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A closed form vector expression has been derived for the mean power pattern radiated from an aperture with random perturbations. The expression is in terms of the Fourier transforms of three unrestricted functions: 1) the vector electric field of the unperturbed aperture, 2) the scattering dyadic of one of defects, and 3) the probability density function of the position of a defect. These functions can be represented by measurement data as well as by simple analytical functions. In particular, the scattering matrix of an actual physical defect can be measured and used in the model. The derivation was made possible by the fact that the aperture mean and correlation functions take the form of convolution integrals.