<title>Uncertainty and confidence intervals in optical design using the Monte Carlo ray-trace method</title>

Abstract

The increasing use of probablistic methods, such as the Monte Carlo ray-trace (MCRT) method, in thermal radiation and optical modeling, has created a general awareness in the community of the need for a protocol to predict, to a specified level of confidence, the uncertainty of the results obtained using these methods. This paper presents such a protocol applied to models of radiometric channels used in spaced-based earth observations. It is anticipated that the same protocol, with suitable modification, may be extended to data from actual instruments. The authors and their colleagues have developed a powerful generic MCRT-based computational environment that, among other features, is capable of simulating radiative exchange among surfaces and within enclosures. As in any MCRT thermal-radiative/optical model, the spatial resolution and accuracy of the results obtained depend on the fineness of the mesh, the number of rays traced, and the accuracy of directional and spectral surface property models. The protocol presented in this paper identifies and quantifies the contribution of these factors to the ultimate uncertainty in predicted results and to their related confidence intervals.

The Past and Future of the Monte Carlo Method in Thermal Radiation Transfer

“…The statistical error that contaminates the estimates can also introduce numerical instabilities, e.g., when calculating the radiant source term in mixed mode heat transfer problems [68] and determining sensitivities during shape optimization [69][70][71]. However, recent developments focused on reducing the variance of the MC estimates [38,[72][73][74][75][76][77][78][79][80][81][82][83], combined with radical improvements in computing power (e.g., multithreaded cores, GPUs) are dissolving these barriers.…”