We use mono-crystalline gold platelets with ultra-smooth surfaces and superior plasmonic properties to investigate the formation of interference patterns caused by surface plasmon polaritons (SPPs) with scattering-type scanning near-field microscopy at 521 and 633 nm. By applying a Fourier analysis approach, we can identify and separate several signal channels related to SPPs launched and scattered by the atomic force microscopy tip and the edges of the platelet. Especially at the excitation wavelength of 633 nm, we can isolate a region in the center of the platelets where we find only contributions of SPPs which are launched by the tip and reflected at the edges. These signatures are used to determine the SPP wavelength of λSPP = 606 nm in good agreement with theoretical predictions. Furthermore, we were still able to measure SPP signals after 20 μm propagation, which demonstrates impressively the superior plasmonic quality of these mono-crystalline gold platelets.