A multi-spectral temperature measurement method based on color temperature difference

Accurate temperature measurement is pivotal in manufacturing, industrial modernization, and scientific research. This study proposes a multi-spectral thermometry method based on the gray body hypothesis and color temperature difference. The methodology involves selecting a target pixel and any other pixel and measuring their gray value with a multi-spectral thermometer. For an n-channel thermometer, 2n equations can be derived from Wien's displacement law. Subtracting these equations yields additional n equations, forming a system of 3n equations. These equations are solved via least squares fitting to determine the color temperature and gray body emissivity of both pixels. By establishing the relationship between gray body emissivity and channel-specific emissivity under the gray body approximation, the variance between theoretical and measured emissivity is calculated. The target pixel is combined with other pixels for calculation, and the resulting variances are compared. The temperature and emissivity of the target pixel are determined when the variance is minimized. If the variance meets the measurement error requirements, the corresponding result is regarded as the true temperature. This approach reduces the required number of spectral channels, circumvents overcomplicated emissivity models induced by wide spectral ranges, and enhances measurement accuracy (error <1%) while improving experimental efficiency. The method's validity is demonstrated through gas discharge temperature measurements, with results cross-verified against rotational temperature data, confirming its applicability in practical scenarios.