Experimental lensless soft-X-ray imaging using iterative algorithms: phasing diffuse scattering

Images of randomly placed two-dimensional arrays of gold balls have been reconstructed from their soft-X-ray transmission diffraction patterns. An iterative hybrid input-output (HiO) algorithm was used to solve the phase problem for the continuous distribution of diffuse X-ray scattering. Knowledge of the approximate size of the clusters was required. The images compare well with scanning electron microscope (SEM) images of the same sample. The use of micrometre-sized silicon nitride window supports is suggested, and absorption filters have been used to allow collection of low spatial frequencies often obscured by a beam stop. This method of phasing diffuse scattering may have application to scattering from individual inorganic nanostructures or single macromolecules.