Beam transit effects in single molecule coherent diffraction

We explore how phase and amplitude gradients, which are almost inevitable in a coherent illumination probe, affect the atomic reconstruction of an isolated molecule based on diffraction intensities. By modeling the probe as a defocused Gaussian source, we show that structural distortion can be introduced in the reconstructed object if plane-wave illumination is assumed in the diffraction phase-retrieval algorithm. For the plane-wave approximation, we conclude that the standard deviation ${\ensuremath{\sigma}}_{d}$ describing the source width should be such that ${\ensuremath{\sigma}}_{d}\ensuremath{\sim}10{R}_{c}$, where ${R}_{c}$ is the nominal radius of the molecule. In a pulsed source, where diffraction data are obtained when the moving molecule is at an instantaneous location within the illumination window, the effects of wave front curvature can be reduced by defocusing the illumination. This improvement comes at the expense of a weaker diffraction signal. For the three-dimensional reconstruction of a molecule, diffraction patterns from many different orientations of identical molecules are required. Since phase-retrieval methods are inherently solving for the probe plus the molecule, irreproducibility of wave front curvature or molecule location within the probe will introduce additional degrees of freedom to the structure solution problem.