A lithographic reticle is illuminated to transfer a pattern to a substrate, inducing distortions due to heating. The distortions are calculated using reference marks in a peripheral portion of the reticle and measuring changes in their relative positions over time. A plurality of cells are defined for which a system of equations can be solved to calculate a dilation of each cell. In an embodiment, each equation relates positions of pairs of marks to dilations of the cells along a line (s, s1, s2) connecting each pair. Local positional deviations can be calculated for a position by combining calculated dilations for cells between at least one measured peripheral mark and the position. Corrections can be applied in accordance with the result of the calculation. Energy may be applied to the patterning device (for example by thermal input or mechanical actuators) to modify a distribution of the local positional deviations.