1. An exposure method comprising: transferring a first pattern onto each of a plurality of target portions of a substrate, the first pattern including at least one alignment mark; measuring a plurality of positions of the respective transferred plurality of alignment marks and determining a plurality of alignment mark displacements (dx, dy) for the respective plurality of alignment marks as a difference between a respective predetermined nominal position of the alignment mark and the respective measured position of the alignment mark; fitting a mathematical model to the plurality of alignment mark displacements to obtain a fitted mathematical model; determining a position of the first pattern in each of the plurality of target portions, based on the fitted mathematical model; and transferring a second pattern onto each of the plurality of target portions, using the determined position of the first pattern in each of the plurality of target portions, wherein the mathematical model comprises polynomials Z 1 and Z 2 : 
 Z 1= r 2 cos(2θ) Z 2= r 2 sin(2θ) in polar coordinates ( r ,θ) or 
 Z 1= x 2 −y 2 Z 2= xy in Cartesian coordinates ( x,y ), and wherein the fitting of the mathematical model includes determining a value for each of one or more parameters representing an amplitude and/or orientation of the polynomials Z 1 and Z 2 .