Abstract: Exposure methods are disclosed for high precision pattern transfer with reduced distortion using an evaluation mask containing distortion-measurement patterns. The distortion-measurement patterns are provided in multiple subfields on a mask, and images of the patterns are projected and exposed onto a wafer by sequentially irradiating the subfields. Distortions in the images are measured. These measurements are then used to correct distortions in subsequent images with a dynamic correcting system comprising focus-correction coils and astigmatism compensators. Additional methods and apparatus are provided in which simultaneous equations are solved to determine currents in focus-correction coils and astigmatism compensators.