Optical systems are used to transfer light in beam diagnostics for a variety of imaging applications. The effect of the point spread function (PSF) of these optical systems on the resulting measurements is often approximated or misunderstood. It is imperative that the optical PSF is independently characterised, as this can severely impede the attainable resolution of a diagnostic measurement. A high quality laser and specially chosen optics have been used to generate an intense optical point source in order to accomplish such a characterisation. The point source was used to measure the PSFs of various electron-beam imaging systems. These systems incorporate a digital micro-mirror array, which was used to produce very high (>105) dynamic range images. The PSF was measured at each intermediary image plane of the optical system; enabling the origin of any perturbations to the PSF to be isolated and potentially mitigated. One of the characterised systems has been used for optical transition radiation (OTR) measurements of an electron beam at KEK-ATF2 (Tsukuba, Japan). This provided an application of this process to actively improve the resolution of the beam imaging system. Presented here are the results of our measurements and complementary simulations carried out using Zemax Optical Studio.