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This paper describes methods for accurate pattern modeling of large axisymmetric paraboloidal focus-fed reflector antenna systems. We demonstrate that the incorporation of the developed pattern models helps in advancing the state-of-the-art in coherent time-domain canceling (CTC) for interference mitigation in radio astronomy. The first method yields a closed form expression for the antenna pattern with parameters accounting for the focal ratio and feed pattern. In subsequent adaptive methods, parameters of this model are calculated using measurements of interference signals. The corrected pattern model improves the prediction of the change in the true pattern for future times. The methods are compared by (1) comparing the error in the pattern model with respect to the true pattern and (2) comparing the pattern value update period required to achieve a specified level of residual interference when used in CTC. The efficacy of the pattern modeling methods is demonstrated by showing that the error in the pattern model decreases and the pattern value needs to be updated at a much slower rate for effective CTC.