We have developed a new scheme to evaluate the atomic pair correlation function analytically and exactly for the combined overlayer and substrate system during the first stages of epitaxy. This function describes the morphology of growth on the atomic scale. The overlayer atoms can be a random lattice gas or islands with an arbitrary distribution of sizes. The atomic pair correlation function is particularly useful in calculating the widths and shapes of the intensity diffracted from epitaxially grown films using low energy or high energy electron diffraction (LEED or RHEED). We have carried out several realistic model calculations involving metal–metal and semiconductor–semiconductor epitaxy. The results are compared to the recent molecular beam epitaxy measurements of W/W(110) and Si/Si(111) reported by Henzler and co-workers.