Optimization of illumination for a full-chip layer is disclosed. A pitch frequency of the full-chip layer is determined so as to generate a pitch frequency histogram of the full-chip layer. The pitch frequency indicates how often a given pitch occurs in the full-chip layer. The pitch frequency histogram is equated to be the first eigenfunction from the sum of coherent system representation of a transformation cross coefficient. An integral equation for the first eigenfunction of the transformation cross coefficient is solved so as to define the optimal illumination for imaging the full-chip layer.