Coherent Diffraction Imaging (CDI) with X-Rays School on Synchrotron - - PowerPoint PPT Presentation

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Coherent Diffraction Imaging (CDI) with X-Rays School on Synchrotron - - PowerPoint PPT Presentation

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Coherent Diffraction Imaging (CDI) with X-Rays School on Synchrotron and Free-Electron-Laser Methods for Multidisciplinary Applications ICTP Trieste, May 15, 2018 Anders Madsen European X-Ray Free-Electron Laser Facility Hamburg, Germany

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Coherent Diffraction Imaging (CDI) with X-Rays

Anders Madsen European X-Ray Free-Electron Laser Facility Hamburg, Germany anders.madsen@xfel.eu

School on Synchrotron and Free-Electron-Laser Methods for Multidisciplinary Applications ICTP Trieste, May 15, 2018

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Anders Madsen, European XFEL

Outline

2

 Motivation  X-ray Imaging  X-ray Coherence  All the tricks of CDI  Image reconstruction  Related methods  Applications  Sources of Coherent X-rays  The European XFEL project  CDI science at XFELs  Summary

  • BREAK -

(50 min) (5-10 min, maybe) (30 min)

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Anders Madsen, European XFEL

Coherent scattering. Motivation

3

Slide courtesy of I. Vartaniants (DESY)

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Anders Madsen, European XFEL

Coherent scattering. Motivation

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Coherent Diffraction Imaging (CDI): Isolated object

Static scattering

Ensemble of objects Correlation spectroscopy: Temporal: XPCS Spatial: XCCA

Dynamic scattering

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Anders Madsen, European XFEL

Coherent scattering. Motivation

5

Diffraction imaging of biomolecules with coherent femtosecond X-FEL pulses

  • R. Neutze et al., Nature 406, 752 (2000)

Coulomb explosion of T4 lysozyme Very much excitement, now for >15 years:

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Coherent scattering. Motivation

6

Simulated coherent scattering image (speckle) of a T4 lysozyme molecule

  • R. Neutze et al., Nature 406, 752 (2000)

Diffraction imaging of biomolecules with coherent femtosecond X-FEL pulses

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Anders Madsen, European XFEL

Different regimes of lensless X-ray imaging

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Fresnel diffraction near-field Fraunhofer diffraction far-field

X-rays size: a L >> a2/l L~m Absorption Phase contrast In-line holography Röntgen (1895) Koch et al. (1998) Zhang (2003) Coherent Diffraction Imaging (CDI) L ~a2/l L~cm

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Anders Madsen, European XFEL

Different regimes of lensless X-ray imaging

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 Absorption regime Easy reconstruction based on attenuation 3D tomographic reconstruction, inverse Radon transformation  Phase contrast regime Edge enhanced contrast Transport-of-intensity (TIE) equation Holotomographic reconstruction (Talbot effect)  In-line holographic regime Holographic reconstuction (detector dependent resolution) Twin image problem  Coherent diffraction imaging Tricky data treatment Resolution like in scattering, i.e. Dmin = 2p/Qmax ….

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Anders Madsen, European XFEL

Coherence

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Quantum mechanics  probability amplitudes (waves) Optics  Young’s double slit experiment, interference X-ray (and neutron) scattering It’s all about probability amplitudes and interference !!! Example: Young’s double slit experiment (Thomas Young, 1801) [wave-character of quantum mechanical particles (photons)] P=|SjFj|2 F: probability amplitude Fj ~ exp[-i(wt-klj)] w=ck, k=2p/l, lj(L,y) P(y) ~ cos2(pyd/lL) Dy=lL/d

Plane, mono- chromatic wave

Laser beam

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Anders Madsen, European XFEL

Nl (N-1)(l+Dl)

p 2p

Longitudinal coherence length ll = l2/(2Dl)

d L

Transverse coherence length lt = lL/2d

Coherence lengths

Coherence

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Anders Madsen, European XFEL

The CDI Challenge

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Speckle pattern does not look like sample. How to determine the sample from I(q) ?

I(q)

Using a lens to form the image

Question

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Anders Madsen, European XFEL

The phase problem in scattering

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E(Q) Q = qin - qout

r(R)

2 *

| ) ( | ) ( ) ( ) ( ] exp[ ) ( ~ ) ( Q Q Q Q R R Q R Q E E E I d i E = = 

 r

Reciprocal space E(Q)  FT  r(R) Real space But…

qin qout |q| = 2p/l |Q| = 4p sin(q)/l

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Anders Madsen, European XFEL

The phase problem in scattering

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Aim: To find E(Q) from measurements of I(Q) = |E(Q)|2 But E(Q) is a complex number with both phase and amplitude E(Q) = A exp(if) Measurement: I(Q) = |E(Q)|2 = A2 No direct access to phase….

FT of XFEL logo  E(Q) I(Q) = |E(Q)|2 (simulation of coherent scattering) Construct E(Q): A = sqrt(I(Q)) Take random phases f Inverse FT transform of A exp(if) Exercise

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Anders Madsen, European XFEL

Phase matters!

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r(R)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ampl A phase f

  • 3
  • 2
  • 1

1 2 3

|FT{r(R)}|2 = |E(Q)|2 = I(Q) FT

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Anders Madsen, European XFEL

Phase matters!

15

I(Q) as amplitude

  • 3
  • 2
  • 1
1 2 3

r(R) ampl phase

0.2 0.4 0.6 0.8 1 1.2 1.4

  • 3
  • 2
  • 1

1 2 3

FT-1{E(Q)} random phases

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Anders Madsen, European XFEL

Phase is more important than amplitude

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100 200 300 400 500 600 50 100 150 200 250 300 350 400

Fourier transform my dog  A eif Keep amplitudes A Substitute with another image’s phases f Inverse Fourier transform

100 200 300 400 500 600 50 100 150 200 250 300 350 400

The phases came from a cat…

100 200 300 400 500 600 50 100 150 200 250 300 350 400

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Anders Madsen, European XFEL

How can the phase be determined?

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r

N2 pixels 2N2 unknowns

I

N2 pixels N2 equations

How can we make this solvable? Unique solution? Question

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Anders Madsen, European XFEL

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

I(Q) ampl phase

  • 3
  • 2
  • 1

1 2 3

N2 pixels, 2N2 unknowns Intensity measured in N2 pixels N2 equations

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Anders Madsen, European XFEL

Finite support constraint

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I(Q) ampl phase

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
  • 3
  • 2
  • 1
1 2 3

N N/sqrt(2)

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Anders Madsen, European XFEL

Finite support constraint

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I(Q) ampl phase

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
  • 3
  • 2
  • 1
1 2 3

N/3 N

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Anders Madsen, European XFEL

Finite support constraint

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I(Q) ampl phase

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
  • 3
  • 2
  • 1
1 2 3

N/6

Angular speckle size ~ l/sample size

N

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Oversampling

22

David Sayre (1952)

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Basic experimental requirements for CDI

23

In 2D:

  • Need that sample dimension a is at least 2 smaller than beam size D:

a < D/2 (reduce number of unknowns)

  • Need to measure the speckle pattern with a resolution that is at least

2 finer that speckle size in both dimensions. Therefore, the pixel size Dp must fulfil: Dp/L < l/(a2), where L is the sample - detector distance (increase number of equations)

  • Beam must be coherent over the sample, otherwise the FT relationship

does not hold How to solve the non-linear system of N2 equations and M unknowns (M < N2) to find r(R)? Question

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Iterative Phase Retrieval Algorithm

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reciprocal space constraints

E'(Q) E(Q) FT r'(x) FT-1

Real space constraints: finite support (r = 0 outside sample) real r ? positive r ? other? Reciprocal space constraints

) I( ) ( E Q Q 

random phases

) Q I( ) Q ( E =

r(x)

real space constraints

Is this the real solution?

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Anders Madsen, European XFEL

Computer simulation

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I(Q)

)] ( exp[ ) ( ) ( ' Q i Q I Q E f =

random phases f E(Q) E’(Q) r’(R)

positive, real r(R) shrink wrap support

) ( | ) ( ' | Q I Q E =

FT-1 FT

4x4 times

  • versampled

Iterative Phase Retrieval Algorithm

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Anders Madsen, European XFEL

Iterative Phase Retrieval Algorithm

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  • R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972)

J.R. Fienup, Appl. Opt. 21, 2758 (1982) Review: R. Millane et al., J. Opt. Soc. Am. A14, 568 (1997) Difference map: V. Elser, J. Opt. Soc. Am. A20, 40 (2003)

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  • J. Miao et al, Nature 400, 342 (1999)

1st Experimental Demonstration with X-rays

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Bio-CDI with soft X-rays

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  • D. Shapiro et al, PNAS 102, 15343 (2005)

No shrink warp, “hand drawn” support Difference map algorithm Averaging iterates (Elser & Thibault) Resolution ~ 30 nm

CDI from a yeast cell (freeze-dried) Speckle pattern, l=16.5 Å (ALS) reconstructed image

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Anders Madsen, European XFEL

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Sample preparation plunge-freezing

In-line optical microscope

Setup for Biological CDI

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Anders Madsen, European XFEL

Bio-CDI with hard X-rays

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Resolution about 30 nm Goal: ~10 nm

  • E. Lima et al, PRL 103, 198102 (2009)
  • D. Radiodurans cell

1 mm

Data taken at ID10, ESRF Frozen, hydrated cells

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Anders Madsen, European XFEL

Ptychography

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 The requirement that sample < beam is a limitation for many practical purposes  Can we find another constraint so the phase can be determined?  The answer is : Ptychography!

Ptych- : (to) fold (from Greek)

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Science, 321, 379-382 (2008)

SEM absorption

Buried zone plate

Ptychography

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  • Proc. Natl. Acad. Sci. USA 107, p. 529-534 (2010)
  • D. Radiodurans

Setup at cSAXS beamline, SLS

Ptychography

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Do you know another method where the phases are encoded in the image, i.e. easy reconstruction? Question

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Holography

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In-line holography (electrons, Gabor 1947); Laser (1960), 1st optical hologram ~1962

Famous method to encode the phases in the intensity pattern

Dennis Gabor Nobel prize 1971

Recording Holographic reconstruction

First SR hologram:

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Anders Madsen, European XFEL

Fourier Transform Holography

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 Spherical reference wave (r) spreads speckles and encodes phases

  • f object wave (o)

 Simple reconstruction by FT:  How to get a spherical reference wave? Iholo = |FT{o+r}|2 = |FT{o} + FT{r}|2 = |O + R|2 = |O|2+|R|2+OR*+RO* FT{Iholo} = o  o + r  r + o  r + r  o

FZP CCD

1st order from a FZP, sample in 0th order beam

McNulty et al, Science 256, 1009 (1992)

r

  • +r
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Anders Madsen, European XFEL

Fourier Transform Holography

37

FT {I(Q)}

I(Q)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Strong reference scatterer

  •  r

r  o r  r

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

  •  o
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FT Holography with soft X-rays

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Holography at BESSY Soft X-rays Imaging of magnetic domains

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Anders Madsen, European XFEL

Biological FT Holography

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1st results from ID10, ESRF @ 8 keV Stadler, Büldt, Madsen et al. (unpublished) Holography of Pichia Pastoris (yeast) cell + 250 nm Au particle

hologram Cell wall nucleus

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Anders Madsen, European XFEL

3D resolution is required

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Tomography: 3D Bio-CDI

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More than 100 different 2D projections necessary for 3D phase retrieval

Neospora caninum parasite

Rodriguez et al., IUCrJ 2, 575 (2015)

1 mm

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Anders Madsen, European XFEL

42

Nature 467, p. 436 (2010)

Tomography: 3D CDI on Bone

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Tomography: 3D Bragg CDI

43

h k

Q FT FT

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Anders Madsen, European XFEL

Tomography: 3D Bragg CDI

44

Rocking scan (Dq) sweeps the detector- plane through reciprocal space Data from APS, 34-ID

  • I. K. Robinson & R. Harder

Nature Materials 8, 291 (2009) Study of Pb nanocrystals

Q

Dq

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Anders Madsen, European XFEL

Tomography: 3D Bragg Ptychography

45

Rocking scan (Dq) sweeps the detector- plane through reciprocal space of the sample

Q

Dq

Illuminate overlapping areas of the crystal

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Anders Madsen, European XFEL

Tomography: 3D Bragg Ptychography

  • C. Kim et al,

unpublished B2 ordered phases

  • f Fe-Al alloy

(001) Superlattice reflection Experiment at ID01 ESRF Looking inside materials

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Anders Madsen, European XFEL

Summary before break:

47

 Why is phase important  How does phase retrieval work in coherent diffraction imaging  How does phase retrieval work in ptychography  How does phase retrieval work in holography  Examples of published work  3D resolution is needed! Next: X-ray sources, new opportunities with Free-electron lasers The European X-ray Free-Electron Laser in Hamburg

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Anders Madsen, European XFEL

Coherent Intensity

48

𝐽𝐷 = l2𝐶/4

B: Brilliance (spectral brightness) of source 𝐶: 𝑞ℎ/𝑡 𝑛𝑛2 𝑛𝑠𝑏𝑒2 0.1%𝐶𝑋

() () only strictly valid for chaotic sources

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Development of X-ray sources

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1880 1900 1920 1940 1960 1980 2000 2020 10

6

10

8

10

10

10

12

10

14

10

16

10

18

10

20

10

22

10

24

10

26

10

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10

30

10

32

10

34

Peak Brilliance year 1880 1900 1920 1940 1960 1980 2000 2020 10

2

10

4

10

6

10

8

10

10

Transistors in CPU

tubes & lab. sources 1st & 2nd gen. synchrotrons 3rd generation synchrotrons European XFEL

ELETTRA, 1keV FERMI

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Free-Electron Lasers Around the World

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Soft X-Rays: FLASH (Hamburg, Germany) [first x-ray laser 2005] FERMI (Trieste, Italy) [first seeded x-ray laser 2012] Hard X-Rays: LCLS (SLAC, Stanford, USA) [first hard x-ray laser 2009] SACLA (Sayo, Japan) [compact XFEL 2011] PAL-XFEL (Pohang, Korea), first beam 2016 SwissFEL (Villingen, Switzerland), first beam 2016 European XFEL (Hamburg, Germany), first beam 2017 Project in Shanghai, China LCLS-II under construction at SLAC

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Undulator radiation

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Undulator: Magnetic device that the electron beam traverses. Installed in the straight sections of the synchrotron or after the FEL linac

F = e(v×B) 1st, 2nd and 3rd generation I  Ne (Bending magnet) I  Ne  N (Wiggler) I  Ne  N2 (Undulator)

N ~100 magnetic poles

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Anders Madsen, European XFEL

X-Ray Free-Electron Lasers

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SASE: Self-Amplified Spontaneous Emission SR undulator: 2 - 5 m SASE undulator at European XFEL: 175 m

XFELS: Operate with a linac feeding short (<100 fs) electron bunches into a long undulator

Interaction between intense EM-field and electrons leads to e-beam instability and micro-bunching of the electrons. Micro-bunching gives lasing & saturation: Coherent sum of emitted fields from all electrons

I  Ne

2 for SASE

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Anders Madsen, European XFEL

Self-Amplified Spontaneous Emission (SASE)

53

The “trick” of Free-Electron Lasers:

SASE: Self-Amplified Spontaneous Emission. First demonstrated at DESY (FLASH) in the soft X-ray range

Spontaneous emission (SR) Uncorrelated X-ray emission Spontaneous emission (SASE) Correlated X-ray emission

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Facility Outline

54

SASE-1

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European XFEL. Overall layout

European XFEL HQ, Schenefeld:

  • Research with photons
  • Center of the international

research facility

Distribution of electron beam electron injection 5 photon beamlines with 3 SASE undulators

Main components:

  • Injector
  • Linear Accelerartor
  • SASE Undulators
  • Photon beamlines
  • HQ building
  • Experimental hall

+

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8 shafts and ca. 5.7 km tunnels, 2.1 km linac tunnel, up to 17.5 GeV energy Total straight length of facility: 3.4 km Underground experimental hall with 6 instruments, space for 6 more

Schenefeld Osdorfer Born Bahrenfeld

XFEL essentially an underground facility

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1st Lasing

First hard X-ray lasing May 24, 2017 at 9:20 pm

Green lasers over Hamburg

Official inauguration

  • f European XFEL
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Simultaneous lasing in 3 braches!

SASE-1 SASE-2 SASE-3

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Vertical profile more structured Data from afternoon May 3rd

Lasing at SASE-2 - 7 keV, ~175uJ

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The First Experimental Stations

60

FXE Femtosecond X-ray

Experiments

SPB Single Particles &

Biomolecules

SQS Small Quantum

Systems

SCS Spectroscopy &

Coherent Scattering

MID Materials Imaging &

Dynamics

HED High Energy

Density Science Experimental hall ~ 90 x 50 m

SASE 2 SASE 1 SASE 3 U 1 U 2

SCS SQS FXE SPB+SFX MID HED

Link to VirtualTour Link to Webcams

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pulse train

10 trains/sec 2700 pulses/train

Time structure of European XFEL

220 ns

European XFEL repetition rate: 4.5 MHz, most other FEL sources ~100 Hz

single pulse, few fs single pulse

220 ns between pulses pulse duration: few fs 1012 – 1013 ph/pulse

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length = velocity × time

Length 10 mm 1 mm 0.1 nm Velocity 10 m/s 100 m/s 1000 m/s (acoustic phonon in matter) Time 1/1000 s 1/100.000 s 1/10.000.000.000.000 s (100 femto-seconds)

The case for ultrafast dynamics investigations

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63

The unique properties:

  • Ultrafast time resolution (pump-probe, movie mode)
  • Ultrahigh peak Brilliance at 4.5 MHz rep rate
  • Ultrahigh average Brilliance (27000 pulses/s)
  • Coherence of the XFEL beam
  • Unique instrumentation

will enable completely new experiments to study structure and dynamics of materials

Mission statement

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64

 Imaging of single molecules  Ultra-fast dynamics of molecules and materials

Diffraction pattern Particle injection

Gaffney and Chapman, Science 316, 1444 (2007) Stephenson et al, Nature Materials 8, 702 (2009)

The XFEL Challenge

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65

XFEL experiments can be destructive… but not necessarily

FLASH (DESY) L = 32 nm, 25 fs pulse duration, 1012 ph/pulse

  • H. Chapman et al, Nature Physics 2, 839 (2006)

The XFEL Challenge

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Diffraction before destruction: Femto-second crystallography (destructive)

66

 Serial crystallography (sample injector)  Femtosecond pulses (diffraction before destruction)  Nanocrystals formed by many proteins

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Diffraction before destruction: Femto-second crystallography (destructive)

67

Chapman et al, Nature 470, 73 (2011)

More than 3 million images collected Structure of Photosystem I determined (already known) Verification of diffraction before destruction in crystallography

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Diffraction before destruction: CDI using single shot exposures

68

X-ray Imaging of a virus in 3D Ekeberg et al, PRL 114, 098102 (2015) Particle injector AMO, LCLS Phase retrieval Tomographic reconstruction 3D resolution

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Non-destructive XFEL Imaging: Combining CDI and pump- probe

69

Au(111) reflection

Measuring phonons in Au nanocrystals by PP CDI at LCLS

  • J. Clark,…& I. Robinson,

Science 341, 56 (2013)

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Sample environment @ XFEL.EU

Coil cryostat

B

Pulse timing James Moore XFEL sample env. group

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Early science possibilities at XFEL.EU Imaging

Image courtesy of A. Schottelius,

  • Univ. Frankfurt

Needle-like nano-particles in solution

  • R. Kurta, XFEL.EU

Imaging of local ordering Unique combination: Nano-beam, small scattering volume, high photon flux ph/s/mm2 Angular correlation studies by electron diffraction Lui et al, PRL 110, 205505 (2013)

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Summary

72

 Coherent Diffraction Imaging is a method developed at synchrotron sources to

  • vercome limitations of optics

 Phase retrieval is difficult but necessary to reconstruct the image from the measured Intensities  Related methods exist that sometimes can make the phase retrieval easier  3D resolution is of course desired in many cases  Novel X-ray laser sources promise a bright future for coherent imaging techniques but new experimental strategies are needed  Serial femtosecond crystallography is, until now, the biggest success of XFELs

  • verall. TR SFX very exciting

 The combination of CDI and ultrafast science (fs-ns) is promising but only few experiments so far…

?? QUESTIONS ??

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Further reading without pay walls

73

www.xfel.eu lcls.slac.stanford.edu/

  • K. A. Nugent, Coherent methods in the X-ray sciences

https://arxiv.org/ftp/arxiv/papers/0908/0908.3064.pdf