Development and Implementation of Talbot-Lau X-ray Deflectometry M. P. Valdivia, D. Stutman Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 NNSA Grants: DE-NA0001835, DE-NA0002955, DE-NA0003882 NLUF Grant: DE-NA0003526
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Development and Implementation of Talbot-Lau
X-ray Deflectometry
M. P. Valdivia, D. StutmanDepartment of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218
C. Stoeckl, C. Mileham, I. A. Begishev, W. Theobald, S. Muller, C. Source, S. P. Regan Laboratory for Laser Energetics, University of Rochester
S. R. Klein, P. A. Keiter*, J. R. Fein**, R. P. DrakeDepartment of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor*Now at LANL ; **Now at SNL
D. J. Clayton, M. Berninger, A. MeidingerNational Security Technologies, LLC, 182 East Gate Drive, Los Alamos
P. M. KozlowskiP-24 group, Los Alamos National Laboratory
M. Vescovi, E. S. Wyndham, F. VelosoInstituto de Física, Pontificia Universidad Católica de Chile, Chile
Alexis Casner1, Michel Koenig2, B. Albertazzi2, P. Mabey2, T. Michel2, G. Rigon2
1CEA, DAM, DIF, F-91297, Arpajon / CELIA, University of Bordeaux, France, 2LULI, École Polytechnique, CNRS, CEA, UPMC, route de Saclay, F-91128 Palaiseau, France
Collaborators
• Demonstrate electron density diagnostic capabilitiesof Talbot-Lau X-ray Deflectometry (TXD)– Elemental composition (Zavg), and Micro-instability as well.
• Further develop TXD technique:– Backlighter optimization: spectra and spatial resolution– Improved processing algorithms– Alignment of interferometers– Recording of reference Moiré interferograms
NNSA + NLUF: * Support for one undergraduate student, two graduate students, two postdocs, five research scientists* Total students involved in research: 3 undergraduate, 7 graduate* 10 peer reviewed publications (4 in preparation)
Goals of Talbot-Lau project
Refraction based ne diagnostic
ICF diagnostics: • Expected density (ρR) >1 g/cm2
• High spatial resolution (<10 µm)• High densities (well above nc)• Resolve high ne gradients• Time resolved (ps-ns)Beryllium PMMA
RefractionAttenuation
For low-Z matter probed at 1-100 keV:Refraction signatures much largerthan attenuation
Direct ne gradient measurement
Talbot-Lau X-ray Interferometry
Phase shift ~ ref. angle
Talbot effect -> self-images: dT = 2mg2/λ
TL for HEDP: Valdivia et al., Journal Appl. Phys. 144 (2013); Ibid., RSI 85 (2014)
= 2.4µm = 4µm = 12µm
Simulation of CH shell probed @8 keV.
• Small rotation of gratings -> Moiré fringes. Period: PM ≈ g/θ.
• Fringe shift proportional to phase shift:
Talbot-Lau X-ray Deflectometry (TXD)
Moiré Fringe shift Areal Ne
Phase unwrapping
Numerical integration
35 µm
a) b) c)
Reference
3 mm• Strong signature of ne gradients and interfaces
• Spatial resolution• Horizontal: Source-size • Vertical: ~ Period
Measurements of ne gradient
Accurate detection of interfaces and (sharp and mild) negradients in low-Z matter.
Talbot-Lau: Valdivia et al., RSI (2014)
Be rod
Area
l Den
sity
Grad
ient
100 µm
17keV x-ray medical tube
Fringe shifts detected: few percent to several periods. For example: at 5 keV and25 keV, the dynamic ranges are ~1023-1025 and ~5x1024-5x1026 cm-3, respectively.
FPg
xLN
AngsAngs
e ⋅⋅×
≈⋅×
≈∆
∆ 02
29
2
29 102.2102.2)(λ
αλ
TXD ne measurement dynamic range
α from ratio of g0 period and g0-plasma distance P, scaled by fringe shift F.
For a CH shell ~200 µm:i)0.1x solid ne ->(few keV)ii)>100x solid ne -> (~20 keV)
TXD: simultaneous information
Wood splinterScatter ~ a0/a1
Attenuation Refraction
Z-average: composition and mixing
‘r’ ~third degree polynomial of Zavg
Z-average: Valdivia et al., Applied Optics 54 (2014)
Fluorocarbon fiber
C LC
BeLBe
X-rays
CBeC
Be 42
6Zavg
Refraction
<Zavg> ≈ (fCZC3 + fBeZBe
3) 1/3 ; fi ≡ Li / ∑ Li
Attenuation Attn./ Refr.
Demonstrate ne diagnostic capabilities in a HEDP experiment:A high power laser produced x-ray backlighterA pulsed power driven x-ray backlighterA flash x-ray tube
Grating survival, Talbot pattern formation, and refraction measurement for electron density retrieval.
Adaptation to HED environment
Multi-TeraWatt experiment
Laser produced 8 keV backlighter
• 25-29 J, 8-30 ps laser• 500 x 500 x 20 µm3 Cu target
500 x 500 x 12.5 µm3 Polymide backed:• 20 µm diameter Cu wire • ~10-30 µm diameter Cu grain
TL laser backlighter: Valdivia et al., RSI 87 023505 (2016)
Source size FWHM:
~70 µm for Cu foil~40 µm for Cu wire~25 µm Cu spheroid
• Extension of TXD technique:• 2D and radial gratings• Lower energies to enable measurements closer to ncrit
Future work
TXD capabilities:
• Areal ne gradients detection through refraction (and attenuation)• Micro-turbulence and material mixing through Z-average• Hydrodynamic instability through scatter
TXD tested in HED environment:
• Grating survival: • 0.2 cm from 50 J laser pulse• 6.5 cm from 350 kA/350 ns pulsed power generator
• Moiré fringe formation: • High-power laser: MTW, LULI, ECLIPSE, OMEGA-EP• Small pulsed power generator
Summary
Talbot–Lau-type interferometer.
Medical setup: Pfeiffer et al., Nature physics 2 (2006)
Measures angular deviations due to refraction index gradients. No spatial/temporal coherence required. Mechanically robust with a large FOV.
Visible light interferometry: M Roth, J Inst. 6 (2011)
C foil
50 TW laser
Ne < NcritNe > Ncrit
Interferogram
Density map
Ne<Ncrit (~1021 cm-3)
Refraction ne diagnostic
Refraction and Attenuation
Refraction diagnostics (x-rays):• Talbot-Lau Deflectometry (Valdivia et al., J. Appl. Phys, 2013; RSI 2016)• ‘Refraction enhanced’ radiography(Koch et al., AO, 2013; Ping et al., J Inst, 2011)• Hartmann sensors (K. Baker Optical Engineering, 2013)
• Phase grating: fringe patterns, due to the Talbot Effect, which are shifted by an object with density changes
Talbot-Lau: x-ray energy response
X-ray backlighter energy modifies range of ne detected:• Medical applications: >30 keV • Materials science (NDT): >60 keV
• HED systems developed using 8 and 17 keV x-ray tubes.
dz] z)y,Ne(x,[ x2
r y)(x,
e∫
∂∂
=πλ2
α
x=0
x=R/2
Accurate density retrieval even with object attenuation of >90%
PMMA sphere: M.P. Valdivia et al., RSI 85(2014)
Areal electron density retrieval
Talbot-Lau order (m): Contrast
Talbot distance: dT = 2mg2λ
g0–g1 (cm) g1–g2 (cm)
m=1 1.56 7.78
m=3 4.67 23.34
m=5 7.78 38.91
m=7 10.89 54.47
Over 30% contrast
Grating period
XR wavelength
G0 = 2.4 µmG1 = 3.85µmG2 = 12.0 µm
Resolution equivalent to radiography (better if g0 << FWHM)
Areal density map
Acrylic prism
Backlighter source size vs. resolution
FWHM FWHM
40 µm 30 ± 5 µm
25 µm 20 ± 4 µm
8 µm* 16 ± 4 µm
15 µm** 17 ± 3 µm
7 µm** 7± 2 µm* with micro-focus** @ 8keV
Direct refraction/density gradient
Vertical resolution: Spheres
Attenuation map
(2π)
Attenuation and refraction components, separated in the Fourier space, deliver simultaneous independent information
a) Moiré. b) Refraction angle. Attenuation from c) Moiré and d) Radiography.
Attenuation measurements
Scatter imaging for micro-instability diagnostic
XWFP TXD simulation:H filamentsρ =2 g/cm3
8 keV15 µm FWHM backlighter
Marinak et alEPJ 2013
100 µm
µ-instabilitiesin ICF
4 micron2 µm dia. 8 micron
Scatter images
Attenuation images
• A third image is also obtained in TXD corresponding to the fringe contrast loss due to scattering on microscopic (sub-resolution) density gradients
• Potential for a µ-turbulence region diagnostic in ICF, which does not require µm radiographic resolution
A line-of-sight average of the mean atomic number, <Zeff>, can be mapped by combining refraction with attenuation
Potential for a simple diagnostic for material mixing in ICF
Z-average: composition and mixing
TXD with laser x-ray backlighting at the Multi-TeraWatt (MTW):
• 25-29 J, 8-30 ps laser focused on • 500 x 500 x 20 µm3 Cu target.
Laser driven backlighter: Copper foils
Grating survival and ne retrieval demonstrated with 30 J, 8 ps laser pulses, K-shell emission from Cu foil targets (500 x 500 x 25 µm3), and CH backed wire (20 µm diameter) and microsphere (~10-30 µm diameter) targets .
To improve source size:• 20 µm diameter Cu wire • ~10-30 µm diameter Cu grain (spheroid)
MTW: micro-backlighter targets
Polymide backing:~500x500x12.5 µm3
TL laser and x-pinch backlighters: Valdivia et al., RSI 87 (2016)
TXD limited by source size -> A smaller source (<10 µm) is necessary
Source gratings survive a 20-30 J and 8 ps pulse at ~1 cm distance using AlMy, Al, and no filters
Original
After 20 J
After 30 J
G0 after 30 J
MTW: Source grating survival
G0 survival: Ablation induced closure
Pinhole closure experiments suggest G0 will survive long enough to produce data
A. B. Bullock et al, JAP 2006
10 µm
5 µm
Source grating estimated to survive for at least tens of ps
Backlighter laser100 J/10 ps
Target laser2.5 kJ/2.5 ns
3 mm 15 mm
2 µm period Au grating
Tamped pinhole estimate
Aperture (µm)
• Long-pulse ‘tamped’ pinhole closure experiments at OMEGA:
- 20µm CH filled pinhole - 0.4 mm C spacer- 10 kJ/7 ns Zn backlighter
• Slow closure rate of 1-2 µm/ns• TL gratings ‘tamped’ by photoresist• 50-100 ps lifetime possible
Soft X-ray heating lifetime estimateReighard et al RSI 2008
• Source grating main challenge• Grating expansion ∆x must be < 0.1 µm • Assuming expansion at the sound velocity Cs ≈0.0036 T1/2 µm/ps → Au bar heating of ∆T=5 eV needed for ∆x=0.1 µm in 10 ps• Estimated soft X-ray heating for above setup is ≈0.6 J/mm2
→ ∆T≤2 eV in 10 ps → Ok• Longer lifetime with grating substrate,shield
~
Talbot-Lau Deflectometry Measurements of Irradiated Foils
to TIM13 port to TIM10 port
Considerations:
• G0 must be protected by an Al foil (~10-25 um)Could G1 mount have the option of adding a protective foil? Not necessary, but it would be good
• The bigger distance ‘p’, the better the angular resolution: • Because pointing distance is fixed at ~ 2cm, the backlighter foil is very close to G0• The closer that G0 is to the backlighter, G0 degradation risk is higher.
• Main goal of experiment: Achieve Moiré fringes (G0 degradation after delivering images)• We want to test how close we can get G0 to the backlighter foil:
• Systematically vary distance ‘p’ keeping Pointing distance at max.
Backlighter foil: Cu
Protective foil: aluminum
Protective foil?
CH foil: 3x3mm2 x 120um
(side)(back)lighter
Main beams
Pointing distance
p
G0 grating survival
Diagnostic TIM Priority Purpose
Talbot-LauDeflectometry
13 1 Image plasma gradients, holds gratings and camera
Spherical crystal imager assembly
10 1 Hold TXD grating and backlighter foil
Angular Filter Refractometry
1 Image plasma gradients at low densities
Diagnostic Configuration
Talbot-Lau Deflectometry Measurements of Irradiated Foils
-> M = 45* Errors given by pixel size and magnification
• Grating survival: • 1cm from target at MTW (90º from gratings)• 1.5cm at LULI (normal)• 4cm at ECLIPSE (100-1000 shots).
Preliminary experiments
X-pinch backlighter: Llampudkeñ
• Pulsed power driven x-pinch (2x64 µm and 4x25 µm Cu wires). Llampudkeñ pulsed power generator, 400 kA peak current, 350 ns rise-time
• First Talbot order chosen due to vacuum chamber geometrical restrictions. Minimum detectable refraction angle ~3 μrad.
~10 cm
g0 g1 g2
8 keV copper backlighter. Free-standing gratings. Pre-aligned rails.Grating survival and Moiré fringe formation using 4 x 25 µm Cu wire x-pinch backlighter driven by pulsed power generator (350 kA, 1 kA/ns).
• Demonstrate g0 survival and Moiré pattern formation with fringe shift from a static object
X-pinch backlighter
L = 1.56 cm d = 7.78 cm
• Image plasma object: - Laser produced plasma- X-pinch - another wire array
Moiré deflectometry routine diagnostic at low Ne
Deflectometry of Z-pinch plasma with laser backlighterRuiz-Camacho et al J. Phys. D 2007
Electron density Ne (cm-3)
40 80 120 160 2000
1019
1018
1017
1016
Moiré deflectometer
radius (µm)
• Strong refraction expected in HEDP (100 µrad)• X-ray backlighter for penetration• High magnification for ≥ 10 µm resolution
0.5 mm
0.5 mm
Llampudkeñ: Grating survival/Contrast
Back
“No Filter damage” “Filter damage”
Front
Back
Front
Source grating survives 400 kA current x-pinch discharge at ~6.5 cm distance. Even when filters are destroyed, we obtain Moiré images of ~13% contrast.
Contrast
XR source and X pinch evolution
4 x 25 µm better than 2 x 64 µm
Backlighter FWHM: <27 µm
107 ns, 2 x 64 µm 88 ns, 4 x 25 µm
Cu Kα 8.05 keV and Kβ 8.91 keV (Heα 8.35 keV, Lyα 8.69 keV)