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In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens.
Differences between Fraunhofer diffraction and Fresnel diffraction. The near field itself is further divided into the reactive near field and the radiative near field. The reactive and radiative near-field designations are also a function of wavelength (or distance). However, these boundary regions are a fraction of one wavelength within the ...
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.
The Fraunhofer diffraction equation is an approximation which can be applied when the diffracted wave is observed in the far field, and also when a lens is used to focus the diffracted light; in many instances, a simple analytical solution is available to the Fraunhofer equation – several of these are derived below.
The result is the Fraunhofer approximation, which is only valid very far away from the object + + Depending on the size of the diffraction object, the distance to the object and the wavelength of the wave, the Fresnel approximation, the Fraunhofer approximation or neither approximation may be valid. As the distance between the measured point of ...
Fraunhofer diffraction returns then to be an asymptotic case that applies only when the input/output propagation distance is large enough to consider the quadratic phase term, within the Fresnel diffraction integral, negligible irrespectively to the actual curvature of the wavefront at the observation point. [5]
There are various analytical models which allow the diffracted field to be calculated, including the Kirchhoff diffraction equation (derived from the wave equation), [16] the Fraunhofer diffraction approximation of the Kirchhoff equation (applicable to the far field), the Fresnel diffraction approximation (applicable to the near field) and the ...
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.