The complex optical conductivity tensor for layered systems is calculated on the basis of the Luttinger formula within the spin-polarized relativistic screened Korringa-Kohn-Rostoker method by means of a contour integration technique. Ab initio Kerr spectra are then obtained for arbitrary geometry and incidence via a 2 Â 2 matrix technique which includes all multiple reflections between layers and optical interferences in the layers. Applied to fcc Co/Pt layered systems it is shown that the Kerr spectra are highly sensitive to the surface orientation, its dependence on the Co slab and cap Pt thickness closely reflects, e.g. the ABCABC . . . stacking of the fcc (111) texture, and even for a moderate number of Co/Pt 3 bilayers a satisfactory good agreement with corresponding measurements is achieved.