Temperature and emissivity measurement algorithm using a moving emissivity retardation spectral window method based on Lagrange mean value theorem

The multi-spectral radiation method is a non-contact technique that can measure the temperature and emissivity of an object. However, its core problem lies in solving the underdetermined equation system. Existing numerical emissivity methods require prior knowledge of emissivity, while emissivity function methods need accurate initial conditions. These approaches are not suitable for measuring unknown targets’ temperature and emissivity. This paper proposes a moving emissivity retardation spectral window method that does not require any prior knowledge or initial conditions. The proposed method defines the emissivity retardation interval based on the Lagrange mean value theorem to provide universal and high-precision constraint conditions for solving the aforementioned underdetermined equation system. Simulation experiments were conducted on four target models with different emissivity, which showed that, compared to the moving narrowband window method, this new, to the best of our knowldge, approach reduced average temperature calculation errors by 31.0% and average emissivity calculation errors by 30.7%. In blackbody experiments, the calculated temperature error is about 0.4 K, and the emissivity is about 0.993–0.999. The described method is expected to meet the practical measurement needs for a wide range of substances.