Precise and fast computation of aerial images are essential. Typical lithographic simulators employ a Köhler illumination system for which aerial imagery is obtained using a large number of Transmission Cross Coefficients (TCCs). These are generally computed by a slow numerical evaluation of a double integral. We review the general framework in which the 2D imagery is solved and then propose a fast and accurate method to obtain the TCCs. We acquire analytical solutions and thus avoid the complexity-accuracy trade-off encountered with numerical integration. Compared to other analytical integration methods, the one presented is faster, more general and more tractable.