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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 Fraunhofer diffraction equation is a simplified version of Kirchhoff's diffraction formula and it can be used to model light diffraction when both a light source and a viewing plane (a plane of observation where the diffracted wave is observed) are effectively infinitely distant from a diffracting aperture. [6]
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 ...
The intensity profile can be calculated using the Fraunhofer diffraction equation as = (), where () is the intensity at a given angle, is the intensity at the central maximum (=), which is also a normalization factor of the intensity profile that can be determined by an integration from = to = and conservation of energy, and ...
A geometrical arrangement used in deriving the Kirchhoff's diffraction formula. The area designated by A 1 is the aperture (opening), the areas marked by A 2 are opaque areas, and A 3 is the hemisphere as a part of the closed integral surface (consisted of the areas A 1, A 2, and A 3) for the Kirchhoff's integral theorem.
Similar equations can also be derived for the obscured Airy diffraction pattern [16] [17] which is the diffraction pattern from an annular aperture or beam, i.e. a uniform circular aperture (beam) obscured by a circular block at the center.
In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement. When the diffracted wave is considered to be in the Fraunhofer field. However, the validity of the Fresnel diffraction integral is deduced by the ...
Now, in Fraunhofer diffraction, ′ / is small, so ′ (note that ′ participates in this exponential and it is being integrated). In contrast the term e − i k x 2 2 z {\displaystyle e^{\frac {-ikx^{2}}{2z}}} can be eliminated from the equation, since when bracketed it gives 1.