High-resolution emission spectroscopy provides valuable information on the physical sputtering process during plasma-wall interaction. Up to now, analyzing the observed spectral lines during sputtering did not account for the finite size of the targets. It becomes crucial if the size of the target becomes comparable with the distance the sputtered atoms travel before emitting the photons. So, for example, the generally used standard emission model based on an infinite target or the point source approximation breaks for observations using two lines of sight: parallel and perpendicular to the normal of the target. It is impossible to achieve consistent results for energy and angular distribution of sputtered atoms. The new space-resolved emission model for finite-size targets developed in this work removes this gap. It incorporates the space-velocity transformation for the distribution function and includes the finite lifetime of excited states. The model was validated using emission spectra of sputtered atoms from a polycrystalline tungsten sample bombarded by monoenergetic Ar+ with kinetic energies of 100 eV to 140 eV at normal incidence in the linear plasma device PSI-2. Using the new model enables the simultaneous fitting of the line shapes of sputtered tungsten for both observation angles. The optimization process is performed using the standard Thompson distribution by separating the energy-dependent parameter and the angular distribution.