Fresnel-Kirchhoff integral

Spatial information, which is described by an electric field f(x, y, 0) at z = 0 in Cartesian coordinates, is transformed while propagating in free space by a relation obeying the well-known Fresnel-Kirchhoff integral. 

The irradiation distribution in the focal plane for a binary amplitude EZP is calculated by the Fresnel-Kirchhoff integral, performing integration across all of the transparent rings Si,..., S [135]... 

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. 

The Fresnel-Kirchhoff (FK) integral for transformation of a light beam through free space and a GI medium is discussed. Here we shall describe how a Gaussian beam changes when propagating in free space and in a GI medium. 

Nonmonochromatic Waves (1.16) Diffraction theory is readily expandable to non-monochromatic light. A formulation of the Kirchhoff-Fresnel integral which applies to quasi-monochromatic conditions involves the superposition of retarded field amplitudes. 

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