Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.
Given a real function , its Fourier transform
has the following properties.
where is the complex conjugate of .
Centrosymmetric points are called Friedel's pairs.
The squared amplitude () is centrosymmetric:
The phase of is antisymmetric: .
Friedel's law is used in X-ray diffraction, crystallography and scattering from real potentials within the Born approximation. Note that a twin operation ( Opération de maclage) is equivalent to an inversion centre and the intensities from the individual reflections are equal under Friedel's law.Friedel G (1904). "Étude sur les groupements cristallins". Extract from Bullettin de la Société de l'Industrie Minérale, Quatrième série, Tomes III et IV. Saint-Étienne: Societè de l'Imprimerie Thèolier J. Thomas et C.Friedel G. (1923). Bull. Soc. Fr. Minéral. 46:79-95.
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