The idealized shapes of satellite reflector antennas are often distorted once they are placed in orbit. The performance of such antennas can be improved by identifying the locations and amount of their surface distortions and then by correcting them using active surface distortion or array feeding. This work presents a method to determine the required discrete surface distortions to correct errors. The algorithm starts by discretizing the entire reflector surface into triangular patches, then by determining the linear relationship between the local distortion and the difference between distorted and undistorted far-fields patterns. A linear system of equations with discrete distortions as unknowns results when this scattered field is sampled at specific observation points. Singular Value Decomposition combined with Tikhonov regularization, is used to solve for the set of distortions, which are translated into a physically realizable continuous surface by projecting onto a Polynomial-Fourier-Series basis. The later scheme is iteratively repeated in order to minimize the residual error. The method has been applied successfully to determine thermal/gravitational distortions on a reflector antenna, with up to 97% accuracy in tenth iteration.