No one is talking about absolute phases of F_hkl. Only the relative phases are important.

To measure the (difference of) phase of a diffracted beam it is necessary to measure the difference of path between this beam and that of a reference one. This can be done in principle, but because the difference of path is of the order of amstrongs it would take a long time and the use of sophisticated instrumentation. Taking into account that the diffraction pattern of a single crystal may contain thousands of diffracted beams, a routine measurement of the phases is practically impossible.

That sounds very pessimistic indeed. What are the comments of the guys who are developing coherent diffraction at the highly advanced synchrotron sources?

Looking forward to answers from "experts"

Have a look at the following publications:

http://elifesciences.org/content/2/e01345

http://www.sciencedirect.com/science/article/pii/S0959440X14000268

Yes Jurgen, but the question is another and concerns the direct measurement of phases. In the microED method you quote, electron instead of X-ray diffraction is used but "Once a complete data set is obtained, the structure can be phased and refined using standard programs for X-ray crystallography such as PHENIX" I read in this article

http://cryoem.janelia.org/uploads/image/pdfs/2014_nannengagonen.pdf

There is no real phase problem in electron diffraction. It is just because the electron beams can be focused and images of structure can be produced that contain the phase information. We cannot do that with conventional X-ray and neutron diffraction because of the problem of producing direct images. However electron diffraction has other problems like strong dynamical effects.

In coherent diffraction you can over sample the data by measuring in between the Bragg peaks. While this does not allow a direct measurement of phases, it does allow you to overcome the "phase problem" in the sense of inverting the Fourier transform: see eg:

http://xrm.phys.northwestern.edu/research/pdf_papers/2004/miao_annrevbiophys_2004.pdf

It goes back to work from Sayre (Sayre D. 1952. Implications of a theorem

due to Shannon. Acta Crystallogr. 5:843) and was more-or-less demonstrated by Perutz on shrinkage states of Haemoglobin in the 1950's, before the heavy atom method was invented.

There are some technical challenges to be overcome, but phasing has already been done with FEL data and conventional SAD methods:

"De novo protein crystal structure determination from X-ray free-electron laser data", Barends et al Nature 505, 244–247 (09 January 2014) doi:10.1038/nature12773

Presumably the area will develop in the coming years - dealing with millions of diffraction images is a lot of work!

In classical crystallography you rely on the number of measured intensities being much larger than the number of parameters in the crystal structure - a kind of "oversampling" that allows to determine the phases of the diffraction peaks more or less as a by-product of the refined crystal structure.

The coherent diffraction techniques available today do something very similar. You record one or several intensity patterns with unknown phase, and from an over-determined data set and some additional information ("support"=areas of known zero intensity, or known sample displacements) you refine a model of the sample and with that the phase of the signal. Usually this is done in a self-consistent way by running a reconstruction algorithm through many cycles. Ptychography is one of these methods.

The length scales that there methods address (10-100nm) are not quite in the crystallography range, they aim more at determining the shape and structure of nanoobjects. They have been applied with Bragg-diffracted data, and thus do take

crystallographic information into account, e.g. the phase shift across a defect.

I cannot see any direct extension of these methods to classical crystallography in general and solving the phase problem in particular. You can profit from coherence by observing interference with a reference beam. For wide-angle scattering this is somewhat tricky to implement. Interference between different Bragg reflections has been shown in the 3-beam case (Qun Shen et al at CHESS, without any use of coherence). Without such tricks, again, that is not exactly straight-forward.

Having said this, coherent scattering from isolated biomolecules seems to show great potential.

Short answer, yes with the coherent light of FEL's it is possible to solve ab initio a phase problem in macromolecular crystallography.

In more detail it is currently for technical reasons very tricky. Therefore there is no general solution for the phase problem. Due to the use of a 2D detector the phase information is gone as for classical x-ray crystallography. The easiest experiment to regain ab initio the phase information is the SAD experiment. Here are two problems to overcome, currently at the most powerful FEL at SLAC in liquid jet or LPC jet thousends of diffraction pattern have to be determined and the shot to shot energy varies, which for this experiment is a big disadvantage. New FEL's like the european will be here in the long run way better perform.

Dear Raimund, I am afraid I am missing your point. Could you please explain (a) how coherent light at FELs helps with phase determination by SAD or any other anomalous scattering technique, and (b) what difference the use of a 2D detector makes, other than data acquisition time, and what other detector could avoid the loss of phase information..

In principle FEL's can for classical phase determination(SAD,MAD) not doing better than conventional synchrotrons. The progress in the long run can be the simultaneous use of detectors to reconstruct the shape of nano/ microcrystals, as we have shown this in Chapman et al. (2011) Nature,470 (7332), 73-77.

The advent of new FEL's and detectors will explore these possibilities.

Then may I conclude that coherent diffraction cannot measure the phase directly. One may then perhaps ask what is the real advantage of coherent diffraction over normal X-ray diffraction? I am not talking about solving protein structures from protein molecules or very small nanocrystals by collecting 3,000,000 reflections or so from the sample before its get radiation damaged at XFEL sources but the technique of direct phase determination. Everyone knows that in most cases the phases can be determined by the several tricks the crystallographers developed for solving their structures but all these do not measure the phases directly.

If I understand correctly then phases cannot be determined directly by coherent diffraction but can be retrieved by using the age-old idea of D. Sayre (Acta Cryst. 5, 843 (1952) based on the pioneering work of C.E. Shannon (Proc. Ins. Radio Engrs., N.Y. 37, 10 (1949). Coherent diffraction enables us to get better data for this method. Can someone explain me in more details?

As far as I can see coherent diffraction has no real advantages for standard crystallography.

Having a large coherence length in direct space means you have a very high resolution in reciprocal space. With a fully coherent incident beam you can therefore determine mesoscopic features such as nanoparticle shapes that are not visible in the incoherent average of many such particles (nicely seen in the Chapman et al paper cited above, Fig 2, or in I A Vartanyants and I K Robinson, JPCM (2001) http://iopscience.iop.org/0953-8984/13/47/305/). The incoherent average blurs out the fringes that you need to determine the shape. The maximum length scale accessible is on the order of the coherence length, provided that you have high enough detector resolution. The minimum length scale=resolution depends on the maximum scattering angle, as usual.

No one is talking about absolute phases of F_hkl. Only the relative phases are important.