1. ERL & Coherent X-ray Applications
Qun Shen
Cornell High Energy Synchrotron Source (CHESS)
Cornell University
Talk Outline
Introduction to x-ray coherence
In this last talk of the morning, I will be focusing on coherent imaging and diffraction applications using the eventual phase-2 ERL machine.
Coherent x-ray applications
Desired ERL properties
Options and improvements
Conclusions

2. Source Emittance and Brilliancex x’
Integrated total flux Fn
Phase-space Emittance:
EM wave: E(r, t) = E0 ei(k·r-wt) x x’ sx
sx’
ex = sx sx’ y y’ sy
sy’
ey = sy sy’ t E st sE
et = st sE / E
Brilliance: photon flux density in phase-space
B = Fn
(2p)2 ex ·ey
Average
B = Fn
(2p)3 ex ·ey·et ^
Peak

3. Spatial (Transverse) Coherenceq
Dl = q · 2s = l/2
2s'
=>
2q · 2s ~ l
q  s'
=>
X-ray beam is spatially coherent
if phase-space area 2ps’s < l/2
Diffraction limited source: 2ps's = l/2 or e = l/4p
Almost diffraction limited: 2ps's ~ l or e ~ l/2p

4. Temporal (Longitudinal) Coherence
l+Dl
Coherence length: lc = l2/Dl
Coherence time: Dtc = lc/c
Temporally coherent source:
pulse length FWHM t £ Dtc
lc = l2/Dl
uncertainty: t ·Dn £ 1
t ·DE £ h
For l = 1 Å, Dl/l = 10-4 :
lc = 1 mm, Dtc = 1 mm / 3x108 m/s = 3.3 fs
Degeneracy Parameter dD
= Number of photons in
coherent volume
= Number of photons within
single quantum mode
X-ray optics can modify Dl/l, but extinction length (~100mm) limits to Dl/l = => Dtc= 330 fs
ERL with st = 100 fs pulses coupled with 10 meV x-ray monochromator could mean temporal coherence at 10 keV.

5. Transverse Coherence from Undulatorq L
q = l/2d
Example: APS, L =2.4m, l =1.5Å
sr' = 13.1 mrad
dy = 2.35x21mm, sy' = 6.9 mrad
q = 1.5 mrad, Q = 2.35x14.8 mrad
=> pc(vertical) = 4.3%
dx = 2.35x350mm, sx' = 23.1 mrad
q = mrad, Q = 2.35x26.6 mrad
=> pc(horizontal) = 0.15%
=> pc (overall) = 0.006%
A portion, q/Q in each direction,
of undulator radiation is spatially
coherent within central cone
Coherent fraction pc: depends
only on total emittances
ERL: pc ~ 20% (45% in x or y)

6. ERL Spatial Coherence
Diffraction 8keV (0.123Å)
ESRF emittance
(4nm x 0.01nm)
ERL emittance (0.015nm=0.15Å)
As we 've heard this morning that, the phase-2 ERL is high-brilliance hard x-ray source with high degree of spatial coherence. Let 's just take a closer look at what this really means.
Here I show the same schematic as you 've seen earlier, of the transverse emittances or the ERL source, as compared to a typical third-generation synchrotron source such as the ESRF. Let us just focus on the high-coherence option, which is represented by the small red dot in the middle here.
If I magnify this region, then you would see the ERL emittances represented by this red circle. In the middle of this circle, I 've plotted on the same scale the diffraction-limit for 8 keV photons. So what this shows is that the 8keV photons from the ERL are almost diffracted limited.
If we use the more precise definitions of diffraction limit based electron beam phase-space areas, then we can say that the phase-2 ERL is a diffraction limited source for x-rays photons below 6.6 keV and is almost diffraction limited all the way to 13 keV.
Diffraction limited source: 2ps's = l/2 or e = l/4p
Almost diffraction limited: 2ps's ~ l or e ~ l/2p
Phase II ERL: diffraction-limited source E < 6.6 keV almost diffraction-limited to 13 keV

7. X-ray Coherence Workshop Program
So what types of experiments can we do using this type of coherent source?
We have thought about about several areas of coherence experiments.
The first area, as you 've just heard from Joel's talk, is the photon correlation spectroscopy or speckle experiments. This of course requires a fully coherent beam. By the way here is my color coded arrow that show the different degree of coherence requirements. So this is something Joel had covered already, so I won't repeat that area.
What I am going focus on is the area of x-ray imaging microscopy. I should state at the very start, that not every form of x-ray microscopy requires a fully coherent beam. So what I am going to talk about are really those types that do require a high degree of coherence. These include phase-contrast imaging and microscopy, far-field diffraction microscopy, and holographic techniques development.
For any of these full-field microscopies, one incorporate the timing aspect in an experiment, which would lead to so called flash imaging studies of time evolution of the specimen. But I don't think I 'll have time to elaborate on that, so I just want to mention it in this introduction.
In principle, x-ray imaging and microscopy can only provide 2D information. So in order to obtain 3D structural information, one usually needs to rotate the sample and take multiple images at different sample orientations. This is the so-called tomography technique, so the natural extension of the phase imaging techniques would be the phase-contrast tomography for 3D structure images.
Finally, at the end of my talk, I will show a few ideas of using coherence in crystalline materials, or in crystallography.

8. X-ray Microscopy Two types: full field & scanning
ESRF ID21: TXM 3-6 keV
ESRF ID21: SXM 2-10 keV & < 2keV
transmission
fluorescence
ERL hi-coherence
XPEEM
Two types: full field & scanning
I 'd like to start with some background on x-ray microscopy, because I don't know whether everyone is familiar with it.
This picture shows a typical x-ray microscopy setup at a synchrotron beam line. It consists of an x-ray beam passing through a monochromator and gets focused by a Fresnel zone plate onto a sample. The transmitted or scattered x-rays are collected by another zoneplate which serves as the objective lens for the microscope. The enlarged image is then projected onto a CCD.
One can study all kinds of materials with this type of setup, ranging from biological to magnetic materials. If you look through the literature, you can find many many examples, but I won't have time to go through them.
In recent years there have been an increasing number of synchrotron based x-ray microscopes worldwide. And that's because of two things that are available recently: one is the high-resolution lens-like optics such as zone plates, and the other is the high-brilliance synchrotron x-ray sources.
However, most of these x-ray microscopes are based on soft x-rays, only a few, maybe 3 or 4 of them use x-rays beyond 3 keV.
So you may want to ask why that is the case?
All types of materials are studied, from biological to magnetic
Increasing number of SR imaging microscopes worldwide due to availability of => lens-like optics: zone plates, KB mirrors, CRLs => high-brilliance & high-energy synchrotron sources

9. Issues in Hard X-ray Microscopy
Phase contrast is x104 higher than absorption contrast for protein in 8keV
Focusing optics
Only recently has Fresnel zone-plate (FZP) achieved <100nm resolution at 8keV (Yun, 1999)
Dose reduced to level comparable to using water-window in soft x-ray region
High coherence sources: Coherence fraction ~ l2/(exey). => Requires 100x smaller emittance product for keV => 10 keV ERL would offer x better emittance product than present-day hard x-ray sources => Better keV keV at ALS
C94H139N24O31S
1010
108
106
104
103
102
Kirz (1995): 0.05mm protein in 10mm thick ice
X-ray Energy (eV)
Dose (Gr)
absorption contrast
phase contrast
Well, I think there are three reasons.
First, only recently have the optics been good enough for hard x-rays. Right now the state of the art is about 100nm for hard x-rays as reported a couple of years. So that' s one reason.
The second reason is the lack of high coherence hard x-ray sources. If you really think about it, the coherence requirement has a very stringent demand on the source emittances, because coherent fraction is proportional to wavelength squared. So suppose you have good coherent beam at 1 keV, and you would like to have the same good coherence at 10 keV, then you have to decrease the source emittance product by a factor That is actually very difficult to do with the current 3rd generation synchrotron sources.
So this is where we believe the ERL would really play an important role. It would offer 100 to 1000 times smaller emittance product than the present-day storage-ring based sources. So potentially it would provide better or similar coherence for hard x-rays than the soft x-rays that is currently available at for example the advanced light source in Berkeley.
So that 's the second reason.
The third reason is actually a scientific question. As we know the absorption is much lower for hard x-rays than soft x-rays. Another way of looking at it is the required dose or exposure time for a given contrast. This is shown in this figure which I took from Janos' review article in It shows the calculated
Absorption vs. phase contrast
Refraction index: n = 1 - d - ib absorption contrast: mz = 4pbz/l ~ l3 phase contrast: f(z) = 2pdz/l ~ l z
In general, phase contrast requires: => coherent hard x-ray beams

10. Phase Imaging & Tomographyl
Cloetens et al. (1999): ESRF, ID19, 18 keV Polystyrene foam 0.7x0.5x1mm3 1.4T wiggler, B~7x1014 4x700 images at 25 sec/image
A form of Gabor in-line holography
Coherence over 1st Fresnel zone (lR)1/2
Image reconstruction (phase retrieval)
Spatial resolution limited by pixel size
With ERL: it would be possible to reduce the exposure times by orders of magnitude.
It offers great potential for flash imaging studies of biological specimens, at ID beam lines.

11. Far-Field Diffraction Microscopy
Diffraction microscopy is analogous to crystallography, but for noncrystalline materials
Coherent diffraction from noncrystalline specimen: => continuous Fourier transform
Spatial resolution: essentially no limit. (only limited by Dl/l and weak signals at large angles)
Coherence requirement: coherent illumination of sample
Key development: oversampling phasing method coherent flux!!
Coherent X-rays
Miao et al. (1999) >>> soft x-rays, reconstruction to 75 nm

12. Diffraction Microscopy recent results
Miao et al. PRL (2002)
reconstructed image: to d~7nm resolution
l = 2 Å
Gold: 2.5mm x 2mm x 0.1mm
SPring-8 BL29XU: standard undulator 140 periods lu=3.2 cm B=2x1019 For Au, exposure time 50 min, d~7nm but: for Si, (ZSi/ZAu)2~1/32 => 26 hrs ! for C, (Zc/ZAu)2~1/173 => 6 days !!
=> could achieve higher resolution,
limited only by radiation damage
ERL high-coherence option: B=5x1022 Exposure time for Si & d~7nm: 0.6 min for C & d~7nm: 3.5 min.

13. Miao et al., Proc. Nat. Acad. Sci. (2003)
E. Coli bacteria ~ 0.5 mm by 2 mm
SPring-8, l = 2 Å, pinhole 20 mm
Total dose to specimen ~ 8x106 Gray
Diffraction image to ~30nm resolution

14. X-ray Photon Correlation Spectroscopy
Dierker (2000), ERL Workshop

15. X-ray Holography with Reference Wave
Leitenberger & Snigirev (2001)
Wilhein et al. (2001).
Howells et al. (2001); Szoke (2001).
Illumination of two objects, one as reference, e.g. pin-hole arrays
X-ray holography is exciting
but not ready for applications
ERL is an ideal source for
further research in this area

16. Coherent X-ray Patterning & Lithography
(invited talk X-ray Coherence 2003)
Maskless pattern
DOE: diffractive optics element
Lithography  X-ray CVD 
Coherent X-rays

17. Desired ERL Properties
full transverse coherence high coherent flux / coh. fraction high Dl/l for high resolution small beam (some cases) large coherent area (some cases) CW operation: long pulses okay
X-ray photon correlation spectroscopy Phase-contrast imaging & microscopy Coherent far-field diffraction Coherent crystallography X-ray holography Coherent x-ray lithography D1 D2
Basic Requirement:
low transverse emittances
long undulators (large Nu)
low machine energy spread
X-ray optical slope error dq << sx/D1 ~ 4mm/40m ~ 0.1mrad
coherence preserving x-ray optics

18. Phase II ERL Coherent Flux
Time-averaged coherent flux comparable to LCLS XFEL
Coherent fraction ~100x greater than 3rd SR sources
Peak coherent flux (coherent flux per pulse) ~1000x greater than 3rd SR sources
Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source.
This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source.
Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux.
So we see the ERL is highly coherent source with a very high coherent flux.
???

19. CHESS Tech Memo 01-002: 3/8/01 http://erl.chess.cornell.edu/papers
Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source.
This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source.
Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux.
So we see the ERL is highly coherent source with a very high coherent flux.

20. Desired Changes to Memo
Performance numbers for micro-beam undulator
transverse exey scale with q
Separate ultra-fast mode: less frequent fat bunch q
Inclusion of effects of machine energy spread sE
Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source.
This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source.
Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux.
So we see the ERL is highly coherent source with a very high coherent flux.

21. Phase II ERL Properties

22. Options for Improvements
Injector emittance ? nm-rad  ??
Separate running modes for hi-coherence & ultra-fast ?
Bunch decompression  longer pulse but smaller sE/g ??
No Compression
st ~ 2 ps
sE/g ~ 2x10-4
on-crest Df = 0
st ~ 0.1 ps
sE/g ~ 2.7x10-3
off-crest Df > 0
st ~ ?? ps
sE/g ~ 1x10-4 ?
off-crest Df < 0

23. Improved Coherence Properties by reducing machine energy spread
Operation Mode:
on-crest Df=0
off-crest Df<0 ?
off-crest Df>0

24. Other Properties

25. Short-Pulse Source Comparison
fat bunch

26. Conclusions
Phase II ERL would offer 100x more coherent flux and coherence fraction for hard x-rays than present-day sources, comparable to prototype XFEL source
Many scientific applications benefit substantially, e.g. in coherent scattering & diffraction, and in x-ray holography and coherent patterning, possibly opening up new research areas
Improvements in ERL coherent flux require long undulator, which in turn requires reducing machine energy spread by bunch decompression or by some other means
Further improvements in coherence are possible only if injector emittance can be further reduced
Ultra-fast mode of ERL can still be a leader in peak brilliance for short-pulses. Further improvement is determined by how much charge in a single bunch and by energy spread from bunch compressor