Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method

Abstract

We report the experiments and procedures to successfully record and reconstruct coherent diffraction patterns at sub-10-nm resolution from noncrystalline samples by using synchrotron x rays with a wavelength of 2 \AA{}. By employing the oversampling phasing method, we studied the quality of image reconstruction of experimental diffraction patterns as a function of the oversampling ratio (a parameter to characterize the oversampling degree). We observed that the quality of reconstruction is strongly correlated with the oversampling ratio, which is in good agreement with theory. When the oversampling ratio is around 5 or larger, the reconstructed images with high quality were obtained. When the oversampling ratio is less than 5, the images became noisy. When the oversampling ratio is very close to or less than 2, the images were extremely noisy and barely recognizable. We believe these results will be of importance to the experiments of imaging nanocrystals and noncrystalline samples using coherent x-ray, electron, or neutron diffraction.