Methods are disclosed for measuring target structures formed by a lithographic process on a substrate. A grating or other structure within the target is smaller than an illumination spot and field of view of a measurement optical system. The position of an image of the component structure varies between measurements, and a first type of correction is applied to reduce the influence on the measured intensities, caused by differences in the optical path to and from different positions. A plurality of structures may be imaged simultaneously within the field of view of the optical system, and each corrected for its respective position. The measurements may comprise first and second images of the same target under different modes of illumination and/or imaging, for example in a dark field metrology application. A second type of correction may be applied to reduce the influence of asymmetry between the first and second modes of illumination or imaging, for example to permit a more accurate overly measurement in a semiconductor device manufacturing process.