Phase retrieval of diffraction patterns

In the phase retrieval (PR) calculations of experimentally obtained diffraction patterns, it is not easy to find the correct electron density maps due to the lack of diffraction patterns around the zero-scattering angle and the Poisson noise in detecting the X-ray photons. In this chapter, we present some approaches to obtain the correct electron density maps from experimental diffraction patterns. The first is the multivariate analysis of a large number of PR maps. The second is the introduction of a similarity score to extract the correct electron density maps. The third is the dark-field PR method applied to diffraction patterns with missing small-angle regions. The algorithms presented would be helpful in solving the phase problem in the structural analyses of non-crystalline particles.