A method and apparatus for generating a source illuminator profile and a mask design, subsequently optimizing the source illuminator profile and mask design based upon a set of target intensity profiles. In various implementations, the Lagrange method of optimization is employed to optimize the radiation source, wherein an optimum intensity for each pixel of the source is determined. Subsequently, a continuous tone mask is generated based upon the diffraction orders of the optimized source. With various implementations, the target intensity profile is generated by deriving a set of band limited target frequencies corresponding to the optical lithographic system. Subsequently, homotopy methods may be employed to optimize the source illuminator profile and the continuous tone mask based upon the set of band limited target frequencies.