# Interferometry of Gas-Phase Flows during Selective Laser Melting
## 4 Discussion
The model of laser plume applied in the present work is based on mass and momentum conservation (see Equation (A1)), but does not use the energy equation to avoid consideration of particular thermo-kinetic processes, which can affect the generality of the results. The velocity and pressure fields shown in Figure 8 are applicable outside the heat-affected zone; namely, in the whole domain of the ambient-gas entrainment flow, as follows from the results [28]. According to the calculations in absolute terms, the pressure change is small and amounts to about 1 Pa. Such a difference is not able to significantly increase the refractive index of the gaseous medium through which the probing laser passes. An increase in temperature, which sharply increases in the laser exposure zone and reaches several hundred degrees [30], is a factor that reduces the \(\Delta\phi\) parameter, since density of gas reduces as temperature increases. Nevertheless, the present experiments indicate that the optical path length in the plume itself increases, which can be explained by an increase in the concentration of metal vapor due to its evaporation from the molten pool. In gas-phase flows, temperature and vapor concentration are functions of spatial coordinates (\(x\),\(y\)). The refractive index of a gas depends on its composition and density. As a result, the optical path length of the probing laser is modulated by the object being studied. All local changes \(\Delta n\) of the refractive index along the ray path are integrated, and an increase in the phase \(\Delta\phi\) of the interference fringes is observed in any pixel of the interference pattern. It is associated with a change in the optical length of the probing laser beam by Equation (4). If the size \(L\) of the perturbed region is estimated from the interferogram as the size of the domain within which the interference fringes change their position during laser processing, then Equation (4) allows estimating the value of \(\langle\Delta n\rangle\) from the recorded values of \(\Delta\phi\). In the experiments performed at laser power of 130 W, \(\Delta\phi\) was about \(4\pi\) rad. For the observed size \(L\approx 2\) mm of the perturbed region, the quantity \(\langle\Delta n\rangle\), as follows from Equation (4), was 0.000532. This value almost doubles the maximum possible change in the refractive index of the air when the air is heated to \(T\rightarrow\infty\). Indeed, in this case, the air density tends to zero, and the refractive index tends to unity. The maximum possible change in the refractive index of air is thus limited and amounts to \(n_{a}-1\), where \(n_{a}\) is the refractive index of air under normal conditions (1.0002926 [31]). A comparison of the maximum possible change in the refractive index of air 0.0002926 with the real value \(\langle\Delta n\rangle=0.000532\) indicates that the change in the refractive index does not decrease, but increase. In this case, this can be caused only by the presence in the recorded zone of another gas with a refractive index greater than the refractive index of air; for example, iron. Evaporated material can affect the intensity of working laser radiation in the case of resonance absorption. According to the data presented in literature [32], the intensity of absorption of radiation by iron vapor in the visible and near-infrared ranges generally decreases with increasing wavelength and it should be expected that absorption of laser radiation with a wavelength of 1064 nm is not significant. Given the short laser path inside the plume (\(\approx\)1 cm), the absorption of laser radiation is most likely negligible. Based on the assumption that the evaporated material is a significant part of the vapor-gas jet, the refractive index of iron vapor was estimated. The refraction of any substance is determined by the polarizability of its molecules and its density. In turn, the polarizability of nonpolar molecules or atoms is determined by their volume.