Density profile information is invaluable to plasma experiments. In particular, the edge and mantle plasma density profile is believed to influence core plasma behaviour of fusion devices such as tokamaks. In low density plasmas, light emission caused by neutral hydrogen gas injection and subsequent excitation can be used to measure the local plasma parameters. A neutral penetration model is required to evaluate plasma density from Hα light emission. This paper verifies that a simple collisionless three-dimensional neutral penetration model can be utilized in low-density, low-temperature plasmas. Since the Hα emission intensity can be linked directly to the local electron density, this model permits the reconstruction of the density profile well beyond the last closed flux surface of the plasma.