Babinet s principle

Keywords radar bistatic radar multistatic radar ambiguity function parasitic radar forward scatter Babinet s principle passive coherent location netted radar. 

Although we shall be interested primarily in diffraction by an opaque circular disk, no extra labor is entailed if the shape of the planar obstacle is unrestricted at this stage of our argument (Fig. 4.1a). It is more convenient to consider diffraction by a planar aperture, with the same shape and dimensions as the obstacle, in an otherwise opaque screen (Fig. 4.1b). If xp(P) is the value of the wave function at P when the aperture is in place, we can invoke Babinet s principle,... 

To account for the total directional scattering from a large sphere, effects of both diffraction and reflection must be considered. When a spherical particle is in the path of incident radiation, the diffracted intensity may be obtained from Babinet s principle, which states that the diffracted intensity is the same as that for a hole of the same diameter. The phase function for diffraction by a large sphere is given by [Van de Hulst, 1957]... 

Babinet s principle The sum of the fields diffracted by two complementary screens (corresponding to a situation in which the second screen is obtained from the first one by interchanging apertures and opaque portions) coincides with the field in the absence of any screen. 

Fraunhofer diiliraction applies to particles that are much larger than wavelength and for which all radiation that is incident on the particle surface is either absorbed or redirected by reflection and refraction. The only forward scattering results from the difiiraction at the edges of the particle. In that sense, the particle can be replaced by an opaque, planar obstacle. According to Babinet s principle, this is complementary to the dififaction at an aperture of the same shape. The amplitude function for that case is given as ... 

That the contrast factor is the square of the difference of the scattering amplitudes is equivalent to Babinet s principle in optics, which states that the diffraction pattern from an opaque body is identical to that from a hole of the same size and shape. For instance, a circular hole scatters like a circular disc of the same diameter. 

If we interchange the dielectric in the aperture opening and the thin film metal, we get a complementary structure, which is an antenna. Is there any relation between the resonance properties of the two structures If we assume that the aperture metal film is infinitesimally thick, and that the metal is a perfect electrical conductor (PEC), the aperture and the complementary antenna structure are connected by a form of Babinet s principle. Supgose that the aperture is illuminated by an incident electric field Ei The interaction with the aperture will set up a total electric field E. Now, suppose that the complementary antenna structure is illuminated by an incident magnetic field that is vectorially equal to the incident electric field in the aperture case. Thus, the mcident magnetic field in the anteima case is E. In this case, let H2 be the total magnetic field. The particular form of Babinet s principle states that... 

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