Feasibility of 3D reconstructions from a single 2D diffraction measurement

We comment on the recent manuscript by Raines et al. [arXiv:0905.0269v2] (now published in Nature, vol. 463, p. 214-217, 2010), which suggests that in certain conditions a single diffraction measurement may be sufficient to reconstruct the full three-dimensional density of a scatterer. We show that past literature contains the tools to assess rigorously the feasibility of this approach. We question the formulation of the reconstruction algorithm used by the authors and we argue that the experimental data used as a demonstration is not suitable for this method, and thus that the reconstruction is not valid. This second version was produced for documentation purposes. In addition to the minimally modified original comment, it includes in appendix a subsequent reply to one of the authors (J. Miao).