Coherence and sampling requirements for diffractive imaging

Coherent Diffractive Imaging (CDI) allows images to be reconstructed from diffraction patterns by solving the non-crystallographic phase problem for isolated nanostructures. We show that the Shannon sampling of diffraction intensities needed in CDI requires a coherence width about twice the lateral dimensions of the object, and that the linear number of detector pixels fixes the energy spread needed in the beam. The Shannon sampling, defined by the transform of the periodically repeated autocorrelation of the object, is related to Bragg scattering from an equivalent crystal, and shown to be consistent with the sampling of Young's fringes established by scattering from extreme points in the object. The results are relevant to the design of diffraction cameras for CDI and plans for femotosecond X-ray diffraction from individual proteins.