A lithographic system includes a lithographic apparatus and a scatterometer. In an embodiment, the lithographic apparatus includes an illumination optical system arranged to illuminate a pattern and a projection optical system arranged to project an image of the pattern on to a substrate. In an embodiment, the scatterometer includes a measurement system arranged to direct a beam of radiation onto a target pattern on said substrate and to obtain an image of a pupil plane representative of radiation scattered from the target pattern. A computational arrangement represents the pupil plane by moment functions calculated from a pair of orthogonal basis function and correlates the moment function to lithographic feature parameters to build a lithographic system identification. A control arrangement uses the system identification to control subsequent lithographic processes performed by the lithographic apparatus.