Friedel's law

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 potential within the Born approximation. Note that a twin operation (a.k.a. Opération de maclage) is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedel's law.

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