Ray BARRETT - Indico€¦ · By cooling Si to cryogenic temperatures (LN2 sufficient) –thermal...

ESI2013 : X-ray Optics for SR Beamlines

Ray BARRETT

X-ray Optics GroupEuropean Synchrotron Radiation Facility

e-mail : [email protected]

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

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


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


Diffractive optics

Mirrors

Polarising Optics

Fresnel lenses

Refractive lenses

Fibre optics/ waveguides

Filters

+ interferometers, …

http://upload.wikimedia.org/wikipedia/commons/e/e8/Cape_Meares_Lighthouse_lens_-_Oregon.jpg

http://upload.wikimedia.org/wikipedia/commons/e/e8/Cape_Meares_Lighthouse_lens_-_Oregon.jpg

http://www.google.com/imgres?imgurl=http://www.hitachi-hitec.com/global/science/uv_vis/img/grating/concave_diffraction_grating.jpg&imgrefurl=http://www.hitachi-hitec.com/global/science/uv_vis/grating_2.html&usg=__MZ3-lj48I1r7ZvYrWMuQd6di5RM=&h=140&w=350&sz=44&hl=en&start=55&zoom=1&tbnid=ifWLALrOKNOR6M:&tbnh=72&tbnw=179&ei=FjrSTayHNYKnhAfLsuSECg&prev=/search?q=diffraction+grating&hl=en&client=firefox-a&hs=wQw&sa=X&rls=org.mozilla:en-US:official&biw=1716&bih=1019&tbm=isch&itbs=1&iact=hc&vpx=691&vpy=737&dur=5172&hovh=112&hovw=280&tx=143&ty=66&page=2&ndsp=53&ved=1t:429,r:21,s:55

http://www.google.com/imgres?imgurl=http://www.hitachi-hitec.com/global/science/uv_vis/img/grating/concave_diffraction_grating.jpg&imgrefurl=http://www.hitachi-hitec.com/global/science/uv_vis/grating_2.html&usg=__MZ3-lj48I1r7ZvYrWMuQd6di5RM=&h=140&w=350&sz=44&hl=en&start=55&zoom=1&tbnid=ifWLALrOKNOR6M:&tbnh=72&tbnw=179&ei=FjrSTayHNYKnhAfLsuSECg&prev=/search?q=diffraction+grating&hl=en&client=firefox-a&hs=wQw&sa=X&rls=org.mozilla:en-US:official&biw=1716&bih=1019&tbm=isch&itbs=1&iact=hc&vpx=691&vpy=737&dur=5172&hovh=112&hovw=280&tx=143&ty=66&page=2&ndsp=53&ved=1t:429,r:21,s:55

http://upload.wikimedia.org/wikipedia/commons/4/4c/Lighthouse_Lens.jpg

http://upload.wikimedia.org/wikipedia/commons/4/4c/Lighthouse_Lens.jpg

http://upload.wikimedia.org/wikipedia/commons/f/f7/Magnifying-fresnel-lens.jpg

http://upload.wikimedia.org/wikipedia/commons/f/f7/Magnifying-fresnel-lens.jpg

http://upload.wikimedia.org/wikipedia/commons/a/ac/Four_solaire_001.jpg

http://upload.wikimedia.org/wikipedia/commons/a/ac/Four_solaire_001.jpg

http://upload.wikimedia.org/wikipedia/en/4/46/Filter-optics-1.jpg

http://upload.wikimedia.org/wikipedia/en/4/46/Filter-optics-1.jpg

http://upload.wikimedia.org/wikipedia/commons/e/ee/2008-03-14_Convex_mirror_in_Atlanta_garage_entrance.jpg

http://upload.wikimedia.org/wikipedia/commons/e/ee/2008-03-14_Convex_mirror_in_Atlanta_garage_entrance.jpg

X-RAY OPTICS


Refractive lenses

Mirrors

Capillary optics

waveguides

Diffractive optics

Fresnel lenses

Filters

+ polarising optics,

interferometers, …



Introduction




Reflectors

Zone plates

Refractive lenses

Summary

Wilhelm Conrad Röntgen

1845-1923

Anna Bertha Röntgen

Taken 1895

X-RAY OPTICS: MANY APPROACHES


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


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


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


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)


REFLECTIVE X-RAY OPTICS


IDEAL SURFACE

Best quality X-ray mirrors: slope errors < 0.1 µrad rms, figure errors < 1nm p.v.

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


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


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


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


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


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


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


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


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




Reflectors

Zone plates

Refractive lenses

SummaryJames Watt

1736-1819

HIGH HEAT LOAD OPTICS


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


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




Refractive lenses

Reflectors

Zone plates

Summary

TYPICAL X-RAY FOCUSING SCHEMES


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


• 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


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




Refractive lenses

Reflectors

Zone plates

Summary Willebrord Snellius

1580-1626

PLANAR COMPOUND REFRACTIVE LENSES


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




Refractive lenses

Reflectors

Zone plates

Summary

MIRRORS FOR MICRO- AND NANO-FOCUSING


‘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


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


J. Cesar da Silva et al, Optica 4, 492-495 (2017);

DIFFRACTION LIMITED FOCUSING AT 34KEV


ESRF ID16A beamline: Fixed figure, elliptical cylinder mirrors:

Figure errors < 1nm pv, roughness < 1Å, Multilayer coatings to

increase aperture

BEAM PROFILE RECONSTRUCTION BY PTYCHOGRAPHY


J. Cesar da Silva et al, Optica 4, 492-495 (2017);

13 x 13 nm2 fwhm beam size

CURRENT BEST FOCUSING PERFORMANCE FOR MIRRORS


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




Refractive lenses

Reflectors

Zone plates

SummaryAugustin-Jean Fresnel

1788-1827

FRESNEL ZONE PLATES


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


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


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


ZONE PLATE ASPECT RATIO


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


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


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


source sample

• Resolution ++++ ++ ++

• Achromaticity -(-) +++ --(-)

• Efficiency + +++ ++

• Imaging (MTF) ++++ (ZP) + ++

Zone plates/MLL Refractive lenses

Energy

Mirrors

SUMMARY & CONCLUSION


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?


Ray BARRETT - Indico€¦ · By cooling Si to cryogenic temperatures (LN2 sufficient) –thermal...

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