In this paper, we study the fluorescence decay rate of a molecule above a corrugated interface, and particularly the variations of the decay rate as a function of the lateral position of the molecule. As a first step, one has to determine the field diffracted by a corrugated interface when the incident field is the field emitted by a dipole. For this purpose, we have used a perturbative Rayleigh method, and we show that the decay rate variations can be connected to the surface profile via a transfer function. Some numerical calculations of this transfer function and of decay rate variation images are presented for dielectric and metallic samples. The visibility of the theoretical images is up to 20% and, moreover, resolution of the images is good enough to use the fluorescence lifetime of molecules as signal in a life-time scanning near-field optical microscope. The technical problems are discussed briefly.