Improving the temperature uncertainty of ${\text{Mg}}_{4} {\text{FGeO}}_{6} {\text{:Mn}}^{{4 + }}$ ratio-based phosphor thermometry by using a multi-objective optimization procedure

Abstract

Surface phosphor thermometry is an attractive remote temperature diagnostic to study heat and mass transfer processes. The spectral intensity ratio method enables to obtain two-dimensional temperature measurements with good spatial resolution, but suffers from sources of uncertainties that limit its use in terms of temperature uncertainties. This study aims to evaluate the improvement of the temperature uncertainty of the Mg₄FGeO₆:Mn⁴⁺ ratio-based phosphor thermometry when selecting different optical filters for the detection. This selection is done with the use of a numerical optimization procedure and multiple objective functions. Assuming a shot-noise limited regime for the phosphorescence signals, a series of experimental phosphorescence spectra recorded at various temperatures are combined with different virtual optical filters in order to minimize the relative temperature uncertainty as well as its standard deviation on the 300–750 K temperature range. The best combination of optical filters is composed of a filter centered on the 660 nm emission band, the other one being shifted towards the red wing. A further analysis indicates that the relative sensitivity is favored while the signal-to-ratios are fairly constant. A parametric study on the impact of the multi-objective function as well as the extent of the explored temperature range highlights that the mean temperature uncertainty criterion mainly drives the optimization procedure, notably with a weighting given to high-temperature spectral properties. Finally, a realistic temperature imaging arrangement composed of an ICCD camera, an image doubler and commercial bandpass filters, validates this new strategy. The relative temperature uncertainty is $\approx 2.9\,\%$ between 300 and 750 K offering enhanced performances (up to three times) when compared to usual optical filters reported in the literature and centered on the two main emission bands.