Post on 03-Apr-2020
ESI2013 : X-ray Optics for SR Beamlines
Ray BARRETT
X-ray Optics GroupEuropean Synchrotron Radiation Facility
e-mail : barrett@esrf.fr
ESI2019: 6th EIROforum School on
Instrumentation
X-ray Optics for Synchrotron
Radiation Beamlines
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett Page 2
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 3
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Refractive lenses
Reflectors
Zone plates
Summary
Scope:
•Non-exhaustive overview
•Primarily ‘hard’ X-ray optics (i.e.
photon energies >2-100 keV)
•Slight bias for ESRF applications
•References for further reading
SYNCHROTRON BEAMLINES
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Source
• spectrum (E/E)
• emittance (size x divergence)
• degree of spatial coherence
• brilliance (ph/s/mm2/mrad2/0.1%bw)
• polarisation (linear, circular, elliptic)
Sample
• beam size (µm)
• beam divergence (µrad)
• flux (ph/s)
• temporal coherence: E/E
• spatial coherence
• polarisation
OPTICS
?
collimating
optics
refocussing
optics
monochromator
Typical optical geometry
10 50Energy (keV)
Bri
llia
nce
(ph
/s/m
m2/m
rad
2/0
.1%
b.w
.)
VISIBLE LIGHT OPTICS
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Diffractive optics
Mirrors
Polarising Optics
Fresnel lenses
Refractive lenses
Fibre optics/ waveguides
Filters
+ interferometers, …
X-RAY OPTICS
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 6
Refractive lenses
Mirrors
Capillary optics
waveguides
Diffractive optics
Fresnel lenses
Filters
+ polarising optics,
interferometers, …
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 7
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Reflectors
Zone plates
Refractive lenses
Summary
Wilhelm Conrad Röntgen
1845-1923
Anna Bertha Röntgen
Taken 1895
X-RAY OPTICS: MANY APPROACHES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 8
REFLECTION
< Ec
Refl
ecti
vit
y
Energy
Ec
• X-ray mirrors
• Capillaries
• Waveguides
DIFFRACTION
d
E,
2dsin =
• Crystals & multilayers
• X-ray gratings
• Fresnel zone plates
• Bragg-Fresnel lensR
eflectivity
Energy
• Very weak refraction
• Quite high absorption
n=1-d+ib with d, b <<< 1
“... The refractive index.... cannot be more than 1.05 at most....
….X-rays cannot be concentrated by lenses...”
W.C. Röntgen
Über eine neue art von Strahlen.
Phys.-Med. Ges., Würzburg, 137, p. 41,
(1895)
English translation in Nature 53, p. 274
d (phase-shift), b (absorption), materials
(and energy) dependent optical constants
•Refractive lenses
REFRACTION
n1=1- d+ ib n1<no
n =1
rio nn coscos 1
o
TOTAL EXTERNAL REFLECTION
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 9
c
E
c
1
n=1-d+ib
]/[ 3][][
83.19cmgcc keVmrad
E
• Gold 9 mrad
• Nickel 6 mrad
• Silicon 3 mrad
E=10keV
Snell’s Law:
r
i
for d << 1 and b << d
Zc d 2
c
The critical angle for total
external reflection.
See also: http://www.coe.berkeley.edu/AST/sxreuv/
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10000 20000 30000 40000Energy [eV]
Re
fle
cti
vit
y
3mrad
incidence
Si Ni Pt
‘real’ materials
• Grazing incidence often long (gravity sag)
• Most SR mirrors manufactured from Si
• One or several coatings applied after polishing
X-RAY MIRRORS : MAIN FUNCTIONS
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Deflection
beam steering (different experiments, Bremsstrahlung)
Power filter
lower incident power on sensitive optical components (e.g. Monochromator)
Spectral shaper
low-pass energy filter (harmonic rejection)
Focusing or Collimation
parabolic mirror: match monochromator angular acceptance with beam divergence
pre-focusing: spherical, cylindrical, and toroidal mirrors …
microscopy & microprobe: ellipsoidal mirror, KB, Wolter …
c
E
c
1
n=1-d+ib
CURVED SURFACES: FOCUSING
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qp
qpR
qp
qpR
is
i
m
sin2
sin
2
Radii of curvature :
Source
Focus
• Often long mirrors (> 1m)
• Off-axis geometry
• Point-to-point focusing ellipsoidal figure
• Fabrication aspects not generally ellipsoidal
• Aberrations (astigmatism and figure errors)
= 10mrad2ms RR ~
~
kmR
mmR
m
s
e.g. toroidal mirror – meridional & sagittal focusing q
p
Material-coating: Silicon-Pt
Supplier: SESO (France)
Roughness 2Å rms
Radii of curvature:
• Sagittal: 71.60 mm
• Meridional: 25 km
Slope error (RMS)
• 0.7 µrad over 450 mm
• 1.0 µrad over 900 mm
TOROIDAL MIRROR (ID09 ESRF)
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 12
REFLECTIVE X-RAY OPTICS
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett
IDEAL SURFACE
Best quality X-ray mirrors: slope errors < 0.1 µrad rms, figure errors < 1nm p.v.
Page 13
REAL SURFACE
Δθ
Δθ
ΔθΔθ
slope errors
figure
errors
1 nm 6 mm
Mirror shape Profile
20 keV, 1.2 mrad
Intensity @ 1m
I
ΔI
ΔI/I ~30%
H. Mimura et al, Rev. Sci Inst 76, [4] (2005) 045102–6 doi:10.1063/1.1868472.
X-RAY DIFFRACTION
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Incident X-rays are “reflected” at atomic planes in the crystal lattice
Path difference of the rays 2dhkl sinB
Constructive interference if the path difference amounts to
2dhkl sinB =
BB
dhkl
Reflecting planes described using Laue indices, h k l (e.g. 1 1 1,
3 3 3, 4 4 4)
Bragg equation:
X-ray diffraction from
highly perfect single
crystals (e.g. Silicon) is
routinely used to
monochromatise
polychromatic X-ray
beams
CRYSTAL MONOCHROMATORS
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Bhkld
hchcE
sin2
BsE
E
cot
2
0
2
X-ray diifraction used to select narrow energy band
from a polychromatic incident beam. Energy
determined by incidence angle, θB, of beam onto
crystal planes:
Energy resolution depends upon type of crystal
and reflecting planes used (described by angular
Darwin width ωs) & divergence of incident beam,
ψ0
e.g. Si 111 reflexion,
dhkl= 3.1355Å
ωs = 35 µrad (@ 8keV):
θB = 14°
with a parallel incident beam:
ΔE/E = 1.4.10-4, ΔE=1.1eV
Monochromators typically need
to be able to position the crystal
planes with µrad resolution and
similar repeatability with
particularly stringent demands
on stability over many hours:
1st crystal support
2nd crystal support
SINGLE CRYSTALS : MAIN APPLICATIONS
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Applications
High resolution monochromator / analyser
10-8 < E/E < 10-3
Focussing monochromators
bent crystals
Collimation / beam expander
asymmetrical cut
Phase retarder (polariser)
Technical requirements
Perfect crystals exist (Si, Ge, Diamond ...)
but they must be tailored into monochromators
orientation, cutting, etching and polishing
strain free crystal preparation, accurate
and stable mounting
Appropriate cooling scheme
B B
Reflection
(Bragg case)
Most common
dh 2B
Transmission
(Laue case)
High energy, beam splitters
dh2 principal geometries:
SR monochromators
mostly Float Zone Si
X-RAY MULTILAYERS
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Substrate: typically
ultrapolished Si
X-ray region : due to refraction, modified Bragg’s law
n 2 d1 d2 1d
sin2 b
sinbVacuum
n1=1- d+ ib
n2=1- d+ ib
'
"
b
d1
d2
21
21
1
)1(
)(
ddd
dd
d
e.g. A.E. Rosenbluth et al., Appl. Phys.
Lett., 40, 486, (1982)
high reflectivity x-ray mirrors…or synthetic crystals
nl=1- d1 + ib1 and n2=1- d2+ ib2
b
layerNR
bd4
222
sin4
Thin film deposition (e.g. sputtering) of
layer system
θB θB
X-RAY MULTILAYER CHARACTERIZATION
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Total
Reflection
regime
Characteristic multilayer reflexions
Typical X-ray reflectivity scan of a multilayer
W B4C W W B4CB4C B4C
[W/B4C]50
•Wide energy band-pass
•Soft X-ray monochromators
•Focusing : b multilayer >> c mirror
→ multilayer length << mirror length
lower spherical aberrations (~L2),
increased numerical aperture
d-spacing
typically
~10x that of
inorganic
crystals
COMPOUND REFRACTIVE LENS
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Example :
Aluminium @ 10keV d
1 hole of 100 µm radius : f = 9 m
15 holes of 100 µm radius: f = 60 cm
bd in 1
RN
f
d21
X-rays :
Rf
d21
R
R
N holes
n1< 1 : concave lens
n1
p q
no= 1
Advantages
- simplicity and low cost
- low sensitivity to heat load
Disadvantages
- efficiency limited by absorption
- small aperture (limited resolution)
- strong chromatic aberrations (dλ2)A. Snigirev et al. Nature, 384 (1996)
( )R
n
f
1121 -
=:Gaussian lens equation
qpf
111+=:Thin lens equation
Be / Al parabolic lenses (Prof B. Lengeler , Univ. Aachen)
50 mm500 mm1.5 mm 300 mm 200 mm1 mm
2D Be lenses
linear Al lens
A =1 x 3.5 mm2
R = 200 mm
10 mm
PARABOLOIDAL & PARABOLIC CYLINDER X-RAY LENSES
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RN
f
d21
Typical parameters :
R = 50 to 1500 µm
2R0 = 0.45 to 2.5 mm
d < 30µm
• Parabolic/oidal profile no spherical aberration
• Be ~2-40 keV absorption↓
• Al ~40-80 keV
• Ni ~80-150 keV
PARABOLIC REFRACTIVE LENSES
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B. Lengeler, C. Schroer, M. Richwin,
RWTH, Aachen, Germany
1mm200
µm
10
µm
Materials:
low Z, high density
Al, Be, B, Si, …
Stack up to ~ 100 lenses to tailor focal length to experiment
Highly chromatic focusing transfocator
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 22
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Reflectors
Zone plates
Refractive lenses
SummaryJames Watt
1736-1819
HIGH HEAT LOAD OPTICS
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ESRF U18 Undulator L=1.65m K=1.3, 90
periods, 200mA Storage Ring Current
Total Emitted Power = 4.5kW
Through 3x3mm aperture @ 30m = 1.4kW
On-axis Power density 210W/mm2
ESRF U18 Undulator K=1.3, 200mA
(3x3mm2 aperture @30m)
0
2E+14
4E+14
6E+14
8E+14
1E+15
1.2E+15
1.4E+15
1.6E+15
1.8E+15
0 20 40 60 80 100
X-ray Energy [keV]
Flu
x [
ph
/s/0
.1%
b.w
.]
Source emission
After 300µm Diamond window
After Rh mirror reflection @ 3mrad
•300µm polished diamond absorber (high pass Energy filter) absorbs 135W
•Rh-coated mirror reflecting at 3mrad (low-pass energy filter) absorbs 700W
•Around 550W incident on monochromator crystal – essentially all absorbed
• efficient cooling to prevent from melting
• minimization of induced thermal deformation
• materials resistant to intense X-ray beams
MONOCHROMATOR COOLING
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Darwin widths of typical crystal reflexions
are in the µrad range:
Monochromator performance is particularly
sensitive to thermal deformations of
diffracting crystals
By cooling Si to cryogenic temperatures
(LN2 sufficient) – thermal deformations due
to beam absorption can be minimised.
Ratio of thermal expansion and thermal
conductivity of Si, /, vs temperature
Example of ESRF first crystal assembly:
(1) silicon crystal; (2) copper cooling blocks
with internal fins; (3) invar clamping rods; (4)
invar base plate; (5) ceramic insulating plates
•Crystal is side cooled with cooling blocks clamped with pressures between 5-10bar
•Deformation of crystal planes due to clamping <1µrad
•Over 17 ESRF beamlines using LN2 cooled monochromators
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 25
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Refractive lenses
Reflectors
Zone plates
Summary
TYPICAL X-RAY FOCUSING SCHEMES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 26
Detection of signals arising from interaction of small probe with sample
Sample scanned through beam to build ‘image’ pixel by pixel
•Condenser optic → illuminated zone on sample
•Objective lens → magnified image of sample on spatially resolving detector
Probe forming
Full field imaging
Source, oobjective lens, focal length f Probe, i sample
p q
spatially resolving
Detector, i (film, CCD)
condenser optic
objective lenssource
Sample, oilluminated zone
magnified image
p q
fqp
111Thin lens
p
q
o
iM Magnification,
For fixed p, M ↑ f ↓
source sample
X-RAY FOCUSING OPTICS
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• Fresnel zone-plate (FZP)
• Bragg-Fresnel
• Crystals
• Multilayers
• Multilayer Laue Lens
• Kirkpatrick-Baez
• Wolter mirror
• Ellipsoidal mirror
• Micro-channel
• (Poly)capillaries
• Compound
refractive lenses
(CRL)
• Waveguides
Diffractive optics
X-ray resonators
X-ray reflectors
Refractive lenses
TECHNOLOGICAL CHALLENGES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 28
Sub-10nm resolution X-ray focusing is possible BUT the technological
challenges are considerable
Diffractive Optics:
Feature size/placement
Structure heights
(efficiency)
Refractive Optics:
Absorption limited
numerical aperture
Side-wall roughness
Reflective Optics:
Figure Error
Thermal, mechanical
stability,
Graded multilayers
Resolution is not the only parameter. Often photon flux, focus
stability is at least as important. Large acceptance, high
efficiencies…
100 μm
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 29
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Refractive lenses
Reflectors
Zone plates
Summary Willebrord Snellius
1580-1626
PLANAR COMPOUND REFRACTIVE LENSES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 30
Si lens: e-beam lithography & deep trench RIE
short f small R
Most easily achieved
using planar fabrication
technologies:
R = 1µm - 3µm
N = 50 - 100
RN
f
d21
2D focusing: separate
lens arrays for H and V
focusing
Best focus: 47 nm fwhm @ 13 keV
C. Schroer et al., App. Phys. Lett. 87 (2005):
doi:10.1063/1.2053350.
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 31
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Refractive lenses
Reflectors
Zone plates
Summary
MIRRORS FOR MICRO- AND NANO-FOCUSING
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 32
‘Ideal’ mirror for 2d imaging of a point source has an
ellipsoidal (3D) surface figure. For micro/nanofocusing
applications high quality ellipsoidal mirrors not readily
manufacturable
Separate horizontal and vertical focusing
Kirkpatrick-Baez (KB) configuration: perpendicular elliptical
cylinder mirrors
Kirkpatrick-Baez
mirror pair
adapt to source asymmetry
•apertures
•demagnification
Vertical
focusing
Horizontal
focusing
Ellipsoidal X-ray mirror
200 mm
Flat, multilayer coated Si
substrate mechanically
bent to elliptical figure
Complete KB
76mm
Sub 50 nm x 50 nm focusFlux > 1012 ph/s (pink) on NA branch
DYNAMICALLY BENT KB SYSTEM
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ESRF ID16B
Large solid angle, high through-putfluorescence detectors
High-resolution imaging detector
On-line microscope optics
Nano-focusing optics:Fixed curvature,multilayer coated KB optics
3D nano-positioning ofMetrology reference undercontrol of capacitive sensors
GOALS: Focus < 20 nmFlux > 1011 ph/s E = 17 keV or 33.6 keVE/E = 1%
In-vacuum + Cryo
X-rays
ID16A-NI NANO-IMAGING END-STATION
Compact, fixed curvature,
multilayer coated KB
mirrors integrated into ESRF
designed mechanics
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 34
J. Cesar da Silva et al, Optica 4, 492-495 (2017);
DIFFRACTION LIMITED FOCUSING AT 34KEV
Page 35 ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett
ESRF ID16A beamline: Fixed figure, elliptical cylinder mirrors:
Figure errors < 1nm pv, roughness < 1Å, Multilayer coatings to
increase aperture
BEAM PROFILE RECONSTRUCTION BY PTYCHOGRAPHY
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J. Cesar da Silva et al, Optica 4, 492-495 (2017);
13 x 13 nm2 fwhm beam size
CURRENT BEST FOCUSING PERFORMANCE FOR MIRRORS
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 37
Advanced Metrology
Techniques
Graded multilayer
deposition
H. Mimura et al., “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat Phys 6, (2010): 122-125
Coherent illumination
SPring-8 1km BL
Wave-optical
Modeling
20keV: 7 nm measured focal spot
Active wavefront
correction
Deterministic sub-
aperture figure correction
SiO2
Si
EEM
Figure errors ~ 1nm p.v.
INTRODUCTION TO X-RAY OPTICS FOR SR
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 38
Introduction
General X-ray optics
High heat-load optics
X-ray micro-/nano-focusing
Refractive lenses
Reflectors
Zone plates
SummaryAugustin-Jean Fresnel
1788-1827
FRESNEL ZONE PLATES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 39
Planar wavefrontHologram (Fresnel Zones)
Reconstruction
by
coherent illumination
focus
Baez (1952)
Schmahl (1969)
Kirz (1971)
Niemann (1974)
Gabor hologram of a point object
Circular transmissive diffraction grating
with radially decreasing line width
X-RAY ZONE-PLATES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 40
E. Anderson, Center for X-Ray Optics, LBNL, USA
• rN = 25 nm
• D = 63 µm
• N = 618 zones
• f = 650 µm
• NA = 0.05
@ = 2.4 nm
Most zone plates are produced using e-beam lithography
FOCUSING BEHAVIOUR OF FRESNEL LENSES
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 41
Multiple diffraction
orders
m = 1
m = 3
m = 0
m = -1f
f/2
f/3
m = 1
ORDER SELECTING APERTURE
FIRST ORDER FOCUS
Rejection of the unwanted diffraction orders
Resolution:m
rNm
22.1d
Focal length:m
rDf N
m
Depth of focus:m
rDOF N
22
CENTRAL STOP
FOCUSING BEHAVIOUR OF FRESNEL LENSES
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ZONE PLATE ASPECT RATIO
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rN
t
Nickel
25%
12 : 1
2.0 keV
Tantalum
32%
28 : 1
8.0 keV
Material t (µm) e (%)
E=0.5keV
Ge 0.28 16
Ni 0.25 24
E=2.0keV
Ni 0.60 25
Au 0.45 24
E=8.0keV
Ta 1.70 32
W 1.50 33
Nickel
24%
6 : 1
0.5 keV
Aspect ratio for rN=50nm
Practical limit for
small rN is ~ 10-15:1
structure height, t, critical for efficiency, rN for resolution
MULTILAYER LAUE LENSES
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substrate
Varied line-
spacing
grating
Depth-graded multilayers
on flat Si substrate
• Deposit varied line-
spacing grating on flat
substrate
(thinnest structures first)
• Section to 5-20 mm
thickness
(high aspect ratio
structure)
• Assemble two into a
single device
(MLL)
8 nm focus @ 22 keV:
Initial development: H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T.
Macrander, and S. Vogt, Phys. Rev. Lett. 96, (2006).
A.S. Morgan, et al. “Scientific Reports 5 (2015).
doi:10.1038/srep09892.
courtesy A. Kubec
PROGRESS IN HARD X-RAY FOCUSING
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Moore’s law adapted to the X-ray world:
ESRF Red Book (1987):
very few beamline projects
aiming even for 10 micron
sized beams
Now optics exist for 10nm
beams
Routine application of sub-
micron beams still
complicated
Also many engineering
issues in implementing
stable, reliable X-ray
nanofocusing systems
Historical evolution of the measured spot size for different
hard x-ray focusing elements (courtesy C. Morawe)
1
10
100
1000
10000
1995 2000 2005 2010 2015 2020S
po
t s
ize
[nm
]
Year
• A. Morgan et al. Scientific Reports, 5, 9892 (2015)
• H. Mimura et al. Nature Physics, 6, 122-125 (2010).
• J. Vila-Comamala et al., Ultramicroscopy,109,1360–1364 (2009)
• H. Kang et al., Physical Review Letters, 96:127401 (2006)
• C. Schroer et al., Physical Review Letters, 94:054802 (2005)
Best focus
Experiments
Ultimate resolution
Theory
• CRL
• KB
• FZP
• MLL
COMPARISON
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source sample
• Resolution ++++ ++ ++
• Achromaticity -(-) +++ --(-)
• Efficiency + +++ ++
• Imaging (MTF) ++++ (ZP) + ++
Zone plates/MLL Refractive lenses
Energy
Mirrors
SUMMARY & CONCLUSION
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett 47
3rd generation synchrotron X-ray sources have driven the
development of new X-ray optics
dramatic improvement in manufacturing and preparation techniques
low roughness, high-accuracy figuring, perfect crystals (Ge, Si), diamond, ...
improved power management strategies
focusing optics (spot size ~ 50- 0.01µm)
zone-plate and refractive lenses, elliptically figured mirrors (Bragg-Fresnel lenses,
capillaries, wave guides)
wide range of experimental requirements – no one ideal optic
R&D programs continuously in progress: current hot-topics
preservation of the wave-front quality – especially important for fully
coherent XFEL sources and DLSR sources
sub-10nm focusing
QUESTIONS?
ESI2019: X-ray Optics for SR Beamlines |14/05/19| R. Barrett Page 48