# Hybrid input-output algorithm

### From Online Dictionary of Crystallography

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

In crystallography, the support is usually not known , and a dynamical support must be used, *i*.*e*. the support is newly defined in each iteration cycle based on a predefined criterion.