Theoretical and experimental verification of wide-spectrum thermometry based on Taylor series de-integration method

In response to the challenges encountered in solving the integral equations and the disadvantages of requiring additional calibration parameters in the existing three-channel wide-spectrum temperature measurement, a wavelength-based Taylor series de-integration method is proposed. By combining the coefficient of determination, which characterizes the approximation effect, the selection criterion of characteristic wavelength (optimal expansion wavelength, OEW) is constructed. In the influence analysis of spectral emissivity on the de-integration method, the insensitivity of OEW to spectral emissivity is revealed. The feasibility of using blackbody OEW for de-integration processing is proved when the spectral emissivity is unknown, which provides necessary theoretical support for the selection of characteristic wavelengths in practical application. Based on this integration method, algebraic temperature measurement equations in the forms of graybody, three-channel fusion, and two-color are derived, and the theoretical errors of each form are discussed from both horizontal and longitudinal perspectives. Furthermore, thermometry experiments with multiple acquisition parameters and diverse samples were conducted corresponding to three solution forms, the universality of acquisition parameters and sample applicability are proven.