Approximate forms for diffraction integrals in high numerical aperture focusing

In diffraction theory for focusing in high numerical aperture systems three generalizations to the low aperture Debye theory are incorporated: small angle approximations to the angles are not made, and apodization and polarization effects are included. It is shown that of these the polarization effects are dominant for a system satisfying the sine condition. This leads to approximate forms for the diffraction integrals. For aplanatic systems analytic solutions are obtained for the field in the focal region.