## 3 Sensitivity
As an example, in Figure 6b we show the sensitivities for \(\tau=0.5\) s corresponding to a thermal diffusion length of \(\mu_{\tau}=0.51\) mm, just coinciding with the depth of the upper side of the square. In this case, the maximum to minimum sensitivity relationship is of the order of 100/1. This points at the benefit of using long enough bursts, guaranteeing that the entire heat source is located within one thermal diffusion length from the surface. However, once this condition is fulfilled, further increasing the duration of the burst does not provide more sensitivity to the angle. This can be confirmed in Figure 6c, where we show the same sensitivity profiles as in 6a and 6b, but for a burst of \(\tau=10\) s, corresponding to a thermal diffusion length \(\mu_{\tau}=2.3\) mm. A comparison between Figure 6a,c confirms that once \(\mu_{\tau}>d_{max}\), an increase in thermal diffusion length does not improve the sensitivity to the angle. Increasing the duration of the excitation \(\tau\) increases the sensitivity to the rest of the parameters, as well. In Figure 7a,b we display sensitivities (original definition in Equation (12)) of the temperature distribution at the end of the burst along the coordinate-axes to the magnitudes featuring the most significant variation along each axis (see Figure 5a-d): \(OY\) profile for \(Sw\) (Figure 7a) and \(OX\) profiles for \(Sh\), \(Sd\) (Figure 7b). In all cases, \(w=h=1\) mm, \(d=0.3\) mm and \(\varphi=90^{\circ}\) (\(d_{max}=1.3\) mm), and we represent three bursts, namely, \(\tau=1\) s (\(\mu_{\tau}=0.72\) mm, black), \(\tau=5\) s (\(\mu_{\tau}=1.6\) mm, blue) and \(\tau=10\) s (\(\mu_{\tau}=2.3\) mm, red). Figure 7c displays \(Sh\) and \(Sd\) of the timing graph at the origin, \(T\)(0,0,0,\(t\)) for \(\tau=1\) and \(5\) s.  
As in the case of the angle, the values of sensitivities tend to saturate for bursts with associated thermal diffusion lengths fulfilling \(\mu_{\tau}>d_{max}\). In the case of \(Sw\) (Figure 7a), an increase in the duration of the burst also entails a loss of contrast in the valley located at the center of the curve. This loss of contrast can eventually evolve towards the disappearance of the valley, leading to a certain degree of degeneracy of \(Sw\) with \(Sd\) and \(Sh\). Figure 7b shows that \(Sd\) and \(Sh\) of \(T\)(\(x\),0,0,\(\tau\)) for \(\tau=5\) s increase dramatically with respect to \(\tau=1\) s as the thermal diffusion length associated to the end of the burst  
Figure 6: \(S^{\prime}\) along the \(OX\)-axis calculated at the end of the burst for different inclinations \(\varphi\) of a squared (\(w=h=1\) mm) heat source buried \(d=0.5\) mm below the surface, emitting a flux of 40 kW/m\({}^{2}\). (**a**) \(\tau=5\) s, (**b**) \(\tau=0.5\) s, (**c**) \(\tau=10\) s. Same color code in three figures. Figure 7: (**a**) \(Sw\) along the \(OY\)-axis calculated for a squared (\(w=h=1\) mm) vertical (\(\varphi=90^{\circ}\)) heat source buried \(d=0.3\) mm below the surface, excited with three bursts \(\tau=1\) s (black), \(\tau=5\) s (blue), and \(\tau=10\) s (red). (**b**) \(Sh\) (solid lines) and \(Sd\) (dashed lines) along the \(OX\) axis calculated for the same heat source and bursts as in (**a**). (**c**) \(Sh\) (solid lines) and \(Sd\) (dashed lines), of the temperature evolution at the origin for the same heat source. Two burst durations are considered \(\tau=1\) s and \(\tau=5\) s. Same color code in three figures. increases from \(\mu_{\tau}\) = 0.72 mm for \(\tau\) = 1 s, to \(\mu_{\tau}\) = 1.6 mm for \(\tau\) = 5 s: the former covers about half of the area of the heat source whereas later includes the whole emitting area.