## 1 Introduction  
Selective laser melting (SLM) is of huge interest for the production of complex shaped metal parts for the gas turbine industry and some nuclear applications [1; 2]. The SLM process uses a laser, which scans over and selectively melts metal powder in a powder bed to build 3D components layer by layer according to the design in a computer-aided design (CAD) file [3]. AlSi10 Mg (a hypoeutectic alloy in the Al-Si-Mg system) is a widely studied material. The AISi10 Mg alloy is highly demanded for many applications in aerospace, automotive industry, and heat exchanger products [3], due to its lightweight, low thermal expansion and recycling costs, and high mechanical properties [4]. There are several studies of this alloy using SLM [5; 6; 7]. Furthermore, AISi10 Mg components have a wide range of mechanical properties, an extremely fine microstructure, and hence a high hardness [8; 9]. Components of AISi10 Mg of nearly 100% relative density can be produced using SLM [7]. However, in addition to the advantageous results, a few papers mention that pores and other imperfections reduce the density of the components [8; 9; 10]. [PERSON] et al. [7] reported that spherical porosity is generally due to entrapped gases. [PERSON] et al. [8] presented the imperfection that is caused by not completely melted powder having a statistically geometric shape. During SLM, if the non-optimized processing parameters were used, different imperfections (cracks, gaps, pores, cavities) would occur, which all reduce the relative density of the component. Furthermore, the porosity directly affects mechanical strength [11], fatigue property [12], and elongation to rupture [13]. The selective laser melting (SLM) process parameters influence the fabrication process and must be carefully adjusted to produce parts without defects such as porosity, cracks, and altered chemical composition by selective vaporization. [14,15]. The energy density is regarded as the only factor for process optimization, which is calculated by  
\[E_{d}=P/(v\cdot h\cdot d), \tag{1}\]  
where \(E_{d}\) is the energy density (J/mm\({}^{3}\)), \(P\) is the laser power (W), \(v\) is the laser scan speed (mm/s), \(h\) is the hatch distance (mm), and \(d\) is the layer thickness of the powder bed (mm) [16]. The energy density and each process parameter are all significant factors affecting mechanical properties [17,18]. The SLMed sample using a lower hatching distance would have a higher ultimate tensile strength (UTS) and yield strength for AlSi10 Mg [18]. Equation (1) does not consider the effect of a single factor such as hatching distance, however, which was also taken into account during the parameter optimization [9,19]. With the decrease in the laser power, the tensile properties deteriorate because of the increasing amount of keyhole porosity [20]. The most economic way to get information about the quality of a SLMed part is the measurement of relative density. The Archimedes method is widely used to measure the solid density and porosity of powder metallurgy products. The relative density of parts has a close relationship with the existence of internal pores [21]. [PERSON] et al. [22] used the Archimedes method and image analysis to assess the relative density of SLM-produced samples of Ni-basedsuperalloyIN-738 LCwith sets of processing parameters. American Society for Testing Materials (ASTM) provides two standards [23,24] for measuring the density of powder metallurgy products. ASTM Standard B311-13 [23] is only suitable for the materials with a porosity of less than 2%, not taking into account the effect of the surface-connected cavities (open cavities).These defects might be porosity and/or cavities because of unmelted powder or cracks formed during SLM.