## 5 Experiments and Results  
In this section we present fittings of experimental data obtained with an inductive thermography set-up on samples containing calibrated metallic inclusions. We have prepared 3D printed photopolymer resin (PR48) samples, whose thermal conductivity and diffusivity are \(K=0.5\) W/mK and \(D=1.3\cdot 10^{-7}\) m\({}^{2}\)/s respectively, with embedded thin Cu slabs. The dimensions of the resin samples are \(2.5\times 2.5\times 1\) cm. During 3D printing, the process is stopped, a Cu slab is placed on the hot resin, and printing is resumed. The Cu films are 25 \(\upmu\)m thick. We have prepared three samples containing Cu films of different lateral dimensions, depths, and inclinations with the surface. The specific values of \(w\), \(h\), \(d\), and \(\varphi\) are listed in Table 1. We put the sample inside an 8 cm diameter coil, with the Cu slab oriented mostly perpendicular to the coil axis. This way, when the coil is fed with an AC current, Eddy currents flow in closed paths within the Cu slab plane, which is heated by the Joule effect, producing a geometrically calibrated heat source. The high conductivity of Cu ensures a fast thermalization of the film, even if the current density is not perfectly homogeneous. The excitation power and frequency are 11 kW and 120 kHz, respectively. The IR radiation coming from the sample surface is collected by an IR video camera equipped with a \(320\times 256\) pixel detector, sensitive in the 3.5-5 \(\upmu\)m range, and with a noise equivalent temperature difference (NETD) of 25 mK. The camera is operated at 100 frames per second and integration time of 4 ms. It was shielded to prevent damage from the AC current in the coil. Although the resin is opaque in the detection range of the camera, the surface where the temperature is measured is covered with a thin layer of graphite paint to improve IR emissivity. Figure 11 shows pictures of the coil with the sample in place for Cu slabs making angles with the surface \(\varphi<45^{\circ}\) (Figure 11a) and \(\varphi>45^{\circ}\) (Figure 11b). Figure 10: Estimated values of the fitting parameters and standard deviations as a function of the angle: (**a**) width \(w\), (**b**) height \(h\), (**c**) depth \(d\), and (**d**) angle \(\varphi\), corresponding to a square heat source (\(w=h=1\) mm), buried \(d=0.5\) mm, excited with a \(\tau=5\) s burst. SNR in the data is 60. The continuous line represents the true value of each parameter. In Figure 12, we show in symbols experimental \(T(x,0,0,\tau)\), \(T(0,y,0,\tau)\) and \(T(0,0,0,t)\) obtained at the end of a \(\tau=2\) s burst, corresponding to sample 1, where a Cu slab of dimensions \(w=h=2.1\) mm, making an angle of \(\varphi=60^{\circ}\) with the surface is buried at \(d=0.4\) mm. The spatial resolution is 0.175 mm/pixel. The solid lines are the best fittings of Equation (10) (Figure 12a,b) and Equations (10) and (11) (Figure 12c) to the data. The values of the best fit parameters are \(w_{f}=2.3\) mm, \(h_{f}=1.2\) mm, \(d_{f}=0.38\) mm and \(\varphi=75^{\circ}\). As expected, the parameter with the worst estimation is the height of the heat source, but the rest of the retrieved parameters are in good agreement with the true values: the retrieved width is off by 10%, the angle by 9\({}^{\circ}\), and the depth only by 0.5%. In Table 1 we summarize the real and fitted parameters corresponding to the three samples we prepared, with Cu slabs making angles of 0\({}^{\circ}\), 30\({}^{\circ}\), and 60\({}^{\circ}\) with the surface. In all cases the duration of the excitation was \(\tau=2\) s. We do not have an independent calibration of the emitted flux, but we record the values of the current feeding the coil in each experiment. The results point at the difficulty of identifying the height of the heat source, especially for heat sources close to the vertical. However, the width and depth can be assessed with an accuracy of about 10%, in experimental data.