Patent ID: 8706442

Claim:
A lithographic system comprising: a lithographic apparatus configured to transfer a pattern from a patterning device onto a substrate; and an alignment system comprising, a measurement device configured to measure a position of a feature of the pattern on the substrate at a plurality of locations over the substrate; and a controller configured to, compare the position with points on a grid of values to determine a displacement of the position relative to points on the grid; and extrapolate values for intermediate positions on the substrate based on values of corresponding intermediate points on the grid, so as to provide an indication of the intermediate positions on the substrate and their displacements relative to the grid, wherein the grid is based on at least one orthogonal basis function and the measurement is performed at the position corresponding to roots of the at least one orthogonal basis function, and wherein the at least one orthogonal basic function is configured to accommodate a shape of the substrate.