Scattering from a conductive plate can be modeled in a manner that virtually parallels the preceding solution to the aperture. In the case of scattering from a conductive plate, the current sources are obtained using the induction theorem. In fact, scattering through the aperture is the exact complement to the scattering off of the conductive plate that was essentially cut out of the conductive screen to create the aperture. If every electric parameter and the corresponding magnetic parameter were swapped, the solutions would be identical. Babinet’s principle originally stated that the sum of the intensities from an obstruction and its complement (i. e., a similarly shaped aperture in an infinite screen) is equal to the intensity that would have existed if no obstruction existed at all:
Sa + Sc — S0
While this relationship works for optics, it does not take account of polarization. To apply Babinet’s principle to vector fields, it must be modified to (23)
The first term in Eq. (27) is the ratio of the field diffracted by the aperture to the field with no screen present at all, and the second term is the ratio of the field produced by the complementary screen to the conjugate source. The conjugate source refers to the opposite field rotated by 90°. In vector form, Eq.
(27) can be rewritten as
Ec — E1 — nHa
which indicates that the electric field scattered from a conductive plate can be calculated from the field scattered from the aperture, by subtracting the latter from the incident field (22).