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Kirchhoff's diffraction formula : ウィキペディア英語版
Kirchhoff's diffraction formula
Kirchhoff's diffraction formula (also Fresnel–Kirchhoff diffraction formula)
can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave passes through an opening in an opaque screen. The equation is derived by making several approximations to the Kirchhoff integral theorem which uses Green's theorem to derive the solution to the homogeneous wave equation.
==Derivation of Kirchhoff's diffraction formula==

Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's theorem to derive the solution to the homogeneous wave equation at an arbitrary point P in terms of the values of the solution of the wave equation and its first order derivative at all points on an arbitrary surface which encloses P.
The solution provided by the integral theorem for a monochromatic source is:
:U(P) = -\frac \int_ \left(U \frac \left( \frac \right) - \frac \frac \right )dS
where ''U'' is the complex amplitude of the disturbance at the surface, ''k'' is the wavenumber and ''s'' is the distance from P to the surface.
The assumptions made are:
* ''U'' and ∂''U''/∂''n'' are discontinuous at the boundaries of the aperture
* the distance to the point source and ''s'' are much greater than λ

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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