In this paper we discussed the possibility of using a suitable pupil function lo compensate the aberrations of optical system. The question is just as a functional minimization problem in Hilbert space. The general form of the solution minimizing the wave variance is obtained, especially the effect of using a ring phase pupil filter to compensate the symmetrical aberrations is studied. The parameters of filter is determined with the S. D as a criterion. Several cases are discussed and compared in terms of MTF.