Unambiguous calibration of power dependence in ratiometric luminescent nanothermometry through multiple intensity ratios and symbolic regression

Abstract

Ratiometric luminescence nanothermometry carries the potential to measure temperature in situations for which established methods are unsuitable. The precision of nanothermometry depends on the excitation power, so calibration and monitoring of the optical power is mandatory—a requirement that complicates optical setups and limits nanothermometry in scenarios where precise power control or measurement is impractical or unfeasible. Here, we use Er³⁺-activated nanothermometers and, besides the well-known 525/545 nm ratio, define a second luminescence intensity ratio involving the emission at 660 nm to achieve a power-calibration-free nanothermometry. The intensity of this emission is strongly correlated with the power and is available anyways when using standard spectroscopic instrumentation. We apply symbolic regression to find an unambiguous mathematical expression that describes the experimental data. From this mathematical expression, we determine the mean temperature deviation resulting from the fitting error to be 0.16 K and a maximum temperature precision as small as 6 mK (0.22 K on average). In summary, our approach makes excitation power measurements in ratiometric luminescent nanothermometry superfluous.