View source for Hybrid input-output algorithm

== Definition ==

An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.

Let <math>\rho^{(n)}</math> be a trial scattering density in the ''n''th iteration cycle. Let <math>\rho'^{(n)}</math> be a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:

<br>[[Image:CF_4.png|500px|center]]<br>

In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion.

[[Category: Structure determination]]