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A rigorous electromagnetic theory describing diffraction by a circular aperture in a perfectly conducting screen is used to model the flux and field intensity profiles in the near field behind the screen. In particular, the case of an aperture having a diameter one‐fifth that of the wavelength of the radiation being used is considered. The degree of collimation of both the Poynting vector and the electric field intensity profiles of the transmitted beam is observed and its decrease with increasing distance from the screen is investigated. The effect of increasing the thickness of the screen is observed. These results are relevant to the study of near‐field microscopy where the sample under investigation is either imaged with a collimated beam or light transmitted through the object is sampled using a probe having an electrically small diameter.