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Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, [3] uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
Fresnel diffraction of circular aperture, plotted with Lommel functions. This is the Fresnel diffraction integral; it means that, if the Fresnel approximation is valid, the propagating field is a spherical wave, originating at the aperture and moving along z. The integral modulates the amplitude and phase of the spherical wave.
Kirchhoff's integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) [1] is a surface integral to obtain the value of the solution of the homogeneous scalar wave equation at an arbitrary point P in terms of the values of the solution and the solution's first-order derivative at all points on an arbitrary closed surface (on which the integration is performed) that ...
Huygens–Fresnel–Kirchhoff principle: ... Kirchhoff's diffraction formula = ... The Cambridge Handbook of Physics Formulas. Cambridge University Press.
The Huygens–Fresnel principle provides a reasonable basis for understanding and predicting the classical wave propagation of light. However, there are limitations to the principle, namely the same approximations done for deriving the Kirchhoff's diffraction formula and the approximations of near field due to Fresnel. These can be summarized ...
Fresnel equations; Friedmann equations; Gauss's law for electricity; Gauss's law for gravity; Gauss's law for magnetism; Gibbs–Helmholtz equation; Gross–Pitaevskii equation; Hamilton–Jacobi–Bellman equation; Helmholtz equation; Karplus equation; Kepler's equation; Kepler's laws of planetary motion; Kirchhoff's diffraction formula; Klein ...
Under spatially coherent illumination and an intermediate distance between sample and detector an interference pattern with "Fresnel fringes" is created; i.e. the fringes arise in the free space propagation in the Fresnel regime, which means that for the distance between detector and sample the approximation of Kirchhoff's diffraction formula ...
The sector contour used to calculate the limits of the Fresnel integrals. This can be derived with any one of several methods. One of them [5] uses a contour integral of the function around the boundary of the sector-shaped region in the complex plane formed by the positive x-axis, the bisector of the first quadrant y = x with x ≥ 0, and a circular arc of radius R centered at the origin.