submitted to and accepted for publication in the Journal of Optics in February 2026, as part of the internship for the Master&#8217;s degree in Applied Mathematics for Industry at ISEL.<\/p>\n","protected":false},"author":9,"featured_media":51400,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[115],"tags":[132,134,133,135],"class_list":["post-51469","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-papers","tag-luminous-flux","tag-monte-carlo-method","tag-photometry","tag-propagation-of-uncertainty","category-115","description-off"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>&quot;Application of Monte Carlo method for uncertainty evaluation in photometric measurements using type C goniophotometers&quot;<\/title>\n<meta name=\"description\" content=\"Scientific article submitted to and accepted for publication in the Journal of Optics as part of the internship for the Master&#039;s degree in Applied Mathematics for Industry at ISEL.\" 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