Sizing the depth and thickness of flat metallic inclusions using modulated photothermal radiometry

• We have calculated analytically the surface temperature of a sample with an inner inclusion. • A simple formula is obtained for thermal insulators containing metallic inclusions. • The thickness and the heat capacity of metallic inclusions are correlated. • For known thermal properties of matrix and inclusion, depth and thickness can be retrieved. • Modulated photothermal radiometry experiments on calibrated samples confirm the validity of the model. Photothermal radiometry (PTR) is based on exciting the sample surface optically and recording the resulting temperature rise by means of an infrared detector. It has been extensively used to detect and size the depth of flat buried defects parallel to the sample surface. Most of the works have dealt with delaminations, horizontal cracks filled by air. However, works dealing with the opposite configuration, i.e. a flat metallic inclusion inside a thermal insulating sample, are scarce. In this work we show the ability of PTR to evaluate quantitatively the depth and thickness of flat horizontal metallic inclusions embedded in insulators. The methodology involves fitting the calculated frequency dependent surface temperature to experimental amplitude and phase spectra. We have checked that both geometrical properties are not correlated, provided the thermal properties of the inclusion are known. Experiments on polymeric samples with calibrated metallic inclusions confirm the validity of the method.