“…According to Boltzmann theory, the fluorescence intensity ratios ( FIR ) of 538 nm and 546 nm generated by the thermal coupling energy levels of Ho 3+ for the transition from ( 5 F 4 , 5 S 2 ) to 5 I 8 are as follows: 18,19
Δ E denotes the energy level difference between the two energy levels of 5 F 4 and 5 S 2 , k B is Boltzmann's constant, A is a constant, and T is the absolute temperature. The experimental results deviate from the Boltzmann equation predictions due to the effect of closely spaced energy levels causing overlapping of the emitted light and stray light from other energy levels or excitation sources; thus, the Boltzmann equation needs to be corrected as follows:
where B is the correction factor.…”