Optimal thermometry theory of three-channel wide spectrum based on three-directional difference

The constant spectral emissivity decoupling method within current wide-spectrum thermometry theories stands as a primary factor contributing to accuracy degradation. This creates a deadlock in the current radiation thermometry framework, where the system's two-dimensional analytical capabilities and resolution accuracy cannot be concurrently achieved, becoming a major theoretical obstacle in the development of this technique. Consequently, based on the Taylor series de-integration method under the wide spectral framework, and taking the first and second derivative terms of spectral emissivity as the starting point, a wide spectral optimization temperature solution theory based on three-directional difference method is proposed. It ensures compatibility and stable solving conditions for imaging systems, while fundamentally removing the dependency on the constantization of spectral emissivity treatment, and realizing the decoupling and inversion of three-channel spectral emissivity. The handling effects of different cutoff precision differential methods on spectral emissivity derivatives are discussed, and the temperature and spectral emissivity solving capabilities of the method are theoretically validated under various spectral emissivity models. Furthermore, this method is used to monitor the continuous temperature rise processes of two different samples. Maximum average relative temperature calculation errors below 6% and 5% are achieved, and the target spectral emissivity variation rate and trend are well reproduced, yielding conclusions consistent with simulations.