Expressions are developed which give the amount of unidirectional radiation from a distant radiation source passing through a cylindrical hole in a slab of material, including the amount of radiation which penetrates the edges of the hole, as a function of angle between the radiation direction and the axis of the hole. The modifications necessary for sources at finite distances are indicated. These functions are integrated over appropriate angles for distant line sources, and for extended sources. It is shown that, to a first approximation, the results are the same as the geometrical aperture for a like diameter hole in a similar slab with one mean free path of material removed from each side. The effects due to scattering from the walls of the collimator are discussed and an approximate method of calculation is presented with results for a specific collimator.