An apparatus measures positions of marks on a lithographic substrate. A measurement optical system comprises illumination subsystem for illuminating the mark with a spot of radiation and a detecting subsystem for detecting radiation diffracted by the mark. A tilting mirror moves the spot of radiation relative to the reference frame of the measurement optical system synchronously with a scanning motion of the mark itself, to allow more time for accurate position measurements to be acquired. The mirror tilt axis is arranged along the intersection of the mirror plane with a pupil plane of the objective lens to minimize artifacts of the scanning. The same geometrical arrangement can be used for scanning in other types of apparatus, for example a confocal microscope.