Richards and Wolf have published a paper on the vector diffraction problem for a uniformly illuminated aperture. This calculation extends it to gaussian optical beams
The Kirchoff description of the diffraction process can be shown to be appropriate when the dimensions of the aperture are much larger than the wavelength. The Kirchoff model can be formulated as a vector model. As the numerical aperture of the lens is increased, one would expect that the vector nature of light would manifest itself as deviations from the Airy disk because the polarization vectors of the light in different azmuthal regions of the converging light cone no longer point substantially in the same direction (as they would for a small angle cone). Since they add vectorally in the region near the focus their vector sum will depend substantially on the azimuthal angle.
