1. A method for illuminating a mask with a source to project a desired image pattern through a lithographic system onto a photoactive material, the method comprising: defining a representation of the mask; obtaining a fractional resist shot noise (FRSN) parameter; determining a first relationship between a first set of optical intensity values and an edge roughness metric based on the FRSN parameter; determining a second relationship between a second set of optical intensity values and a lithographic performance metric; imposing a set of metric constraints in accordance with one of the first and second relationships; setting up an objective function of optimization in accordance with the remaining of the first and second relationships; determining optimum constrained values of the representation of the mask in accordance with the set of metric constraints and the objective function of optimization; and outputting the optimum constrained values of the representation of the mask.