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 potentials within the Born approximation. Note that a is equivalent to an inversion centre and the intensities from the individual reflections are equal under Friedel's law.