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In electron diffraction, a diffraction pattern is produced by the interaction of the electron beam and the crystal potential. The real space and reciprocal space information about a crystal structure can be related through the Fourier transform relationships shown below, where () is in real space and corresponds to the crystal potential, and () is its Fourier transform in reciprocal space.
Because diffraction is the result of addition of all waves (of given wavelength) along all unobstructed paths, the usual procedure is to consider the contribution of an infinitesimally small neighborhood around a certain path (this contribution is usually called a wavelet) and then integrate over all paths (= add all wavelets) from the source to the detector (or given point on a screen).
In a digital camera, diffraction effects interact with the effects of the regular pixel grid. The combined effect of the different parts of an optical system is determined by the convolution of the point spread functions (PSF). The point spread function of a diffraction limited circular-aperture lens is simply the Airy disk. The point spread ...
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Diffraction patterns arise because the paths sum differently at different detector positions. According to these principles the Airy disk and diffraction pattern can be computed numerically by using Feynman photon path integrals to determine the detection probability at different points in the focal plane of a parabolic mirror. [14]
Kinematic diffraction is an approximation for diffraction of waves. It assumes that the waves are only scattered once, neglecting multiple scattering . For linear wave equations , it i volves summing the contribution of the partial waves emanating from different scatterers, where only the incident field drives the scattering.
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays , neutrons or electrons and the regular lattice are atomic crystal structures or nanometer -scale multi-layers or self-arranged systems.
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.