Continuous and Laplace transformable approximation for the temporal pulse shape of Xe-flash lamps for flash thermography

Flash thermography is widely used in non-destructive testing and material characterisation. The use of analytical modelling utilising the Laplace transform allows one to calculate the temperature transients of flash-heated samples and therefore characterise them by fitting of the results of model calculations to experimental data. However, for samples with high thermal diffusivity or very thin samples, the temperature transient is strongly influenced by the temporal shape of the heating pulse, especially in reflection configuration. To incorporate this into the model, the temporal shape of the heating pulse and its Laplace transform have to be known. Here we present a close phenomenological approximation of the temporal shape of pulses of Xe-flash lamps. It is a non-stitched solution, has a simple Laplace transform and is suitable for different lamps and energy settings. As an example for a practical application of the pulse shape approximation, we use it to determine the thickness of polymer samples with thicknesses down to 80 μm by means of flash thermography, both in transmission and reflection configuration. Using a rectangular pulse shape or a delayed Dirac pulse shape, the thickness results are very sensitive to the start time of the fit and an additional calibration is needed.