A precise Boltzmann distribution law for the fluorescence intensity ratio of two thermally coupled levels

Noncontact monitoring temperature is very important in modern medicine, science, and technologies. The fluorescence intensity ratio (FIR) technique based on the Boltzmann distribution law exhibits excellent application potential, but the observed FIR deviates from the Boltzmann distribution law in the low temperature range. We propose a fluorescence intensity ratio relation FIR∗ = ηFIR by introducing a quantity η representing thermal population degree, which can be obtained from measured fluorescence decay curves of the upper emitting level. Using Eu³⁺ as an example, the method is confirmed that the deviated FIR is able to be corrected and return to follow the Boltzmann law.