A Thermopile-Based Colorimetric Temperature Measurement Method for Arbitrary Bandwidth

Colorimetric temperature measurement is an essential technique in radiometric thermometry. Traditional colorimetric methods determine temperature by comparing the ratio of radiative energies within two narrow bands at specific wavelengths, effectively mitigating the effects of the emissivity of the measured object and ambient conditions. However, these methods typically approximate integration using area calculations when calculating radiative energy. This article eliminates this approximation and calculates the radiative energy with accurate integration. Based on the principle of monotonicity, this article demonstrates for the first time that when two narrow-band infrared radiations are selected, as long as their wavelength ranges do not overlap, the ratio of radiative energies within these bands maintains a monotonic relationship with the measured temperature. This allows the temperature to be inferred from the energy ratio. Furthermore, this conclusion is extended to arbitrary widths of bands as long as their wavelength ranges do not overlap. Building on this foundation, a thermopile-based colorimetric temperature measurement method for arbitrary bandwidth is proposed. Simulation experiments validate this method, showing that the energy ratio maintains a monotonic relationship with the measured temperature as long as the infrared radiation wavelength ranges absorbed by the thermopile do not overlap. The simulation results are consistent with the mathematical proof.