Id01 diffraction imaging

ESRF IMAGING SEMINAR SERIES
Microscopy with and without microscopes:
X-ray imaging under diffraction conditions
TOBIAS SCHÜLLI
ESRF seminar April 28th 2015
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INTENTION OF THIS SEMINAR
To be interesting
Show the motivation and the wider context &
origin of our methods
Be comprehensive for everybody
Abbé limit of resolution in microscopy
1.22*λ
∆x =
2*n*sinα
Avoid equations
sinα 0.66
∆x
≥
λ
n
Heisenberg uncertainty
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∆x∆p ≥ h
OUTLINE
Imaging with light and microscopes
Diffraction (and) imaging techniques, review of the potential of x-rays
Short examples on what can be done with diffraction imaging
What exactly is “coherence” and why do we need it ?
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LIGHT MICROSCOPY (SINCE 16TH CENTURY)
Refraction used to produce lenses
defocusing lens:
Focusing lens:
Makes an image
“short sighted person”
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At equal lens
diameter a short
sighted person can
look with a larger
collection angle at
objects.
MAGINFICATION (THE VERY INTEREST OF MICROSCOPY)
Magnification depends on : distance of object from lens and the lens curvature,
The magnification depends NOT on the diameter of the lens.
Be careful with “1000-times magnification” Microscopes
Magnification is not in itself a figure of merit
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MAGNIFICATION AND RESOLUTION
Be careful with “1000-times magnification” Microscopes
Bigger lens
Very big lens
Magnification: geometrical optics (no reasonable limits, everything is allowed)
Resolution (=∆
∆x): real information: limited (at least) by quantum mechanics
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MICROSCOPY, RESOLUTION AND WAVELENGTH
Abbé limit for resolution (1870):
∆x is the smallest object that can be resolved
∆x=
1.22 * λ
λ
≈ 0.66
2 * n* sin α
sin α
at best ∆x ~ 0.6..1.0*λ
n: refractive index (1 in air)
Ernst Abbé (1840 (Eisenach) -1905 (Jena) ),
Physicist and Mathematician,
1863: Lecturer in Jena
1866: Hired as Research Director by Carl Zeiss Optics (Jena)
1870: Formulation of Abbé’s law
1871: Marriage with Else Snell (Karl Snell’s daughter)
1874: Co-owner of Zeiss Optics
1884: Co-founder (with C.&R. Zeiss and Otto Schott) of Schott company
1889 (+ C. Zeiss): Sole owner of Zeiss Optics
1890-1900: Zeiss foundation: company becomes independent of personal
ownerships’ interests.
2α
High resolution means small wavelengths and large apertures (large collection angles)
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RESOLUTION, X-RAY WAVELENGTH AND LENSES
2α
Abbé limit for resolution:
∆x ≈ 0.66
Light wavelength
λ~400…800 nm
X-ray wavelength (typical)
λ=0.01…0.1 nm
X-rays have a 10 000 times smaller wavelength than light
To produce lenses for x-rays we need refraction (as for light), refraction
depends on the polarizability of a material
X-rays have a way too high frequency for electron clouds to follow ,
-> they polarize materials only very little (almost no refraction)
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λ
sin α
USING X-RAYS WITHOUT OPTICS
1. Shadow play:
Resolution depends (roughly) on source size
2. X-ray (light) scattering (no images but averaged information)
Moon Halo: refraction by ice particles.
Average shape (angles between
facets) can be extracted.
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(BRAGG) DIFFRACTION OF X-RAYS
Constructive interference of waves reflected by atomic planes spaced by d
depends on angle of incidence θ and wavelength λ:
Bragg’s law
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sinθ = n
λ
2d
, n =1,2,3,...
DIFFRACTION (AND) IMAGING TECHNIQUES
Radiography vs. Diffraction
Imaging: full field technique
with spatial resolution ~sub
mm (traditional sources)
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Diffraction : spatial resolution
limited in any case and traded in for
angular resolution
DIFFRACTION AND SCATTERING: ADVANTAGES
Objects can be far away (leaves a lot of space
around the sample)
Angular resolution obtained by diffraction
leads to spatial information below λ ->
“interferometric” technique(~0.0001 nm for
Bragg diffraction in crystals)
Limits: requires spatially homogeneous samples
Position 1: interatomic distance a
Position 2: interatomic distance b
In many interesting systems,
heterogeneity happens to be on the
“mesoscale” (not atomic scale).
Combining small x-ray beams with
diffraction
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DEVELOPMENT OF X-RAY OPTICS
Mirrors:
P. Kirkpatrick (1894-1992)
A. Baez (1912-2007)
Refractive lenses:
small radii of curvature+ use many of them,
Excellent imaging devices
Diffractive optics: Fresnel zone plates
Excellent focusing devices
Some geometric drawbacks in imaging
Today, focusing down to 100 nm (or less) is possible
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COMBINATION OF LIMITING OPTICS AND DIFFRACTION
Abbé limit for resolution:
∆x ≈ 0.66
λ
sin α
2α
Collection angle 2α
Wavelength λ
Light
~90°
500 nm
X-rays
~0.1°
0.05 nm
X-rays 1000 times worse
X-rays 10 000 better
Disappointing.. It looks like we can only win a factor of 10.
BUT
Combining the “good” spatial resolution of ~100 nm
with diffraction (small fractions of atomic distances resolved) offers
a great potential
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DIFFRACTION IMAGING: SCANNING PROBE
Use of focused beam/ scanning
technique.
Resolution limited by beam spot
Sub 100 nm are possible
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Detector
Diffracted signal
DIFFRACTION IMAGING: X-RAYS SEE MORE THAN LIGHT
Light interference microscopy
Scanning x-ray diffraction
microscopy
After growth
After polishing
Zöllner, Richard, Chahine:
Appl. Mat.&Interf. In press
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Surface roughness
Lattice undulations
SCANNING DIFFRACTION TECHNIQUES
0.1mmx0.1 mm ESRF logo written in a Si crystal: imaging of lattice strain and tilt:
Relative strain levels of ∆a/a = few 10-6 can trace a landscape:
We can “see” a ∆T of a few °C potentially in buried systems
(working devices),
G. A. Chahine, M.-I. Richard, R. A. Homs-Regojo et al., J. Appl. Cryst. (2014)
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DIFFRACTION IMAGING: FULL FIELD
Detector
Full field technique
Resolution ultimately limited
by numerical aperture of the
Imaging optics
Sub 100 nm within reach
Diffracted signal
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T. U. Schulli
DIFFRACTION IMAGING: FULL FIELD (DARK FIELD IMAGING)
Similar information as before but “in one shot”(no scanning across the sample)
Ideal full-field application:
J. Hilhorst et al. J. Appl. Cryst. (2014). Processes (growth, annealing, ….
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FROM FULL FIELD TO COHERENT DIFFRACTION IMAGING (CDI)
Detector
Full field technique
Resolution ultimately limited
by numerical aperture of the
imaging optics
Sub 100 nm within reach
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T. U. Schulli
COHERENT DIFFRACTION IMAGING (CDI)
Coherent Diffraction Imaging:
Detector
Theory of optics is very well known.
-> Measure all emitted rays from the
sample and replace the lens by a
computer to calculate the image
What we can do
The physics of resolution remains the same
∆x=
1.22*λ
2*n*sinα
2α
Instead of the lens we need a detector
with a large opening angle.
We need perfect detectors: A noisy detector is like a sandblasted lens.
And we need single photon detection at near 100% efficiency
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T. U. Schulli
COHERENT DIFFRACTION IMAGING (CDI)
Another Problem : Waves have amplitudes and phases: they interfere to form an
image;
Refraction (as in a real lens) preserves the phase information, crucial for the image
Detection measures only the intensity (number of photons) and not their phase
From a quantum mechanical point of view, refraction (preserves ∆p) by a lens
cannot be replaced by detection (destroys ∆p): Equivalence between Abbé and
Heisenberg.
Detector
The loss of phase information cannot be recovered by a computer.
We have thus to know the phase beforehand.
The sample has to be illuminated with photons that are all in phase with each other
This is the definition of a coherent beam
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PHASE OF PHOTONS AND COHERENT BEAMS
Marathon:
photons=runners
Phase depends on the exact departure time of
the runners
We have to select one single
phase. The rest of the
runners cannot be used for
the experiment.
We select the “coherent fraction” (Runners that all have roughly the same
departure time).
ESRF coherent fraction: <1%
Flux available for “normal” light imaging and coherent diffraction x-ray imaging:
5 Watt LED: 1019 photons/second (incoherent but with optics we can use them all)
ESRF coherent flux: 1011 photons/second (@ 8keV ) -> 1019 photons in 1 year
X-ray tube coh. flux: few photons/second,1019 photons in 1010 years (the age of this
world)
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COHERENT DIFFRACTION IMAGING: ANTIPHASE DOMAINS IN GAN WIRES
GaN: semiconductor for
optoelectronic and high
power applications.
Problem: crystal quality
N-polarity
Ga-polarity
2 µm
SEM image from J. Eymery (CEA-Grenoble)
GaN nanowires: M. I. Richard
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SUMMARY AND OUTLOOK
-Diffraction imaging allows combinations of x-rays diffraction with the limiting
performances of optics to obtain information in two length scale regimes.
-Lensless imaging using coherent beams can push the resolution below 10 nm.
This technique can currently only use a small fraction of the beam, the
coherent fraction.
-After phase II this fraction will increase by a factor of 40 and be of the order of
10 % for low x-ray energies (<10 keV).
-Diffraction imaging techniques are nowadays exploited at ID01, ID16, ID13,
ID11, ID10, ID19, ID03,… and likely by even more BLs after phase II.
Thank you
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