title: Friedel's law
text: # 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
  
      $F(k)=\int _{-\infty }^{+\infty }f(x)e^{ik\cdot x}dx$
  
  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 $\phi$ 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.
  
  