Phasing diffuse scattering. Application of the SIR2002 algorithm to the non-crystallographic phase problem

A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV energy. The reconstructed image ®ts well with a scanning-electron-microscope (SEM) image of the same sample. The algorithm, which uses only the density modi®cation portion of the SIR2002 program, is compared with the results obtained via the Gerchberg± Saxton±Fienup HiO algorithm. The new algorithm requires no knowledge of the object's boundary and proceeds from low to high resolution. In this way, the relationship between density modi®cation in crystallography and the HiO algorithm used in signal and image processing is elucidated.