Fresnel-Kirchhoff formula

Figure 1.5. Diagram of the geometry of the Fresnel-Kirchhoff formula.

We can use Huygens principle to explain qualitatively the essential features of diffraction, but a quantitative treatment involves casting Huygens principle into a precise mathematical form, the Fresnel-Kirchhoff formula ... 

As one can see from relation (13.112), the wavefield at the point r D may be viewed at the moment of time t as the sum of elementary fields of point and dipole sources distributed over the surface S with densities dP r,t)/dn and P r,t) respectively. The interference of these fields beyond the domain D results in complete suppression of the total wavefield. Thus, the Kirchhoff integral formula can be treated as the mathematical formulation of the classical physical Huygens-Fresnel principle. 

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