Analytical Solutions in the Framework of Brightness and Color Spectral Pyrometry Methods

The article provides an analytical solution to the problem of pyrometric determination of the actual surface temperature T(K) by calculating its value from a system of three equations, including the results of three measurements of the brightness temperature TS (λі), which were obtained at three wave length sof the spectrum: λ1<λ2<λ3 with unknown emissivity e1, e2 and e3, in the framework of the two main methods of spectral pyrometry according to the patents of Ukraine No.73231 (color) and No.82870 (brightness). It is shown in the article that exact analytical solutions are possible only in cases when the nature of the dispersion of the selective surface e=f(λ) (for example, linear, logarithmic, etc.) is known apriori, which, together with the equation of coupling e2 = F(e1, e3), allows us to determine the exact value of the intermediate (effective) length λ2 waves based on the extreme (or basic) values of λ1 and λ3. The arithmetic mean (for the color method) and the proportional mean (for the brightness method) are use dascoupling equations.