## 2 Theory
In Figure 2, we present surface temperature distributions calculated at the end of a \(\tau=1\) s burst, \(T(x\),\(y\),0,\(\tau)\), using Equation (10) with \(K=0.5\) W/mK and \(D=1.3\cdot 10^{-7}\) m\({}^{2}\)/s (thermal properties of the photo-polymeric resin used in the experiments) produced by a square heat source (\(w=h=2\) mm) emitting a power density of \(\varPhi=10\) kW/m\({}^{2}\) (total emitted power 40 mW), whose upper side is buried \(d=0.1\) mm below the surface. From now on, all the calculations will be performed for these material properties. We show three inclinations of the heat source: (a) parallel to the surface, \(\varphi=0^{\circ}\), (b) at an angle of \(\varphi=30^{\circ}\) with respect to the surface, and (c) a vertical heat source, perpendicular to the surface (\(\varphi=90^{\circ}\)). As can be seen, the angle of inclination has a noticeable impact on the surface temperature, both on the temperature elevation and on the particular distribution. The temperature elevation caused by the horizontal heat source is the highest one because for \(\varphi=0^{\circ}\) the whole area producing heat is buried \(d=0.1\) mm, whereas for increasing \(\varphi\) (notably for the vertical heat source, \(\varphi=90^{\circ}\)), the positions emitting heat are buried deeper below the surface. As the inclination of the heat source has the direction of the \(OX\)-axis, the surface temperature distribution is mostly affected in this direction. To illustrate this, in Figure 3a,b we present surface temperature profiles along the \(OX\)- and \(OY\)-directions, \(T(x\),0,0,\(\tau)\) and \(T(0\),\(y\),0,\(\tau)\), respectively, produced by heat sources of the same dimensions, depth, flux, and burst as in Figure 2, for six different inclinations \(\varphi=0^{\circ}\), \(10^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(90^{\circ}\). As pointed out in Figure 2, the \(OX\)-profiles are asymmetric, except for the horizontal (\(\varphi=0\)) and vertical (\(\varphi=90^{\circ}\)) heat sources although, according to the geometry depicted in Figure 1, the former is displaced with respect to the origin. The inclination does not significantly affect the shape of the \(OY\)-profiles, which remain symmetric. Figure 3c shows the evolution of the temperature at the origin \(T(0\),0,0,\(t)\) for the same heat sources. Similarly to the \(OY\) profile, the inclination does not significantly affect the shape of the temperature-time curve. Figure 3: (a) \(T(x\),0,0,\(\tau)\) and (b) \(T(0\),\(y\),0,\(\tau)\) surface temperature profiles calculated at the end of a \(\tau=1\) s burst produced by tilted squared (\(w=h=2\) mm) heat sources buried \(d=0.1\) mm below the surface and emitting a flux of \(10\) kW/m\({}^{2}\). (c) Evolution of the surface temperature produced by the same heat sources at the origin \(T(0\),0,0,\(t)\). Six inclinations are considered: \(\varphi=0^{\circ}\), \(10^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(90^{\circ}\). Same color code in the three figures. Figure 2: \(T(x\),\(y\),0,\(\tau)\) calculated for a \(\tau=1\) s burst produced by squared (\(w=h=2\) mm) heat sources buried \(d=0.1\) mm below the surface and emitting a flux of \(10\) kW/m\({}^{2}\). Three inclinations are considered: (a) \(\varphi=0^{\circ}\), (b) \(\varphi=30^{\circ}\), (c) \(\varphi=90^{\circ}\). Note the different temperature scales in the three figures. According to the previous results, we can infer that the inclination of the heat source affects mainly the shape of the temperature distribution along the \(OX\) direction, featuring an asymmetry. However, the evidence of this signature depends on the depth \(d\) of the heat source and the duration of the burst, \(\tau\).