Hi Jacob, Thanks a lot for your reply! Yes, by comparable data quality I did mean the comparable resolution and SNR. I now understand the original question and kinda confirm what I thought. But I am also learning myself and I don't quite get why the continuous sampling would get rid of the phase problem. My first thought would be that mathematically speaking, the difference between solving the structure from a crystal diffraction pattern and solving the structure from a single molecule diffraction pattern only means the transition from a discrete Fourier summation to a continuous Fourier integral, but the phase term is always there. I am sorry for my lack of knowledge and I only knew the very basics in the sampling theorem many years ago.
Another related question is, do different crystal lattices sample the reciprocal space equally well (or lose the same amount of information)? My intuition is yes because of the symmetry in the real space stays in the reciprocal space, but maybe I am wrong. Sorry for keeping bothering, Chen On Tue, Jan 20, 2015 at 10:41 PM, Keller, Jacob <kell...@janelia.hhmi.org> wrote: > >The question is, as I rephrased it, assuming we are able to measure > the diffraction pattern of a single molecule with acceptable accuracy and > precision (comparable to what we have now for the common crystals), is it > better than we measure the diffraction spots from a crystal, given that the > spots are just a sampling of the continuous pattern from a single molecule > and there is loss of information in the space between the spots that are > not sampled by the lattice? Of course this is more of a thought experiment, > so we don't need to consider that all measurement is discrete in nature > owing to the limitation of the pixel size. I kinda agree with him and I > have a feeling that this is related to the sampling theorem. I do > appreciate your valuable comments. If this is not true, why? If this is > true, what is its effect on electron density? > > This question depends on how you set your criteria for the goodness of > the single-molecule data; in a way by saying the data quality is comparable > to crystals, the question is tautological, since the cases would by > stipulation be the same. If you mean the resolution would be equal, and all > amplitudes would be of SNR similar to crystal data, of course the > continuously-sampled version would be far better. There would be no phase > problem (sampling theorem), and maps would be outstanding. > > > > This type of thing was, I think, the original vision of the XFEL > projects—you could check out those early papers for more details. > > > > JPK > > > > >
