Introduction to X-Ray Optics,
Coherence and Standing Waves
David Attwood
University of California, Berkeley
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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The short wavelength region of the electromagnetic
spectrum
n = 1 – δ + iβ
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
δ, β << 1
ICTP_Trieste_Lec2_Nov2014.pptx
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Characteristic absorption edges for almost all
elements in this spectral region
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Energy levels, quantum numbers, and allowed
transitions for the copper atom
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Electron binding energies, in electron volts
(eV), for the elements in their natural forms
www.cxro.LBL.gov
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Available x-ray optical techniques
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Wave propagation and refractive index at x-ray
wavelengths
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Glancing Incidence Optics
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Total external reflection of soft x-ray
and EUV radiation
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Total external reflection with finite 
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Buried, trace amounts of iron in a defective
silicon solar cell
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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X-ray microprobe at SPring-8
Optical microscope
PIN photodiode
Now focused
to 7 nm
SDD
Mirror manipulator
DCM
Undulator
TC1Slit
Ion chamber
Incident Slit
Beam monitor
Sample & Scanner
Experimental hutch
S. Matsuyama et al.,
Rev. Sci. Instrum.
77, 103102 (2006)
Front end
Courtesy of K. Yamauchi and
H. Mimura, Osaka University.
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Multilayer mirrors can provide high reflectivity
at the Bragg condition
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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A High Quality Mo/Si Multilayer Mirror
Small reflections at many interfaces add in phase at the Bragg angle
N = 40
d = 6.7
Courtesy of Sasa
ˇ Bajt (DESY)
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Multilayer mirrors have achieved 70% reflectivity
Courtesy of Sasa Bajt, LLNL
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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A Fresnel zone plate lens
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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A Fresnel zone plate lens used as a diffractive lens for
point to point imaging
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Depth of focus and spectral bandwidth
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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New x-ray lenses: Improving contrast and resolution
for x-ray microscopy
C. Chang, A. Sakdinawat, P.J. Fischer, E.H. Anderson, D.T. Attwood, Opt. Lett. 2006; Sakdinawat and Liu, Opt. Lett. 2007;
Sakdinawat and Liu, Opt. Express 2008
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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New ultra high aspect ratio, high efficiency, hard x-ray
zone plates for high spatial resolution at 30-50 keV
Δr = 100 nm
Δh = 6.6 µm
3.4 µ
Courtesy of Anne Sakdinawat and Chieh Chang (SLAC)
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Coherence
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Born and Wolf, Chapter 10
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spatial and temporal coherence
Temporal Coherence
Ability of a light beam to form fringes with a delayed version of itself
Spatial Coherence
Ability of spatially separated points in a wavefront to form fringes.
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Marching band and coherence lengths
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spatial and spectral
Courtesy of A. Schawlow, Stanford
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Coherence, partial coherence, and incoherence
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spatial and temporal coherence
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spectral bandwidth and longitudinal coherence length
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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A practical interpretation of spatial coherence
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Partially coherent radiation approaches uncertainty
principle limits
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Young’s double slit experiment: spatial coherence and
the persistence of fringes
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Young’s double slit experiment: spatial coherence and
the persistence of fringes
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Young’s double slit experiment: spatial coherence and
the persistence of fringes
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Undulator beamline for high spatial coherence
measurements
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Measuring the spatial coherence of undulator
radiation: double pinhole experimental results
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spatially coherent undulator radiation
Courtesy of Kris Rosfjord, UCB
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Coherent soft x-ray science beamline
K. Rosfjord, Y. Liu, D. Attwood, “Tunable Coherent Soft X-Rays”, IEEE J. Sel. Top. Quant. Electr.10, 1405 (Nov/Dec 2004)
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Spatial coherence measurements of undulator
radiation using the classic 2-pinhole technique
Courtesy of Chang Chang, UC Berkeley and LBNL.
l = 13.4 nm, 450 nm diameter pinholes, 1024 x 1024 EUV/CCD at 26 cm ALS, 1.9 GeV, lu = 8 cm, N = 55
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
38
Spatial coherence measurements of undulator
radiation using the classic 2-pinhole technique
Courtesy of Chang Chang, UC Berkeley and LBNL.
l = 13.4 nm, 450 nm diameter pinholes, 1024 x 1024 EUV/CCD at 26 cm ALS, 1.9 GeV, lu = 8 cm, N = 55
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
39
Lensless imaging of magnetic nanostructures
by x-ray spectro-holography
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Coherent power at BESSY II
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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High spectral resolution (meV) beamline
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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Beamline 7.0 at Berkeley’s
Advanced Light Source
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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X-ray Standing Wave (XSW): Interference between the
incident and reflected waves above a surface
d = λ/2sinθ
Professor David Attwood / UC Berkeley / ICTP-IAEA School, Trieste, November 2014
ICTP_Trieste_Lec2_Nov2014.pptx
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I
Reference-free GIXRF nanolayer characterisation
PIB
X-ray and IR
spectrometry
• reference-free GIXRF analysis uses the XSW to characterize
nanolayered samples (layer composition and thickness, surface
calibrated
instrumentation
and interface mass and composition) without any calibration
samples nor reference materials
wellknown
• XSW calculation using IMD or own software
depth-dependent
modification of the
excitation conditions
revealing information about
the sequence of the layers
Anal. Chem. 83, 8623 (2011)
1.
2.
3.
4.
oxygen
carbon
boron
silicon (substate)
carbon contamination
at surface visible
J. Anal. At. Spectrom. 23, 845 (2007)
R. Unterumsberger, B. Pollakowski, B. Beckhoff
I
Synchrotron radiation based GIXRF depth profiling
PIB
X-ray and IR
spectrometry
• GIXRF can be used to depth profile gradient
(e.g. ion implants) or nanolayered samples
• Calculation of the XSW using IMD software
or iteratively based on X-ray reflectivity data
3 keV As implant into Si , dose: 1015 cm-2
1 keV Al implant into Si, dose: 1016 cm-2
TRIM
SIMS
MEIS
STEM
GIXRF
Anal. Bioanal. Chem. 396, 2825 (2010)
P. Hönicke, B. Beckhoff
TRIM
GIXRF
GIXRF+XRR
J. Anal. At. Spectrom. 27, 1432 (2012)
I
Non-destructive interface speciation by GIXRF-NEXAFS
PIB
X-ray and IR
spectrometry
•
Development of a methodology for non-destructive
interface analysis, which is traceable and reliable
•
A priori X-ray standing wave analysis in order to keep
the mean penetration depth constant when changing
the photon energy during NEXAFS scans
•
Methodology has been proven by a model system
consisting of boron carbide and Nickel
Anal. Chem. 85, 193-200 (2013)
•
Application-oriented samples system: thin
film Si photovoltaic -> interface between
Si and TCO material
J. Appl. Phys. 113, 044519 (2013)
B. Pollakowski, B. Beckhoff