The use of radial basis function (RBF) expansion as a means to represent the generalized pupil function for aberration retrieval from intensity point-spread function has been investigated in this research article. The optimal choice of RBF hyper-parameters is derived empirically to achieve an increased accuracy of approximation along with well-conditioned basis. The phase retrieval problem is solved using PhaseLift, an algorithm based on matrix rank minimization and also using a variant of the alternating projections algorithm proposed by Gerchberg-Saxton. The performance of the RBF-based method is compared in terms of accuracy and execution time with that based on the extended Nijboer-Zernike approach. Numerical results based on simulations are presented.