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Analytical expression of aperture efficiency affected by Seidel aberrations

The effect of aberrations on the aperture efficiency has not been discussed analytically, though aberrations determine the performance of a wide field-of-view system. Expansion of a wavefront error and a feed pattern into a series of the Zernike polynomials enables us to calculate the aperture efficiency. We explicitly show the aperture efficiency affected by the Seidel aberrations and derive the conditions for reducing the effects of the spherical aberration and coma. In particular, the condition for coma can reduce a pointing error. We performed Physical Optics simulations and found that, if the Strehl ratio is higher than 0.8, the derived expression provides the aperture efficiencies with a precision of < 2%.