An algorithm for the characterisation of multi-exponential decay curves

Abstract

An algorithm for the non-ambiguous reduction of multi-exponentially decaying luminescence signals to scalar lifetimes is described and characterised. Whereas this investigation stems from the research of thermographic phosphor thermometry, the technique can also be useful for the analysis of various other decay phenomena. Thermographic phosphors are activator-doped ceramics, whose phosphorescence decay characteristics depend on their temperature. Although the underlying energy transfer processes of the generally multi-exponential phosphorescence decay are not understood in detail, this property can be exploited for remote thermometry. Thereby, the temperature measurement is converted to the measurement of a phosphorescence lifetime evaluated by the approximation of a single-exponential term within a fitting window where mono-exponential decay characteristics prevail. In contrast to multi-exponential approaches, ambiguity due to the attribution of various exponential terms is eliminated provided that the fitting window is the same for the evaluation of all measurement data obtained at unknown temperatures and all temperature-referenced calibration data. In order to achieve this, an iterative algorithm was applied that selects a fitting window dependent on the decay waveform itself. This algorithm was characterised in detail using data detected for two different thermographic phosphors ( Mg 4 FGeO 6 : Mn and Y 2 O 3 : Eu ), at two different temperatures each. Compared to less elaborate routines applying a predefined fitting window depending on an ambiguous setting of the phosphorescence signal's detection length, the evaluation-induced systematic error of temperature determination could be reduced by a factor of 10 3 at similar precision.