Artificial superlattices of amorphous germanium (a-Ge) and amorphous silicon (a-Si) were deposited using dual-target magnetron d.c. sputtering on Si(001) substrates. The superlattices were fabricated with modulations according to deterministic aperiodic sequences as well as periodic sequences. The deterministic aperiodic sequences were made according to the generation of generalized Cantor sets. Optical characterization of the superlattices were carried out with spectroscopic ellipsometry. The optical properties of the Cantor and periodic superlattices with equal a-Ge:a-Si volume ratios were compared. We found that the interference peaks from the Cantor superlattices are more pronounced compared with the interference peaks from the periodic superlattices. The periodic superlattices could be modelled with both multilayer and effective-medium models, in contrast to the Cantor superlattices for which only multilayer models were appropriate. This is, to our knowledge, the first study of Cantor superlattices.