Fresnel-Kirchhoff diffraction integral (source code)

= Fresnel-Kirchhoff diffraction integral
{c}

A scalar aperture approximation that sums the secondary waves reaching an observation point. For a point source with incident spherical <amplitude> $Ae^{iks}/s$, one common forward-normal convention is
$$
U(P)=\frac{A}{i\lambda}\int_{\mathcal A}\frac{K(Q)e^{ik(s+r)}}{sr}\,dS.
$$
Here $s$ and $r$ are source-to-aperture and aperture-to-observer distances and $K$ is an <obliquity factor>. The <Fresnel diffraction> approximation retains quadratic path phase; <Fraunhofer diffraction> additionally neglects the quadratic phase across the aperture. Kirchhoff boundary assumptions do not give an exact electromagnetic solution at a sharp edge.