Radiation from a lighted convex surface by means of Kottler's formula

In this paper Kottler's formula is extended to treat the radiation from a fictitious and enclosing convex regular surface of zero thickness where we know the electromagnetic field distribution at each point. When the product of the two main radius of curvature is lower than the square of the free space wavelength, the field calculated with Kottler's formula may be wrong. Acorrection term applied to the electromagnetic field components at each surface point means that a right radiated far field can be obtained by means of Kottler's formula.