An apparatus and method of compensating for lens imperfections in a projection lithography tool, includes extracting from a diffraction image created by the projection lithography tool a lens transmittance function, and then using the extracted lens transmittance function as a compensator in the lithography projection tool. Another preferred apparatus and method of synthesizing a photomask pattern includes obtaining a phase and an amplitude of a transmittance function of an imaging system; forming a computational model of patterning that includes the transmittance function of the imaging system; and then synthesizing a mask pattern from a given target pattern, by minimizing differences between the target pattern and another pattern that the computational model predicts the synthesized mask pattern will form on a wafer.