Thanks Keoki. Interesting that they come out similar, since usually the horizontal source size is so much larger than the vertical. Or maybe there is an intermediate slit that turns it into a round beam. For an incoherent source, the formula I know for the coherence length is lambda D/(2 pi sigma) (p. 66 of "Undulators, Wigglers, and their Applications" by Onuki and Elleaume) lambda is wavelength, D is distance to source, and sigma is size of source.

Hi, we have bending magnet source at the TopoTomo bemaline. The vertical coherent length is about 20 um. Of course the larger cohent lenght would be better but it depends on the aplication you want to do. For the phase contrast mode in so called edge regime this is enough. We can improve the coherent lenght by closing the source slit (4 m downstream from the source) but this cost a flux.

If you want do do quantitative phase contrast imaging so to retrieve refraction index distribution at the sample position from the measured phase map you need to have at best case full coherent illumination.

The sorce size and the souce to sample distance and the sample to detector distace also influence the penumbral bluring. And then this can limit then the resolution.

Ok, thanks for the further answers, Keoki and Patrik. It sounds like in both cases, you have a kind of slit or pinhole to reduce the beam size (and flux as a side effect) and thus increase the coherence.

I'm also not so familiar with the beamline design part. Maybe it is a bit complicated to go from the coherence of the initial source in the undulator (or bending magnet) to the coherence of the beam at the sample. But one of the arguments for why the X-FELs will be good is better coherence properties. But we still have some ability to control the emission from these 3rd generation sources- e.g. decreasing the vertical emittance. But it also may depend on whether you choose the x-ray energy right on a peak of one of the harmonics (for undulator radiation). Off peak, the radiation is non-Gaussian and the meaning of diffraction limit may be different.

Following up on this topic, I spoke with someone from ID1 at ESRF and found out that the coherence size there is typically 20 microns horizontally and 60 microns vertically. I was given this reference:

http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-20-19223 by Mastropietro et. al.

and the coherence length measurements described here

http://scripts.iucr.org/cgi-bin/paper?ie5039

I think the issue of the coherence addressed in the answers was mostly concerning the transverse coherence (the longitudinal coherence depends on the monochormaticity). This transverse coherence can be easily calculated (horiz. and vert.) knowing the source size and the distance to the source. What is important for the experiments using highly coherent X-rays (there is always some coherence, if not no X-ray diffraction experiments will be possible) is the coherent length, but also the coherent flux. And depending of the experiment, one or the other can be privileged. Let me give some examples, maybe point also some issues in addition to the ones already mentioned by the other contributors, reflecting my views on the subject:

- in a full field imaging experiments with coh. beam one might want the largest full field accessible, so increasing the coh. values might be asked / useful.

- in full field imaging (ptychography approach), large area samples can be measured by superposing small area images in a raster scanning approach (the superposition has to be rather important). Each small area image is obtained using a coherent beam, so one could imagine that larger the coherence length is, larger the probed area will be so the

acq. of large images will take less time (less raster points to make).

- in a lot of imaging exp. (CDI, coherent diffraction imaging), the aim is to image single / isolated micro and/or nano-objects. Their whole volume have to be illuminated coherently for this aim, so in principle a lateral coherence length of few microns would be largely enough in a lot of cases. In some experiments of 'holography' with a reference object, the distance between this one and the object to investigate is also in the few um range. This is rather easy to achieve at a synchrotron source (ex slitting the beam somewhere upstream the sample with a pinhole). Of course, this reduces drastically the photon flux illuminating the sample. But the scattering volume (the volume of the sample) is very small, below 1 um3 or way below for the (single) nanostructures, so these experiments are extremely 'photon hungry'. Each photon one can have, is to be taken. Focusing the beam can be an option. This brings me then to the next example

- focusing to nanometer sizes (few 100 nm or below 100 nm) (ex. of an X-ray Zone Plate, ZP). I believe this is the example given at ID01 / ESRF. First, a good quality ZP have to be used (parameters like % efficiency, aperture, focal distance, secondary focusing, last zone width in the 10nm range, ... have to be thoroughly balanced; such ZPs are easier to manufacture for the soft X-rays, but not so easy for the hard X-rays, in the several 10keV range). Then in order to achieve the smallest spot after focusing (diffr. limited), the ZP has to be illuminated coherently ! Of course, since one wants as much flux as possible in the tiny spot, one would like that the illuminated area covers the most of the ZP, i.e. that the coherence lengths in the incoming X-ray beams, hitting the ZP, are increased. This is, at least forme, one of the strong arguments (but from many others) demanding an increased coh. for extreme focusing.

Hope that you will find these reflections useful

Bests

cristian