Rapid calculation of defocused partially coherent images

A rapid method for evaluating partially coherent images of 1-D periodic patterns including focal error is described. A transmission cross-coefficient approach is used. For a square source and objective, the cross-coefficient is calculated analytically. For a circular source and objective, a 1-D integration which has been transformed for rapid convergence is performed. Images of a mask with 1-microm lines and spaces for several values of defocus and various degrees of partial coherence are given for both circular and square apertures.