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A unified formulation of the optimization of monopulse antenna performance indices for a specified sidelobe envelope function and/or specified nulls of the pattern is presented. The performance indices considered are beam efficiency, gain factor, and angular sensitivity factor of rectangular and circular apertures. The unconstrained optimization of beam efficiency result in an integral equation, the solutions of which are prolate spheroidal wave functions for rectangular aperture and hyperspheroidal wave functions for circular aperture. These functions reduce, respectively, to Legendre and Zernike polynomials in the case of gain factor and angular sensitivity factor. The double orthogonality properties of these eigenfunctions are used for constrained optimization. The results obtained by this technique for the near-in sidelobes constrained at a uniform level are shown to be in agreement with the earlier works. The method is applicable for other aperture surfaces such as elliptical, ellipsoidal, and spherical.