The three-dimensional atom probe (3DAP) technique gives the elemental identities and the position of atoms within the small volume analysed (on the order of 10 x 10 x 100 nm(3)). The large number of atoms collected (up to two million) and the excellent spatial resolution of this instrument allows the observation of some crystallographic features of phases chemically identified. This paper shows that the application of a discrete Fourier transform algorithm to a 3DAP dataset provides information that is not easily accessible in real space. The derivation of the mean size of particles from Fourier intensities is an example. Using 3D 'dark-field' imaging, single ordered grains were isolated from the disordered matrix of a ternary alloy. Moreover, the intrinsic spatial resolution of the instrument was evaluated by this method for pure metal; the resolution reaches 0.2 nm laterally and 0.06 nm in depth. This excellent resolution is shown to be sufficient to give access to the crystalline lattice. The use of image filtering in the reciprocal space enables for atomic columns to be imaged the first time from 3DAP data.