A lithographic apparatus includes an alignment sensor including a self-referencing interferometer for reading the position of an alignment target comprising a periodic structure. An illumination optical system for focusing radiation into a spot on said structure. An asymmetry detection optical system receives a share of positive and negative orders of radiation diffracted by the periodic structure, and forms first and second images of said spot on first and second detectors respectively, wherein said negative order radiation is used to form the first image and said positive order radiation is used to form the second image. A processor for processing together signals from said first and second detectors representing intensities of said positive and negative orders to produce a measurement of asymmetry in the periodic structure. The asymmetry measurement can be used to improve accuracy of the position read by the alignment sensor.