An approach is used to estimate and correct the overlay variation as function of offset for each measurement. A target formed on a substrate includes periodic gratings. The substrate is illuminated with a circular spot on the substrate with a size larger than each grating. Radiation scattered by each grating is detected in a dark-field scatterometer to obtain measurement signals. The measurement signals are used to calculate overlay. The dependence (slope) of the overlay as a function of position in the illumination spot is determined. An estimated value of the overlay at a nominal position such as the illumination spot's center can be calculated, correcting for variation in the overlay as a function of the target's position in the illumination spot. This compensates for the effect of the position error in the wafer stage movement, and the resulting non-centered position of the target in the illumination spot.