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ERL & Coherent X-ray Applications Talk Outline Qun Shen Cornell High Energy Synchrotron Source (CHESS) Cornell University Introduction to x-ray coherence Coherent x-ray applications Desired ERL properties Options and improvements Conclusions x x’

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erl coherent x ray applications

ERL & Coherent X-ray Applications

Talk Outline

Qun Shen

Cornell High Energy Synchrotron Source (CHESS)

Cornell University

  • Introduction to x-ray coherence
  • Coherent x-ray applications
  • Desired ERL properties
  • Options and improvements
  • Conclusions



Integrated total flux Fn

et = st sE / E




ex = sxsx’

ey = sysy’















B =

B =

(2p)2 ex ·ey

(2p)3 ex ·ey·et

Source Emittance and Brilliance

  • Phase-space Emittance:

EM wave: E(r, t) = E0 ei(k·r-wt)

  • Brilliance: photon flux density in phase-space

Spatial (Transverse) Coherence




Dl = q· 2s = l/2


2q · 2s~ l



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


Temporal (Longitudinal) Coherence



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


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 = 10-6 =>Dtc= 330 fs
  • ERL with st = 100 fs pulses coupled with 10 meV x-ray monochromator could mean temporal coherence at 10 keV.

Transverse Coherence from Undulator




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 = 0.091 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)

erl spatial coherence

Diffraction limited @ 8keV (0.123Å)

ERL Spatial Coherence

ESRF emittance

(4nm x 0.01nm)

ERL emittance (0.015nm=0.15Å)

Diffraction limited source: 2ps's = l/2 ore = l/4p

Almost diffraction limited: 2ps's ~ lore ~ l/2p

Phase II ERL: diffraction-limited source E < 6.6 keValmostdiffraction-limited to 13 keV

x ray microscopy

X-ray Microscopy

ESRF ID21: TXM 3-6 keV

ESRF ID21: SXM 2-10 keV & < 2keV

  • transmission
  • fluorescence

ERL hi-coherence

  • Two types: full field & scanning
  • 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
issues in hard x ray microscopy

Kirz (1995): 0.05mm protein in 10mm thick ice



absorption contrast

Dose (Gr)



phase contrast

Refraction index: n = 1 -d- ibabsorption contrast: mz = 4pbz/l ~ l3phase contrast: f(z) = 2pdz/l ~ l






X-ray Energy (eV)

Issues in Hard X-ray Microscopy

  • Phase contrast is x104 higher than absorption contrast for protein in water @ 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 1keV => 10 keVERL would offer 102-103x better emittance product than present-day hard x-ray sources=> Better coherence @10 keV than @1 keV at ALS
  • Absorption vs. phase contrast
  • In general, phase contrast requires:=> coherent hard x-ray beams
phase imaging tomography


Phase Imaging & Tomography

Cloetens et al. (1999): ESRF, ID19, 18 keVPolystyrene foam 0.7x0.5x1mm31.4T wiggler, B~7x1014ph/s/mr2/mm2/0.1% @100mA4x700 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.
far field diffraction microscopy

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

diffraction microscopy recent results

ERL high-coherence option:B=5x1022 ph/s/mr2/mm2/0.1% @10mAExposure time for Si & d~7nm:0.6 min.for C & d~7nm:3.5 min.

=> could achieve higher resolution,

limited only by radiation damage

Diffraction Microscopyrecent 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 cmB=2x1019 ph/s/mr2/mm2/0.1% @100mAFor Au, exposure time50 min, d~7nmbut: for Si, (ZSi/ZAu)2~1/32 => 26 hrs ! for C, (Zc/ZAu)2~1/173 => 6 days !!


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


X-ray Photon Correlation Spectroscopy

Dierker (2000), ERL Workshop


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

Coherent X-ray Patterning & Lithography

(invited talk X-ray Coherence 2003)

Maskless pattern

DOE: diffractive optics element

Lithography X-ray CVD 

Coherent X-rays

desired erl properties



Desired ERL Properties

full transverse coherencehigh coherent flux / coh. fractionhigh Dl/l for high resolutionsmall beam (some cases)large coherent area (some cases)CW operation: long pulses okay

X-ray photon correlation spectroscopyPhase-contrast imaging & microscopyCoherent far-field diffractionCoherent crystallographyX-ray holographyCoherent x-ray lithography

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
phase ii erl coherent flux

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


desired changes to memo

transverse exey scale with q

Desired Changes to Memo

  • Performance numbers for micro-beam undulator
  • Separate ultra-fast mode: less frequent fat bunch q
  • Inclusion of effects of machine energy spread sE

on-crestDf = 0

st ~ 2 ps

sE/g ~ 2x10-4

No Compression

off-crestDf > 0

st ~ 0.1 ps

sE/g ~ 2.7x10-3

off-crestDf < 0

st ~ ?? ps

sE/g ~ 1x10-4 ?

Options for Improvements

  • Injector emittance ? 0.015 nm-rad  ??
  • Separate running modes for hi-coherence & ultra-fast ?
  • Bunch decompression  longer pulse but smaller sE/g ??

Improved Coherence Properties

by reducing machine energy spread

Operation Mode:


off-crestDf<0 ?




  • 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 machineenergy 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