Friedel's law

Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.

Given a real function f ( x ) , its Fourier transform

has the following properties.

where F ∗ is the complex conjugate of F .

Centrosymmetric points ( k , − k ) are called Friedel's pairs.

The squared amplitude ( | F | 2 ) is centrosymmetric:

The phase ϕ of F 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.