Uncertainty budget of temperature measurement by the methods of monochromatic one- and two-color thermometry with emissivity correction

Abstract

The work is directed on accuracy increasing of the thermodynamic temperature measurement of heated objects by their own thermal radiation, utilizing no more than two monochromatic channels for the spectral density of radiance measurement. The classification of the methods of one- and two-color thermometry with emissivity correction have been proposed. It has been determined that these methods are based on generalized measurement equation originated from the spectral density of radiance approximation by the Wien’s formula. Temperature measurement equations have been reformulated basing on the set of common input quantities. This set includes conditional one-color (radiance) temperatures, wavelengths and correction parameters, that account for spectral emissivity of controlled object. The number of input quantities for one-color methods is 4, and for the most part of twocolor methods – 6. Taking into consideration the specific of hardware realization of thermometry system (microspectrometer with multielement CCD-sensor of radiation), uncertainty components of input quantities have been researched and systematized, as well as the formulas for input quantities uncertainties evaluation basing on these components have been obtained. The uncertainty budget of indirect temperature measurement by the methods of monochromatic one- and two-color thermometry has been formed on the base of the input quantities set. The formulae for evaluation of combined standard and expanded, with confidence level 0.95, uncertainties of temperature measurement result have been obtained. They account for the possible correlation between correction parameters. For expanded uncertainty evaluation the kurtosis method has been utilized. It has been shown, that under conditions of the same uncertainties of input quantities, the accuracy of thermometry methods depends on the corresponding sensitivity coefficients only. The necessity of obtaining analytical expressions for sensitivity coefficients have been argued. This will allow analyzing the complex influence of input quantities uncertainties on temperature measurement accuracy by investigated thermometry methods, in order to determine the method, which demonstrates minimal possible uncertainty under specified measurement conditions.