Printing a mask with maximum possible process window through adjustment of the source distribution

A lithographic mask is illuminated with light from different directions such that intensities of a plurality of incident beams of light provide a largest possible integrated process window defined in terms of an allowed range for defining shapes. Constrained sets of intensity parameters are imposed. A first set of intensity parameters represents maximum possible intensities that can be permitted for overexposed tolerance positions. A second set of intensity parameters represents minimum possible intensities that can be permitted for underexposed tolerance positions. Optimum source intensities of incident beams are defined using a linear program and constraints. The optimum source intensities maximize an integrated range of dose and focal variations without causing printed shapes to depart from the allowed range. Apparatus are detailed and variations are described.