Electron-density histograms and the phase problem.

The specific properties of the range of possible electron-density values may serve as useful additional information for the determination and refinement of structure-factor phases. Fourier synthesis histograms (showing the spectra of frequencies of different possible values) produce the most adequate representation of these properties. The mathematical background and practical uses of these histograms are discussed. The investigation provides new information on some traditional methods of phase refinement, including density-modification procedures, maximization of Cochran's integral value and other techniques.