# Interferometry of Gas-Phase Flows during Selective Laser Melting
## 2 Materials and Methods  
To register gas-phase flows in the zone of laser irradiation by interferometry, a compact setup has been developed that is placed above the desktop of the laboratory SLM unit. The optical setup is shown in Figure 1. It is based on Jamin interferometer, which was tested earlier in similar tasks and demonstrated the reliability of results [20; 21; 22]. Laser beam 1 (532 nm), expanded by lens 2, is divided into two beams (the probing one and the reference one) using plane-parallel glass plate 3. After the probing beam passes through the laser-interaction zone 4, both beams are brought together using the same glass plate 5. Next, lens 6 builds an image of the studied area together with a reference beam superimposed on it in the recording camera 7. The beams together create an interference pattern. The interferometer is configured so that in the absence of exposure, the interference pattern looks like closely spaced parallel fringes. The presence of a gas-phase jet leads to the change of the optical path length \(\Delta S\) of the probe beam, which leads to the change of its phase \(\Phi\) and, accordingly, to a local change in the position of interference fringes near the laser exposure zone. Interferograms were recorded using a high-speed Photron Fastcam SA 5 camera (Photron, Tokyo, Japan) with a frame rate of 5000 frames per second, which corresponds to an exposure time of 0.2 ms per frame. The interpretation of the interferogram allows one to obtain the spatial distribution of the change in the optical path caused by the presence of a gas-phase jet. To interpret the interferograms, the spatial Fourier filtering method was used [23; 24]. The decryption algorithm included a two-dimensional Fourier transform from the periodic intensity distribution in the interferogram, as a result of which the zero and \(\pm\) first maxima were formed in the Fourier spectrum, reflecting the spatial frequency of the interference fringes. The first-order maxima contained information on phase distribution \(\Delta\phi\)(x,y) in the cross-section of the working beam. To obtain this distribution, only the 1 st maximum was highlighted by filtering and shifted to the center of the Fourier plane, which meant the elimination of the spatial frequency in the phase distribution \(\Delta\phi\)(x,y), and the inverse Fourier transform was performed. The resulting complex-valued function:  
\[I(x,y)=a\dot{e}^{i\Delta\varphi(x,y)} \tag{2}\]  
contains the required function \(\Delta\phi\)(x,y):  
\[\Delta\varphi(x,y)=\tan^{-1}\frac{\text{Im}(t)}{\text{Re}(t)}. \tag{3}\]  
Figure 1: Experimental set-up: 1—probing laser; 2—lens; 3,5—plane-parallel glass plate; 4—laser-interaction zone; 6—lens; 7—camera; 8—screen; 9—working laser; 10—substrate with powder layer. Using Equation (3), the spatial distribution of the increment \(\Delta\phi\) of the phase of the probing laser beam caused by the interaction of the working laser with the processed substrate was obtained. Since the phase found in this way is a multivalued function and can break at the points where it takes the values \(\pm\pi\)/2, phase unwrapping algorithm is used to remove discontinuities by adding a constant value \(\pm\pi\) to all values of the \(\Delta\phi\) after every discontinuity. As a result, a continuous smooth phase surface \(\Delta\phi\) (\(x\),\(y\)) was obtained. According to this scheme, the process of powder melting of corrosion-resistant steel 12X18H10T (Poelema LLC, Tula, Russia) with an average particle size of 20-63 \(\upmu\)m was recorded (Figure 2). The same steel was used as the substrate (Table 1). The gas-phase jet was recorded when the powder was treated with the Nd:YAG working laser with a wavelength of 1064 nm (IPG Photonics LK-200, Fryazino, Russia) across the probing beam of the probing laser.