High temperature measurements based on unknown spectral emissivity using a joint two-color and three-color pyrometry method

Abstract

This study addresses high-precision and high-stability measurements at rapid high temperatures in specialized industries such as aerospace engineering, metal welding, and metallurgy. Starting from blackbody furnace calibration under the gray-body assumption, we derive an explicit colorimetric pyrometry formula. To extend its applicability beyond gray-body materials, we introduce a calibration framework that accounts for unknown spectral emissivity through constrained optimization. We propose a dynamic selection methodology based on the sensitivity of the pyrometry formula to temperature fluctuations, which effectively reduces the subjectivity inherent in traditional pyrometry formula selection and significantly enhances the stability of temperature measurements. Furthermore, we have systematically analyzed the interrelationships between spectral emissivity, colorimetric temperature, true temperature, and calibrated radiant temperature. The proposed algorithm transforms these interrelationships into a multi-constraint optimization problem, ensuring a comprehensive and precise calibration process. It utilizes a generalized inverse to derive optimized initial values, which serve as a foundation for subsequent refinements during calibration. The algorithm incorporates a simulated annealing technique to iteratively improve the estimates of the unknown spectral emissivity. This strategy effectively explores the solution space, thereby increasing the accuracy of the final emissivity estimates and enabling accurate temperature estimation for high-temperature materials within the range of 1000–2000 °C. We conducted a large-scale experimental study, acquiring 1168 high temperature radiation images across the specified temperature range. The experimental results indicate that in three out of the four data sets, the absolute error was consistently maintained within 10 °C, with a relative error of 1%. The average absolute error across all four experimental groups remained within 5 °C, with an average relative error of 0.5%, demonstrating a significant enhancement in both accuracy and stability of the measurements.