Multilayered product structures are formed on substrates by a combination of patterning steps, physical processing steps and chemical processing steps. An inspection apparatus illuminates a plurality of target structures and captures pupil images representing the angular distribution of radiation scattered by each target structure. The target structures have the same design but are formed at different locations on a substrate and/or on different substrates. Based on a comparison of the images the inspection apparatus infers the presence of process-induced stack variations between the different locations. In one application, the inspection apparatus separately measures overlay performance of the manufacturing process based on dark-field images, combined with previously determined calibration information. The calibration is adjusted for each target, depending on the stack variations inferred from the pupil images.