A lithographic apparatus includes an alignment sensor including a self-referencing interferometer for reading the position of a mark including a periodic structure. An illumination optical system focuses radiation of different colors and polarizations into a spot which scans said structure. Multiple position-dependent signals are detected in a detection optical system and processed to obtain multiple candidate position measurements. Each mark includes sub-structures of a size smaller than a resolution of the optical system. Each mark is formed with a positional offset between the sub-structures and larger structures that is a combination of both known and unknown components. A measured position of at least one mark is calculated using signals from a pair of marks, together with information on differences between the known offsets, in order to correct for said unknown component of said positional offset.