Applying the perturbation theory to Helmholtz's equations of spherical and sphero-conal systems of coordinates, the author deduces the expressions for the perturbation terms of diffraction due to a plane angular sector with its angle nearly equal to π and those due to an elliptic cone with θ nearly equal to π/2 respectively. Then, following the principle in [10], substituting the diffracting plane disk of arbitrary form by its inscribed polygonal disk and the diffracting surface of arbitrary form by a surface which consists of many small inscribed elliptic cones of the original surface, we make the summations of the perturbation terms for the sectors of the polygon and those of the tops of the small cones respectively. In the limiting case these two summations become integrals, hence the diffraction fields of first-order due to the disk (thereof, the complementary plane screen with a hole) and the surface of arbitrary forms are derived respectively.