Microscopy with Coherent X-Rays
Christian G. Schroer
DESY & Universität Hamburg

X-Ray Microscopy
K

Broad field of applications:>Physics, chemistry, biology, earth- and environmental science,nano-technology, ...
>Main advantage: large penetration depth!

in-situ and in-operando studies

quantum dots

>X-ray analytical contrasts: XRD, XAS, XRF, ...
atomic scale resolution
M. Hanke, et al.,
APL 92, 193109 (2008)

Today: „mesoscopic gap“

catalysts

real-space resolution: down to about 10 nm

Cu(I)2O

XRD and XAS: atomic scale
What happens on (mesoscopic) 1 - 10 nm scale?
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page2

X-Ray Microscopy
Today: „mesoscopic gap“
real-space resolution: down to about 10 nm
XRD and XAS: atomic scale
What happens on (mesoscopic) 1 - 10 nm scale?
Many interesting physics and chemistry questions:investigate local states:> individual defects (0D): changes in electron density, charge ordering> (structural) domain boundaries (2D), e. g., in multiferroics> mesoscopic dynamics at (solid-state) phase transitions> catalytic nanoparticles (activity in operando)> ...

Mesoscale also very important for nanotechnology (e. g., defects in devices)!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page3

Current State of X-Ray Microscopy
Conventional x-ray microscopy
optics limit spatial resolution: diffraction limit(typically: a few tens of nanometers)

optics are technology limited!
Theoretical extrapolation of x-ray optical
performance to the atomic level.
[PRB 74, 033405 (2006); H. Yan, et al., PRB 76, 115438 (2007)]

Ernst Abbelensaperture

Coherent x-ray imaging techniques (CXDI, ptychography)↵

no imaging optic!
Airy disclimited by statistics of far-field diffraction patterns ...
highest resolution: a few nanometers, focusing coherent beam
[PRL 101, 090801 (2008); Y. Takahashi, et al., PRB 80, 054103 (2009);
A. Schropp, et al., APL 100, 253112 (2012)]

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page4

Free Propagation of X-Rays
X-rays are electromagnetic radiation
propagation is described by homogeneous
Maxwell equation.
Simplification: scalar wave field (small angles, paraxial)
r2 '

1 @2'
= 0,
2
2
c @t

': scalar wavefield

Monochromatic radiation: Helmholtz equation
r

2

r)
! (~

k

2

r) = 0,! (~'(~r, t) =r) · e
! (~

i!t

,

!
k=
c

Polychromatic radiation is superposition of different frequencies ω

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page5

Free Propagation of X-Rays
Helmholtz equation
r

2

r)
! (~

k

2

r) = 0,! (~'(~r, t) =r) · e
! (~

i!t

,

!
k=
c

can be solved with appropriate boundary conditions using
Green’s theorem (Born & Wolf, pp. 417-425).
Boundary conditions:yx

New nomenclature: ~r = (~x, z)(⇥x, 0) given in plane of source
other boundaries in half space z > 0
are far away and absorbing

sourceplane
0zChristian G. Schroer | Cheiron School 2014 | 29. September 2014 | page

6

Free Propagation of X-Rays
Particular solution is the Fresnel-Kirchhoff integral:(Propagation mainly along the z direction)x, ⇥) =z (⇤eikr(x,x )· (⇤x, ⇤x )dx dy
x , ⇥) ·0 (⇤r(⇤x, ⇤x )y’

inclination factor:
x’

x

y

r(x, x )

x

θ

i cos
2⇥

(⇤x, ⇤x ) =x(Fresnel integral,
inclined incidence)0z

propagation
direction

initial planetarget plane

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page7

Modeling Objects
X-rays interact with electrons in sample.
Sample can be described by complex index of refraction:n(x, y, z) = 1⇥(x, y, z) + i (x, y, z)Thin sample:z0

No multiple scattering(1. Born approximation)x, !) = O z (~x) ·
z (~

x, !)
0 (~

z

d

With the transmission function
O z (~x) = eik

R

n dz

= eik z · e ik

R

dz

·e k

R

dz

objectChristian G. Schroer | Cheiron School 2014 | 29. September 2014 | page8

Coherent Imaging
absorption

near field

FresnelFraunhofer

coherent
radiation

object

z

z=0

z⌧

d2

z⇡

d2

z

d2

object: Cudthickness:> frame: 2 µm
> thin stripes: 0.5 µm!

energy: 20 keV
15 µm
characteristic distance: d2 / = (30 µm)2 /0.62 Å = 14.5 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page9

Coherent Imaging
absorption

near field

FresnelFraunhofer

coherent
radiation

objectzz=0

object: Cu

z⌧

d2

z⇡

d2

z

d2

8% contrast

d

15 µm
characteristic distance: d2 / = (30 µm)2 /0.62 Å = 14.5 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 10

Coherent Imaging
absorption

near field

FresnelFraunhofer

coherent
radiation

objectzz=0

object: Cu

z⌧

d2

z⇡

d2

z

d2

22x contrast

d

15 µm

z = 3 mmcharacteristic distance: d2 / = (30 µm)2 /0.62 Å = 14.5 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 11

Coherent Imaging
absorption

near field

FresnelFraunhofer

coherent
radiation

object

z

z=0

z⌧

d2

z⇡

d2

z

d2

object: Cu

d

15 µm

z = 14.5 mm

characteristic distance: d2 / = (30 µm)2 /0.62 Å = 14.5 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 12

Coherent Imaging
absorption

near field

FresnelFraunhofer

coherent
radiation

object

z

z=0

z⌧

d2

z⇡

d2

z

d2

object: Cu

d

15 µm

z!1

characteristic distance: d2 / = (30 µm)2 /0.62 Å = 14.5 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 13

Fraunhofer Diffraction: Far Field
Extreme far field:r = r0

x
x
r0

y
y
r0

r
x
x’

with

r0 =

r0

z 2 + x2 + y 2⇥z (⌅x, ⇤) ==ikr0 ⇤

ie
2 r0

ikr0 ⇤ie
2 r0z

xx + yyik
r0⇥0 (⌅x , ⇤) · exp⇤0 (⇧x , ⌅) · exp

⌅

⇧x
i⇥⇧

⇧

⇥

dx dy ,

dx dy
k
⇧
⇥=
r0

cos in inclination vanishes due to projection on sphere!
Far field is Fourier transform of wave field in initial plane!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 14xy⇥Fraunhofer Diffraction: Far Field
Example: (E = 8 keV)
Au (150 nm) on Si3N4:

far-field
!

image

1 µm
(3 µm)2= 58 mm = z
1.55 Å

L2 = 3.1 m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 15

Coherence
So far, we considered the propagation of pure states only!
The ideal experiment:>prepare probe (x-ray beam) in well defined initial state:
x, 0)
! (~

unimodal source> propagate through fixed experimental setup
Z
00
00
2 00
(~
x
,
det)
=
P
(~
x
,
~
x
)
(~
x
,
0)
d
x
!
!
Also sample static and in well-defined state!
>detection:
probability to detect photon ~ | ! (~x, det)|2
Repeat experiment many times under identical conditions!!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 16

Coherence
Main problem:
We have no full control over the experiment:>initial state not fully determined: ensemble of initial states that are realized
statistically:
from statistical ensemble with density

x, 0)
!i (~

>experimental setup varies in time
Z
00
00
2 00
(~
x
,
det)
=
P
(~
x
,
~
x
,
t
)
(~
x
,
0)
d
x
!(i,j)
j!ii

dynamics of sample
and setup describedby j.

time dependence of sample (dynamics)!

>detection:
Idet (~x) =Xi,j⇢(i,j) · | !(i,j) (~x, det)|2

ensemble average underassumption of ergodicity!

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 17

Coherence
Main problem:
What information can be extract fromIdet (~x) =Xi,j⇢(i,j) · | !(i,j) (~x, det)|2

about the experiment! Can we deducex, det)!(i,j) (~and⇢(i,j) ?

If the states !(i,j) (~x, det) are very different, e. g., when the initial state isbadly prepared, this becomes more and more difficult!
Intensity washes out
coherence:visibility of interference: how much does Idet (~x) resemble theprobability density | !(i,j) (~x, det)|2 ?

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 18

Coherence
Visibility of interference:
2
|
(~
x
,
det)|
how much does Idet (~x) resemble the probability density !(i,j)?

Statesx, det) must be sufficiently similar that the interference fringes!(i,j) (~are not washed out!
Influence of the source>transverse coherence
spatial differences ofx, det) as function of i.
!(i,j) (~>longitudinal coherenceenergetic differences ofx, det) as function of i.
!(i,j) (~Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 19

Example: speckle size varies inversely with object size

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 20

Transverse Coherence

D

d
z
L1

sourcesampledetector

Interference observable:

D
>
d
L1

d

: angle between two speckles as seen from sampleD: angle of source as seen from sample
L1

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 21

Transverse CoherenceDdzsourceL1

sampledetector

Transverse coherence length:

L1
lt =
D

d < lt : interference visible

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 22

Example: Transverse Coherence Lengthlt

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 23

Example: Transverse Coherence Lengthlt

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 24Longitudinal Coherence: Monochromaticity
Wave packet generated from superposition of monochromatic waves:(n + 1) = n( +

)

n=

ll =

,

n

1

+
ll

ll characteristic length of wave packet
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 25

Longitudinal Coherence: Monochromaticity
Difference in length of different paths through sample must notexceed ll:
diffraction to large angles:
path length difference large

sourceobjectdiffraction in forward direction:
path length difference small

reduction of longitudinal coherence destroys visibility of interferenceat large momentum transfer!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 26

Example: Longitudinal Coherence Length= 0.12

Diffraction grating in lightsof the bus to Kyoto
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 27

Lensless Imaging: Coherent Diffraction Imaging
A dream:biomolecule

diffraction patterninjection

e
s
l
u
p
y
x-ra

the promise:> data up to large momentum transfer q(large numerical aperture NA)high resolution
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 28

Reconstruction by Phase Retrieval

Difficulty: no direct image
Diffraction pattern: intensity (phase of wave field lost)
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 29

What Information is Coded in Phase and Modulus?
Test object:diffraction

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 30

What Information is Coded in Phase and Modulus?
Amplitudes:square root of diffraction pattern

FFT-1

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 31

What Information is Coded in Phase and Modulus?
Phase: modulus of all components set to 1
(shown: real part in gray scale)

FFT-1

phases are most important!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 32

Phase Problem: Information Lost
Is diffraction pattern unique?
>NO! Half of the information is missing!
(complex amplitudes vs. real diffraction pattern)
What additional information can be used to help solve the problem?
>Knowledge of part of the object:
Example:>Object confined to certain area!
(rest of image empty)
Support constraint!
>Object must be positive: positiveelectron density [small (real) object]
Number of unknowns reduced
below the number of measured
data!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 33

How to Obtain a Large Support?

detector furtheraway

2k x 2k detector
Large pixel and large field of view:

number of unknowns too large!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 34

How to Obtain a Large Support?

2k x 2k detector
Small pixel and small field of view:
very few unknowns (a lot of redundant information)!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 35

How to Obtain a Large Support?

2k x 2k detector
pixel half the size as in first example:
sufficiently few unknowns & high information content!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 36

Right Information Content: Oversampling

important result:in order for the diffraction pattern
to contain sufficient information torecover the real and imaginary partof the field amplitude, the speckles
have to be nicely resolved:
appropriate sampling:oversampling

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 37

Is Solution Now Unique?
No!!

Object can be arbitrarily shifted!
Both objects yield same diffraction pattern!

rFourier transform:
additional phase:e iq·rvanishes when taking
absolute square of
amplitude!
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 38

Is Solution Now Unique?
Diffraction pattern nearly point
symmetric!
transmission function:>real:
pure absorption
FT symmetric>imaginary:
pure phase object
FT anti-symmetric
In both cases:
Diffraction pattern has point
symmetry!

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 39

Is Solution Now Unique?
No!!

Object and its point inversion are both solutions
Both objects yield same diffraction pattern!

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 40

Is Solution Now Unique?
No!!

Object and its point inversion are both solutions
Both objects yield same diffraction pattern!
(except for central beam usually covered by beam stop.)

Babinet’s theorem!!

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 41

Iterative Phase Reconstruction

x, obj)i (~q , obj)i (~real-space constraint

Fourier-space constraint

0x, obj)i (~0q , obj)i (~real-space constraint:> support> positivity
> ...

FFT

FFT-1

Fourier-space constraint:0q , obj) :=
i (~

|

0
x, obj) pi (~· Idet (~q )0 (~i q , obj)|

R.W.Gerchberg & W.O. Saxton, Optic (1972) 35, 237
J.R. Fienup, Appl Opt. (1982). 21, 2758
R.P. Millane & W.J. Stroud, J. Opt. Soc. Am. (1997) A14, 568
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 42

Example

FT

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 43

Reconstruction

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 44

Reconstruction: Stagnation

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 45

Repeat Reconstruction
Deviation of model from diffraction pattern:
stagnatedconverged

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 46

Coherent Diffraction Imaging with Soft X-Rays
Object: Gold on Si3N4

light micrograph:diffraction pattern:reconstruction:

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

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 47

XFEL: Image and Destroy

1 µm

single-pulse
diffraction pattern

structure etched into membranereconstruction

H. Chapman et al.,Nature Phys. 2, 839 (2006)
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 48

XFEL: Image and Destroy
first pulse

second pulse:
sample destroyed

H. Chapman et al.,Nature Phys. 2, 839 (2006)
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 49

CXDI of Biological Samples: Mimivirus

reconstruction

M. Seibert, et al.,Nature 469, 78 (2011)
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 50

Spatial Resolution
Diffraction pattern ofa yeast cell:increase
fluence

{

{

~ q-4

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

increase
resolution

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 51

Nanofocusing Optics
pair of mirrors
in KB-geometryreflection:>mirrors (25 nm)

focus

source>capillaries>wave guides (~10 nm)
diffraction:

(a)

(b)

>Fresnel zone plates (~20 nm)>multilayer mirrors (7 nm)>multilayer Laue lenses (16 nm)>bent crystals
refraction:>lenses (43 nm, 18 nm)

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 52

Refractive X-Ray Lenses> first realized in 1996 (Snigirev et al.)> a variety of refractive lenses have been developed since> applied in full-field imaging and scanning microscopy> most important to achieve optimal performance:
parabolic lens shape
nanofocusing lenses

100 µmLengeler, RXOptics
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 53

Nanofocus
Large focal length f: aperture limited by absorption
De↵

p
f
/ f
µ

minimize µ/δ (
1
De↵
/p
NA =
2f
f

small atomic number Z)(

minimize focal length f)

apertureDe↵ = 4

s

NA

focus

f

transition tonanofocusing
lenses (NFLs)
100 µmChristian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 54

Nanofocusing Lenses (NFLs) Made of Silicon

single lensMade at IHM at TU Dresden together
with SAW Components.
3136 NFLs on wafer!
about 600000 single lenses!
high accuracy, reproducibility

opticalaxis
APL 82, 1485 (2003).

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 55

Nanofocusing Lenses (NFLs)
point focus requires two lenses incrossed geometry

synchrotron
radiation beamvertical lensslits

horizontal lens
ESRF ID13
point
focus

sample &scannerhoriz. focus. lensvert. focus. lens

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 56

Nanoprobe: Coherent X-Ray Diffraction Imaging
Nanoprobe at ID13 of ESRF

samplebeamstop

E = 15.25 keV
λ = 0.813 Å
beam size:< 150 x 150 nm2(amplitude)
gain: 104
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 57

Imaging of Small Objects
4 gold particles:
diameter ~ 40 nm
7.5·106 atoms

200 nmfluence:
1·105 ph/nm2
dose:
1 µm

1·1010 ph

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 58

Reconstruction
100 nmHIO
shrink wrap

resolution: ~ 10 nm
record resolution: 5 nm (1.5·106 ph/nm2)
diffraction at
single gold
particle
100nm

PRL 101, 090801 (2008).

4 gold particles:>fluence 10 x smaller>resolution reduced by⇥
4
10 1.8Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 59

CXDI of Silver Nanocube
SPring-8:

11.8 keV

total fluence:
16·106 ph/nm2

Y. Takahashi, et al., Phys. Rev. B, 80, 054103 (2009).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 60

Hard X-ray Scanning Microscopy at PETRA III
Microscope:~98 m from source
different contrasts:> fluorescence> diffraction (SAXS, WAXS)> absorption (XAS)> ptychography & CXDI
spatial resolution:
down to < 50 nm
down to < 5 nm (CXDI)
mono.

mirrorprefocusing

microprobe
nanoprobe

X-ray energy:
10 - 50 keV

Nucl. Instrum. Meth. A
616 (2-3), 93 (2010).

38.5m

43.3m

98.2m
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 61

Christian G. Schroer | Coherence 2014 | 28. Aug. 2014 | 62

Scanning Coherent Diffraction Imaging: Ptychography>Sample is raster scanned through confined beam
>At each position of scan: diffraction pattern is recorded>Overlap in illumination between adjacent points

samplefar-field
diffraction pattern

J. Rodenburg, H. Faulkner. Appl. Phys. Lett. 85, 4795 (2004),
P. Thibault, et al., Science 321, 379 (2008),
A. Schropp, et al., Appl. Phys. Lett. 96, 091102 (2010),
M. Dierolf, et al., Nature 467, 436 (2010).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 63

Ptychographic Microscopy
Experiment at P06:
detector:
Pilatus 300k (172µm pixel size)
sample-detector distance:
2080 mm
exposure time:
1.5 s per point

Sample: NTT AT test pattern

SEM image (I. Snigireva)
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 64

Ptychography: Reconstruction

generatetransmitted
wavefieldOscan position(⇥r) = O(⇥r) · P (⇥r

⇥ri )

cycle
many
times

propagateIi

updateamplitudes

P
updateobject &illumination

0

(⇥r)

backpropagatep0= Ii · ei·phase( )Maiden & Rodenburg, Ultramicroscopy 109, 1256 (2009).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 65

Scanning Microscopy: Fluorescence Imaging
Ta Lα fluorescence

E = 15.25 keV
50 x 50 steps of 40 x 40 nm2
2 x 2 µm2 FOV
exposure: 1.5 s per point
500 nm50 nm lines and spaces
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 66

Scanning Microscopy: Ptychography
0.0

-0.2

[rad]

-0.1

-0.3
-0.4

im
re
A. Schropp, et al., APL 96, 091102 (2010),
S. Hönig, et al., Opt. Exp. 19, 16325 (2011).

500 nm

E = 15.25 keV
50 x 50 steps of 40 x 40 nm2
2 x 2 µm2 FOV
exposure: 1.5 s per point
detected fluence: 2.75·104 ph/nm2
A. Schropp, et al., APL 100, 253112 (2012).

50 nm lines and spaces
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 67

Scanning Microscopy: Ptychography
pixel size: 3.84 nm
2
Different features have different resolution!!

31
4500 nm
A. Schropp, et al., APL 100, 253112 (2012).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 68

Scanning Microscopy: Ptychography
local diffraction pattern

qmax

2

3
Resolution of a feature depends
on its structure factor!
qmax
1
4500 nm
A. Schropp, et al., APL 100, 253112 (2012).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 69

Contrast in Coherent Diffraction Imaging
Mimivirus (TEM)

Microchip
M2
C2
M1
C1
M0
CG
CS

silane nitride
titanium/titanium nitride
silicon oxide
voids
aluminium
tungstensilicongate stack

200 nmOnly tungsten!
Where is theAl, Si, ... ?

M. Seibert, et al., Nature 469, 78 (2011).

A. Schropp, et al., J. Microscopy, 241(1), 9 (2011).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 70

Resolution and Contrast in Ptychography
For a given feature:
Signal = fluence * scattering cross section
coherent fluence on feature:
6.7·103 ph/nm2(a)~ structure factor of feature:

3.9·102 ph/nm2(b)

500 nm

500 nm
-0.4

-0.2
[rad]

0.0

-0.3

-0.1
[rad]

0.1

Schropp & Schroer, NJP 12, 035016 (2010).
Christian G. Schroer | DLSR Workshop | 5. Sept. 2014 | 71

Imaging at the X-Ray Free-Electron Laser
Linac Coherent Light Source (LCLS at SLAC)> short, dense electron bunches> long undulator
ultra short, very intense
x-ray pulses (10 - 100 fs)

Investigating the dynamics ofmatter on nanoscale.

Christian Schroer | SNI 2014 | 23. September 2014 | Seite 74

Focusing Hard X-Ray FEL PulsesgsourceFocusing needed:>increase fluence for imaging
resolution determined by!
fluence on sample

lens

L1

!

L2

b

Diffraction limited imaging of source

X-ray optics:>increase intensity on sample
induce non-linear opticaleffects!
>increase energy deposited insamplecreate matter inextreme conditions>...
beryllium parabolic
refractive x-ray lenses
B. Lengeler, RXOptics
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 75

Experiment at MEC at LCLS unattenuated beam

undulatorz = -464.0 m
monochromatorz = -376.4 m

test object (KTH)

Be-CRLsz = -0.25 m
samplez=0m

E = 8.2 keV, λ = 1.51 ÅEmonochrom. beam:⇡ 10 4E
Focusing by CRLs:>N = 20>R = 50 µm>300 µm aperture}CCD
z = 4.14 m

Attenuation: ⇡ 10 3

f = 250 mm
dt = 115 nm
A. Schropp, et al., Sci. Rep. 3, 1633 (2013).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 76

2 µm

Experiment at MEC at LCLS
512 x 512 pixel
54 x 54 µm2 pixel size

undulatorz = -464.0 m
monochromatorz = -376.4 m

Be-CRLsz = -0.25 m
samplez=0m
CCDz = 4.14 m

E = 8.2 keV, λ = 1.51 Å
Ptychogram:
20 x 20 steps
100 x 100 nm2 step size
single shot exposure: 2 exposures per point
384 out of 400 (800) images for reconstruction

A. Schropp, et al., Sci. Rep. 3, 1633 (2013).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 77

Reconstruction
0.0

phase [rad]object

-0.3
-0.6
-0.9
-1.2
-1.5

illumination

-1.8

im
2 ѥm

re

relative intensity

1.0

averageposition 1
position 2

0.8
0.6

125 nm

0.4
0.2
0.0

2 ѥm

-1000

-500
0
500
horizontal position [nm]A. Schropp, et al., Sci. Rep. 3, 1633 (2013).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 78

1000

Nanofocused LCLS Beam Profile

im

5 μm

re

1
5 μm

5 mm

z

2
identify aberrations of lens
feed into fabrication

A. Schropp, et al., Sci. Rep. 3, 1633 (2013).
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 79

High Resolution X-Ray Imaging at XFEL Sources
Method: magnifying phase contrast imaging> imaging with secondary point source: efficient use of fluence> phase contrast: for quantitative results, phase retrieval required
Alternatively:
Time-resolved diffraction in focus of nanobeam
Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 80

An X-Ray Microscopists Dream
Quantitive in-situ measurement of physical properties of matter>on all relevant length scales>on all relevant time scales
Key technology: brilliant, coherent x-rays with time structure
Fusion of real and reciprocal space:access to all length scales(in principle) from Å to millimeters
Requirement: a lot of coherent light
X-ray free-electron lasers
diffraction limited storage rings

Christian G. Schroer | Cheiron School 2014 | 29. September 2014 | page 82