Effectiveness of iterative algorithms in recovering phase in the presence of noise

Inversion of coherent X-ray diffraction patterns allows the imaging of three-dimensional density distributions. The recovery of such shapes often requires application of iterative algorithms, such as Fienup's error reduction or hybrid input/output. Since the measurement of such a pattern records the intensity in reciprocal space, any errors due to noise will probably not have a straightforward impact on the final real-space result. In this paper, the effect of the types of noise common in coherent X-ray diffraction (CXD) experiments, counting statistics, scatter from alien particles and detector noise, on the recovered real-space density projection is explored by simulating a two-dimensional CXD pattern and adding noise. It is found that an R factor measuring the reproducibility between the best and second-best real-space result is a leading indicator of performance.