The scattering of atoms from surfaces is studied within the classical Wigner formalism. An analytical expression is derived for the angular distribution and its surface temperature dependence. The expression is valid in the limit of weak coupling between the vertical motion with respect to the surface and the horizontal motion of the atom along the periodic surface. The surface temperature dependence is obtained in the limit of weak coupling between the atomic motion and the surface phonons. The resulting expression leads to an almost symmetric double peaked angular distribution, with peaks at the rainbow angles. The analytic expression is compared to model numerical computations. We show that it provides a good qualitative description for the experimentally measured angular distribution of Ne and Ar scattered from a Cu surface. |