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<p>The 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 theory 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(80 \%\)</EquationSource> </InlineEquation> of overall variability. Results showed that Root Sum of Squares Method yielded an expanded uncertainty of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(3.4\%\)</EquationSource> </InlineEquation>, whereas the first, second, and third Monte Carlo models achieved <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(3.0 \%\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2.5\%\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(2.3\%\)</EquationSource> </InlineEquation>, 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.</p>

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Application of Monte Carlo method for uncertainty evaluation in photometric measurements using type C goniophotometers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月26日

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  • Pedro B. Nogueira,
  • André Carvalho,
  • João Ribeiro,
  • José A. Rodrigues,
  • Thomas Langhof

摘要

The 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 theory 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.