An innovative analytic strategy for the estimation of the average pattern behavior of reflector antennas when surface deformations are present on the parabolic disc is proposed. Since measuring the surface deviations from a reference ideal shape is a complex task, the root-mean-square (rms) surface deformations are modeled as intervals and their impact on the power pattern as well as the sensitivity of the beam features is efficiently predicted by exploiting the rules of the interval arithmetic throughout interval analysis (IA). The result is the definition of closed-form relationships between the bounds (upper and lower values) of the radiated power pattern and the rms interval surface deformations. Uniformly and non-uniformly distributed perturbations of the ideal surface are analyzed to assess the effectiveness of proposed approach. Comparisons with state-of-the-art solutions are also carried out by varying the deformation thickness as well as the reflector geometry and illumination.
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Rocca et al. (2014) studied this question.