Huygens’ principle diffraction

The wave function v /ex (r) of electrons at the exit face of the object can be considered as a planar source of spherical waves according to the Huygens principle. The amplitude of diffracted wave in the direction given by the reciprocal vector g is given by the Fourier transformation of the object function, i.e. 

Figure 14. (a) Schematic of Huygens Principle showing construction of a new wave front 2 from the preceeding wave front S 0>) plane wave front incident on a slit of width b (c) diffraction for case where b < (d)... 

We can use Huygens principle to explain qualitatively the essential features of diffraction, but a quantitative treatment involves casting Huygens principle into a precise mathematical form, the Fresnel-Kirchhoff formula ... 

Electron diffraction is a collective elastic scattering phenomenon in which the electrons are scattered by atoms in a regular array or a crystal. Secondary waves are generated when an incoming plane electron wave interact with the atoms. Analogous to Huygens principle for diffraction of light waves, the secondary waves interfere with each other, and diffraction patterns thus can be obtained. 

Hence, by applying the Huygens principle to aplane just beyond the sphere ([200], Chap. 11 Sect. 3), the anomalous diffraction scattering amplitudes yield ... 

Spectral selection techniques discussed so far are based on bulk material properties and on interference phenomena. The spectral selection effect of gratings rests on diffraction phenomena. Diffraction theory has its roots in the Huygens (1690) principle, which considers every point of a wavefront as a source of a secondary... 

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