Recently a novel method called nonlinear Fourier-filtering was suggested for temporal and spatial cleaning of high-brightness laser pulses. In this paper experimental demonstration of the associated spatial filtering of this method and significant improvement of the temporal filtering feature are presented. The formerly found limit of ~103 for the temporal contrast improvement is identified as diffraction effects caused by the limited numerical aperture of imaging. It is shown by numerical simulation that proper apodization of the object can lead to sufficiently higher limit (>108). Using an advanced experimental arrangement the improvement of >2 orders of magnitude is experimentally verified in the ultraviolet and an indirect proof is presented that the background caused by the optical arrangement is reduced below 10-7.