Glow discharge optical emission spectroscopy (GDOES) has been recognized for allowing direct solid sample elemental analysis with high depth resolution. However, the lateral resolution it affords has been historically restricted to some millimetres or the diameter of the sputtered area. Recently, it was shown that one can obtain laterally resolved information from within the sputtered area by operating the discharge in pulsed power mode. The newly available data dimensions require a new approach to the collection of the GDOES signal with lateral (to recover X and Y positions), spectral (to qualify and quantify elemental information), and temporal resolution (to improve lateral resolution and allow depth profiling). Previous studies have utilized spectral imagers of whisker-broom and staring geometries. In this study we characterize the advantages and disadvantages of using a push-broom geometry hyperspectral imager for GDOES elemental mapping. The results show that the higher light throughput of the push-broom geometry allows faster image acquisition times, compared to other spectral imaging systems with the same components, and thus maintain depth resolutions below 10 nm.