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In this letter, we present results of a study of the magneto-optical Kerr response in Co/Pt superlattices by solving for optical constants and Voigt parameters of constituent layers in the structure. The absolute values of the Voigt parameters of Co/Pt interfaces were found to be about twice as large as for the Co layer in the superlattice. Furthermore, using the determined optical constants and Voigt parameters, we can generate the Kerr rotations and ellipticities for Co/Pt superlattices or sandwich structures with continuously changed layer thicknesses and different repeat numbers. Comparison of these theoretical results to the experimental magneto-optical responses for selected structures exhibits strong consistency.