Measurement of x-ray coherence

Ian McNulty

Argonne National Laboratory

Cairns, QLD AustraliaMonday, 30 June 2003

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Summary

Motivation

Recent work

Experiments at APS

Future directions

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Why bother?

• Synchrotron sources produce highly brilliant, partially coherent x-ray beams; x-ray lasers are around the corner

• High resolution x-ray experiments require more complex beamline optics -- coherence "degradation"?

• Unique coherence-based experiments now possible

• Aim: develop means to quantify spatial coherence and wavefront quality of high brilliance x-ray beams

Cohereometer

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Source degeneracy

10 -11

10 -9

10 -7

10 -5

10 -3

10 -1

10 1

10 3

10 5

10 7

10 9

10 0 10 1 10 2 10 3 10 4 10 5

LCLS

TTF

LEUTL

APS U3.3

NSLS U8.0

ALS U3.9

ALS U8.0

PEP U7.7

ALS W13.6

ALS bend

NSLS bend

ave

Energy [eV]

Photons per temporal and spatial mode = B3/4c = Fcc

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Peak degeneracy

10 -8

10 -6

10 -4

10 -2

10 0

10 2

10 4

10 6

10 8

10 10

10 12

10 14

10 16

10 0 10 1 10 2 10 3 10 4 10 5

LCLS

TTF

LEUTL

APS U3.3

NSLS U8.0

ALS U3.9

ALS U8.0

PEP U7.7

ALS W13.6

ALS bend

NSLS bend

p

Energy [eV]

Photons per temporal and spatial mode, per pulse

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Applications of coherent x-rays

• Micro/nano-focusing

• Holography

• Interferometry

• Quantitative phase contrast

• Coherent scattering (speckle, XIFS, diffraction, microdiffraction)

• Novel coherent optics

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• Cell is transfected with TiO2-DNA nanocomposites

• DNA targets specific chromosomal region

• TiO2 photocleaves DNA strands upon illumination

• Potential use in gene therapy

5 m

2.2

0.0

g/cm2

5.8

0.0

g/cm2

TiO2-DNA nanocomposites in mammalian cells

ZnTi

Map Ti distribution with x-ray induced K

fluorescence to quantify success rate ofTiO2-DNA transfection and visualize target

Affinity of transfected DNA to ribosomalDNA causes nanocomposites to localizeto the nucleolus

S. Vogt, J. Maser, I. Moric, D. Legnini (ANL)G. Woloschak, T. Paunesku, N. Stojicevic(Radiation Biology Dept., Northwestern Univ.)

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Full-field coherent phase imaging

B. Allman et al., JOSA A17, 1732 (2000)

Full-field image of ~2 µm spider silk

Difference between in-focus, defocused images

Reconstructed phase

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Phase nanotomography of Si AFM tip

3D reconstructions of real part of refractive index of projections.(a, b) Horizontal slices through tip. (c) Vertical slice. (d-f) Volume renderings. Measured = 5.0 ± 0.5 x 10-5 , calculated = 5.1 x 10-5.

P. McMahon et al., Opt. Commun., 217, 53 (2003)

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X-ray speckle

• Access to high momentum transfer at short wavelengths

• Scatter from core electron, magnetic, and nuclear charge

• Study physics of nanoscale structure and disorder

• Study fluctuations in domain position, size, and orientation

Magnetic speckle observed with circulary polarized x-rays tuned to the Gd M5 resonance at 1183.6 eV. Radius of ring corresponds to ~115 nm domain size.

J.F. Peters et al., ESRF Newsletter 34, 15 (2000)

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Definitions

Temporal (longitudinal) coherence:Degree to which waves have well defined phase.

Temporal coherence of beam is function of source bandwidth.

Spatial (transverse) coherence:Degree to which wave front has well defined phase.

Spatial coherence of beam is function of source size.

Coherent beam does not necessarily imply coherent source!

lc ~

2

c ~

2

c

wc ~

za

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Coherent field from incoherent source

van Cittert-Zernike theorem

Fourier-invert to obtain source size and shape (assumes symmetry)

P.H. van Cittert, Physica 1, 201 (1934)F. Zernike, Physica 5, 785 (1938)

I(x,y) FT1 12

12, ei

I(x,y)e ik xy /zdxdy

I(x,y)dxdy

Observation PlaneSource Plane

y

x

z

I(x,y) )12

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Partially coherent field

K. Nugent, J. Opt. Soc. Am. A8, 1574 (1991)

G FT g

g FT 1 Ipar FT 1 Icoh

where Ipar GIcoh

Iparr G

r /z Icoh

r r d r

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Undulator radiation

• VCZ assumes incoherent, quasi-homogeneous source where wavefront is assumed to be spherical

• Undulator source interesting when photon emittance not dominated by electron emittance: ~ (sin Nx)/Nx

• SR sources (except FEL) are incoherent, but are highly forward directed due to relativistic effects: ~ 1/

Dependence of µ12 on ?

R. Coisson, Appl. Opt. 34, 904 (1995)Y. Takayama, Phys. Rev. E59, 7128 (1999)

Electrons

N u

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How to measure it?

Temporal (longitudinal) coherenceMeasure fringe visibility off-axis (count fringes)Measure spectral width directly

Spatial (transverse) coherenceMeasure fringe visibility on-axis

Measure wavefront phase

Spatial methodsDiffraction by aperture/objectAmplitude interferometer (Young, Shack-Hartmann)Intensity interferometer (Hanbury Brown-Twiss)Time-domain (A. Baron, Phys. Rev. Lett. 77, 4808 (1996))Speckle contrast (D. Abernathy, J. Synchr. Rad. 5, 37 (1998)) Non-intermerometric (K. Nugent, Phys. Rev. A61, 063614 (2000))

Desire complete 2D coherence function, µ12(x,y)

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Amplitude interferometer (Young)

SN

12

Sensitive to 1st-order coherence

gr1,r2 r1,r2 r1,r1 r2,r2

r1,r2 E r1, E* r2,

Optic AxisMono- chromator

Source Slits Screen

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Intensity interferometer (Hanbury Brown - Twiss)

SN

122

Tr

Sensitive to 2nd-order coherence g2 r1,r2

I r1 I r2 I r1 I r2 1

Det A

Optic AxisMono-

chromator

Source

Correlator AB

ElectronicsSlits

<AB>

Output

Integ <A>

<B>Det B

Integ

Integ

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EUV laser and undulator experiments

– Collisionally excited laser (20.7 nm)

• URA

J. Trebes et al., Phys. Rev. Lett. (1991)

– Undulator beamline (13.4 nm )

• Youngs

C. Chang et al., Opt. Commun. 182, 25 (2000)

– Capillary discharge laser (46.9 nm)

• Youngs

R. Bartels et al., Opt. Lett. 27, 707 (2002)

• Shack-Hartmann

S. Le Pape et al., Phys. Rev. Lett. 88, 183901 (2002)

Full measurement of field amplitude and phase

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Single-aperture method

V. Kohn et al., Phys. Rev. Lett. 85, 2745 (2000)

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Young's experiment (hard x-rays)

Young's interferograms at 10 keV for two secondary source sizes M at 23 m.

Measured and calculated coherence profile at 10 keV as a function of Youngs slit spacing

W. Leitenberger et al., Opt. Lett. 191, 91 (2001)

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2-ID-B beamline (1-4 keV)

Source degeneracy 0.001 - 0.01

Monochromaticity 40 - 4000

Coherence time 0.1 - 10 fs

Long. coherence length 0.025 - 2.5 µm

Transverse coherent area 5 - 100 m (H) 50 m (V)

Coherent intensity 2 105 ph/m2 /s/0.1% BW

Coherent flux 1 109 ph/s/0.1% BW

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Young's experiment (1.1 keV)

Optic Axis

Effective Source

Young's Slits

APD and 5 µm slit

8.01 m 1.07 m

Experiment geometry (top view)

Young's slits (1.6 µm Au, 3 µm wide, 10 µm apart)

20 µm slit separation

50 µm slit separation

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Coherence function at 2-ID-B

Horizontal degree of spatial coherence |µ12|measured 8 m from monochromator exit slit.|µ12| is dominated by beamline optics.

Energy = 1.1 keVEntrance slit = 50 µmExit slit = 220 µm

|µ12| measured with 120 µm exit slit. |µ12| isdominated by exit slit, producing sinc profile.

D. Paterson, et al., Opt. Commun. 195, 79 (2001)

wc wslit

2 wsource2

12

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How to speed up? parallelize measurement

Uniformly redundant array:

All possible aperture separations occur with same frequency

1D URA equivalent to many simultaneous Young’s experiments

1D 2D

K. Nugent et al., Rev. Sci. Instrum. (1992)

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Experiments at APS

• Fast measurement of 1D and 2D coherence functions with URAs and CCDs (< 1 min exposures)

• Performed at APS 2-ID-B (soft) and 2-ID-D (hard x-ray) beamlines

• Measured with 8, 2.5 nm-rad electron beam emittance

• Obtained |µ12| by Fresnel inversion 1D URA (1.18 µm Au, 2.5 µm min. width)

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Spatial coherence function by phase URA (8 keV)

J.J.A. Lin, et al., Phys. Rev. Lett. 90, 074801 (2003)

Coherence function measured 43.4 m from source slits of size(a) 10 µm, (b) 50 µm, © 90 µm, and (d) 170 µm

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Intensity interferometry

• Soft and hard x-ray experiments

Y. Kunimune et al., J. Synchrotron Rad. 4, 199 (1997)

E. Gluskin et al., J. Synchrotron Rad. 6, 1065 (1999)

• But ... few data points, long acquisition time (days!), large uncertainty in |µ12|

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Recent HBT experiment (14.4 keV)

M. Yabashi et al., Phys. Rev. Lett. 87, 140801 (2001)

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Coherence "degradation"?

CCD image of Young's interference pattern with 10 µm slit separation at 1.07 m, using 1.5 keV x-rays. Image is 820 µm by 420 µm and fringe spacing is 90 µm.

Condition for full utilization of coherence by experiment: daperture < dspeckle

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Future directions

• Measure wavefront, phase by TIE method to obtain complete determination of (complex) µ12

• Spatial coherence mapping of lasers, other "flash" x-ray sources– Hard x-ray XFEL pulse (unseeded) contains ~ 102 temporal modes

• Intensity interferometry with XFEL ( >> 1) ?– Noise in correlation signal > Poisson noise

• With sufficiently high , can we prepare nonclassical photon number (Fock) states?

– Novel correlations, multiphoton interference (Mandel, Ghosh, Zhou, …)

Interesting x-ray quantum optics problems addressable soon

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Acknowledgements

Ercan Alp APS, Argonne National LaboratoryJoe ArkoEfim GluskinBarry LaiDerrick ManciniMike MoldovanDavid PatersonCornelia RetschWolfgang SturhahnJohn Sutter

Chris Chantler School of Physics University of MelbourneTom IrvingJon LinPhil McMahonKeith NugentAndrew Peele

Brendan Allman Iatia Corp.