Huygens-Fresnel principle

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. 

Huygens-Fresnel principle Every point on a primary wavefront serves as the source of secondary wavelets such that the wavefront at some later time is the envelope of these wavelets. 

Of interest is the light intensity measured on plane II, located a distance / from plane I. Huygen s principle simply states that the field at plane II is the sum of spherical waves emanating from all points in plane I. However, the field at point A will be primarily influenced by the spherical wave at point A, with a similar relationship between the fields at points B and B. Fresnel s extension of Huygen s principle quantifies this statement. The spherical wave emanating from a differential area, dS, located at point A is... 

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 ... 

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