Dear Ethan, Zhijie and Keller, Thank you so much for your detailed reply! Now I think I have a much deeper view of this problem and understand the relationship between X-ray, XFEL and EM much better. I did learned a lot from your replies!
Best, Chen On Wed, Jan 21, 2015 at 7:51 AM, Keller, Jacob <kell...@janelia.hhmi.org> wrote: > Phases can be deduced mathematically from a continuous transform, a la > David Sayre’s and others’ work. Compared to a crystallographic pattern, a > continuous pattern has huge amounts of information—every pixel (roxel?) > would be equivalent to a reflection, so instead of having ~10^4-5 data > points you would have, say, 10^8-12, all to define ~10^3-4 atoms. And no > b-factors to fit at 100K, since the molecule would not be moving at that > temp. Of course this would be totally impossible to actually measure, at > least for now (!). > > > > JPK > > > > > > > > *From:* CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] *On Behalf Of *Chen > Zhao > *Sent:* Tuesday, January 20, 2015 11:47 PM > *To:* CCP4BB@JISCMAIL.AC.UK > *Subject:* Re: [ccp4bb] A basic question about Fourier Transform > > > > Dear Steven, > > Thank you for your reply! I understand that it is nearly impossible to > measure the diffraction of a single molecule, and I am just bringing this > up as a thought experiment to help understand the basics in > crystallography. But I never thought that some molecules actually allow > such measurement because you can burn it over and over again without severe > damage. Thanks a lot for this piece of information. > > But for the phase problem, the difference is that, you can have magnetic > lens for the electrons in EM, but you cannot have any lenses for X-ray > beam. This is why I am still confused about this point. > > Thanks a lot again, > > Chen > > > > On Tue, Jan 20, 2015 at 11:21 PM, Steven Chou <stevezc...@gmail.com> > wrote: > > I would say you cannot measure the diffraction pattern of a single > biological molecule accurately thus far, because biological molecules are > not strong scatters and can be damaged easily. For other molecules, > actually you can! > > In high-resolution electron microscopy, the diffraction pattern in the > back focal plane is actually the diffraction pattern of a projection of > your sample, which is usually composed of one to several hundred biological > molecules. For biological molecules, this pattern usually is dampened to > almost zero at a resolution between 30A-4A (actual resolution, not > theoretical); for some metal compounds, the resolution can reach up to 1 A, > or even better. > > The diffraction pattern in the back focal plane is the Fourier transform > (achieved by a convex lens) of the a 2D projection of your sample. If you > apply another Fourier transform (using another convex lens) to the > diffraction pattern, you can get the 2D image of your sample (which > contains both amplitude and phase). That is, in single particle EM (imaging > mode), people don't have the phase problem. In diffraction mode (2D > electron crystallography), only the diffraction pattern (intensity) is > recorded, so they also have the phase problem. > > > > HTH, > > > > Steven > > > > On Tue, Jan 20, 2015 at 10:18 PM, Chen Zhao <c.z...@yale.edu> wrote: > > Dear all, > > I am sorry about this slightly off-topic question. I am now a graduate TA > for crystallography course and one student asked me a question that I > didn't ask myself before. I don't have enough knowledge to precisely answer > this question, so I am seeking for help here. > > 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? > > Thank you so much for your attention and your help in advance! > > Best, > Chen > > > > -- > > Steven Chou > > > > > > >
