Virtual Wave Concept for thermographic parameter estimation using modulated laser excitation

In this work, the Virtual Wave Concept (VWC) is applied on measurement data from laser-excited thermography. Therefore, a virtual temperature signal is calculated by applying a local transformation to the temperature data. This transformation is a linear inverse problem and can be formulated as a Fredholm integral of the first kind. Since the problem is severely ill-posed, the “Alternating Direction Method of Multipliers” (ADMM) is used for regularization to get an appropriate solution for the virtual temperature. The propagation of the virtual temperature can be described by the wave equation, whereby for the parameter estimation ultrasonic test methods can be used, e.g. pulse-echo method for time-of-flight measurements. So, after the local transformation the active thermography data can be shown in form of a virtual A-Scan, which is well known from ultrasonic testing. The time-of-flight determined from the virtual temperature is directly related to the thermal diffusion time. Therefore, if the specimen thickness is known, the effective thermal diffusivity can be derived from the virtual back wall echo. For this purpose, the main advantage of the Virtual Wave Concept is the possibility to use the same data processing method for measurements in reflection as well as in transmission configuration.
Laser-excited thermography experiments are carried out on carbon fiber reinforced plastics (CFRP). The measurement of the thermal diffusion time with the VWC allows a thickness estimation of a step wedge sample as well as a porosity estimation of different test coupons. The first study on the step wedge allows a statement on the measurement uncertainty of the VWC. In a second step, the measured diffusion time is used for an effective-medium-model based porosity estimation on a range of different calibrated porous CFRP specimens with different number of plies and varying porosity contents. Porosity values derived by thermographic reconstruction are validated with X-ray computed tomography.