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Electrically small clear aperture dual offset reflector systems often exhibit a directivity ripple over frequency due to the interference of the diffracted field from the sub-reflector with the main beam field. This paper investigates the cause of the ripple, and presents a technique to predict the expected system directivity, including the ripple, using the feed radiation pattern augmented by an efficient simulation strategy in a clear aperture offset Gregorian system. The method allows for accurate prediction of the directivity ripple using a severely under-sampled set of simulation results. Predicted results are compared to several simulations, and agreement to better than 0.5 % is found for the majority of configurations using both analytical and full wave simulated feed patterns.