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A method is presented for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrary geometry. This method utilizes near-field data to determine an equivalent magnetic current source over a fictitious surface which encompasses the antenna. This magnetic current, once determined, can be used to ascertain the near and the far fields. This method demonstrates that once the values of the electromagnetic field are known over an arbitrary geometry, its values for any other region can be obtained. An electric field integral equation is developed to relate the near fields to the equivalent magnetic current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometric surfaces, illustrate the accuracy of this method.