# Uncertainty of Temperature Sensitive Paint

7.5.1. Error Propagation and Limiting Temperature Resolution

In principle, the above uncertainty analysis for PSP can be adapted for TSP since many error sources of TSP are the same as those of PSP. For simplicity, instead of the general Arrhenius relation, we use an empirical relation between the luminescent intensity (or the photodetector output) and temperature T for a TSP uncertainty analysis (Cattafesta and Moore 1995; Cattafesta et al. 1998)

T -Tref = Kt ln( Iref /I) = KT ln(U2 Vf /V), (7.25)

where KT is a TSP calibration constant with a temperature unit and U 2 is the factor defined previously in Eq. (7.2) for the PSP uncertainty analysis. Without model deformation and temporal illumination variation, the factor U 2 equals to one. Eq. (7.25) can be used to fit TSP calibration data over a certain range of temperature. The error propagation equation for TSP is

var(T) = KT у var( <Tt) + var( Kt )

(T – TKf)2 (T – Tref )2 i=f kK, (. )

where the variables (С,,1 = M} denote a set of the parameters Dt(At),

where (npere/ )max is the full-well capacity of a CCD camera in the reference conditions. The minimum resolvable temperature difference (AT)min is inversely proportional to the square-root of the number of collected photoelectrons, and approximately proportional to the calibration constant KT. When (npere/ )max is

500,0 electrons, for a typical Ruthenium-based TSP having KT = 37.7oC, the minimum resolvable temperature difference (AT)min is shown in Fig. 7.21 as a function of T at a reference temperature Tre/ = 20oC. When N images are averaged, the limiting temperature resolution given by Eq. (5.27) should be

divided by a factor N1/2.