An inspection method, and corresponding apparatus, enables classification of pupil images according to a process variable. The method comprises acquiring diffraction pupil images of a plurality of structures formed on a substrate during a lithographic process. A process variable of the lithographic process varies between formation of the structures, the variation of the process variable resulting in a variation in the diffraction pupil images. The method further comprises determining at least one discriminant function for the diffraction pupil images, the discriminant function being able to classify the pupil images in terms of the process variable.