Differential SAR Interferometry (DInSAR) has proven its unprecedented ability and merits of monitoring ground deformation on a large scale with centimeter to millimeter accuracy. However, atmospheric artifacts due to spatial and temporal variations of the atmospheric state often affect the reliability and accuracy of its results. The commonly-known Atmospheric Phase Screen (APS) appears in the interferograms as ghost fringes not related to either topography or deformation. Atmospheric artifact mitigation remains one of the biggest challenges to be addressed within the DInSAR community. State-of-the-art research works have revealed that atmospheric artifacts can be partially compensated with empirical models, point-wise GPS zenith path delay, and numerical weather prediction models. In this study, we implement an accurate and realistic computing strategy using atmospheric reanalysis ERA5 data to estimate atmospheric artifacts. With this approach, the Line-of-Sight (LOS) path along the satellite trajectory and the monitored points is considered, rather than estimating it from the zenith path delay. Compared with the zenith delay-based method, the key advantage is that it can avoid errors caused by any anisotropic atmospheric phenomena. The accurate method is validated with Sentinel-1 data in three different test sites: Tenerife island (Spain), Almería (Spain), and Crete island (Greece). The effectiveness and performance of the method to remove APS from interferograms is evaluated in the three test sites showing a great improvement with respect to the zenith-based approach.