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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 ...
When a beam of x-rays illuminates a crystal, a detector in the far field measures the Fraunhofer diffraction pattern given by the intensity of the Fourier transform of the refracted near field. These diffraction orders of crystals for x-rays where discovered by Von Laue and are used to study the atomic structure of crystals.
If the conditions for Fraunhofer diffraction are not met, it is necessary to use the Fresnel diffraction approach. The diffraction pattern at the right is taken with a helium-neon laser and a narrow single slit. The pattern below was made with a green laser pointer.
5 de mar. de 2022 · (i) Fraunhofer diffraction takes place when \(\ z / a >> a / \lambda\) – the relation which may be rewritten either as \(\ a<<(z \lambda)^{1 / 2}\), or as \(\ k a^{2}<<z\). In this limit, the ratio \(\ k x^{, 2} / z\) is negligibly small for all values of \(\ x^{\prime}\) under the integral, and we can approximate it as
Originating along the fronts of (A) circular waves and (B) plane waves, wavelets recombine to produce the propagating wave front. (C) The diffraction of sound around a corner wavelets recombine to produce the arising from Huygens' wavelets. propagating wavefront.
Fraunhofer diffraction patterns can qualitatively explained by considering directions in which destructive and constructive interference occurs. Consider two mutually coherent point sources \(S_{1}, S_{2}\) on the \(x\) -axis as shown in Figure \(\PageIndex{1}\).
Fraunhofer diffraction, on the contrary, describes the diffraction pattern observed in the far field (i.e. at large values of L) where geometric optics is completely inapplicable. We will postpone Fresnel diffraction until a later date, and concentrate here on the far-field case.
Diffraction is a strong function of source coherence, and its impact is discussed. It is demonstrated that Fraunhofer diffraction is mathematically identical to the Fourier transform integral, and this is used to calculate diffraction from rectangular and circular apertures as well as arrays of apertures.
Fraunhofer diffraction deals with the limiting cases where the source of light and the screen on which the pattern is observed are effectively at infinite distances from the aperture causing the diffraction. The more general case where these restrictions are relaxed is called Fresnel diffraction.
Topics: Fraunhofer diffraction; review of Fourier transforms and theorems. Instructors: George Barbastathis, Colin Sheppard
