Interferometry is one of the most sensitive and successful diagnostic methods for plasmas. However, owing to the design of most common interferometric systems, the wavelengths of operation and, therefore, the range of densities and temperatures that can be probed are severely limited. Talbot–Lau interferometry offers the possibility of extending interferometry measurements to x-ray wavelengths by means of the Talbot effect. While there have been several proof-of-concept experiments showing the efficacy of this method, it is only recently that experiments to probe High Energy Density (HED) plasmas using Talbot–Lau interferometry are starting to take place. To improve these experimental designs, we present here the Talbot-Interferometry Analyzer (TIA) tool, a forward model for generating and postprocessing synthetic x-ray interferometry images from a Talbot–Lau interferometer. Although TIA can work with any two-dimensional hydrodynamic code to study plasma conditions as close to reality as possible, this software has been designed to work by default with output files from the hydrodynamic code FLASH, making the tool user-friendly and accessible to the general plasma physics community. The model has been built into a standalone app, which can be installed by anyone with access to the MATLAB runtime installer and is available upon request to the authors.
References
1.
J.
Kilkenny
, G.
Richau
, C.
Sangster
, S.
Batha
, P.
Bell
, D.
Larson
, D.
Bradley
, R.
Leeper
, H.
Herrmann
, C.
Bourdon
et al., “The ICF national diagnostic plan (NDP) 9/19/17
,” Technical Report No.
LLNL-TR-739376 (Lawrence Livermore National Laboratory (LLNL)
, Livermore
, CA
, 2017
).2.
D.
Stutman
and M.
Finkenthal
, “Talbot–Lau x-ray interferometry for high energy density plasma diagnostic
,” Rev. Sci. Instrum.
82
, 113508
(2011
).3.
H. F.
Talbot
, “LXXVI. Facts relating to optical science. No. IV
,” London, Edinburgh, Dublin Philos. Mag. J. Sci.
9
, 401
–407
(1836
).4.
E.
Lau
, “Beugungserscheinungen an doppelrastern
,” Ann. Phys.
437
, 417
–423
(1948
).5.
J.
Kiyohara
, C.
Makifuchi
, K.
Kido
, S.
Nagatsuka
, J.
Tanaka
, M.
Nagashima
, T.
Endo
, S.
Ichihara
, W.
Yashiro
, and A.
Momose
, “Development of the Talbot–Lau interferometry system available for clinical use
,” AIP. Conf. Proc.
1466
, 97
–102
(2012
).6.
F.
Horn
, M.
Leghissa
, S.
Kaeppler
, G.
Pelzer
, J.
Rieger
, M.
Seifert
, J.
Wandner
, T.
Weber
, T.
Michel
, C.
Riess
, and G.
Anton
, “Implementation of a Talbot–Lau interferometer in a clinical-like c-arm setup: A feasibility study
,” Sci. Rep.
8
, 2325
(2018
).7.
J.
Nejdl
, M.
Kozlová
, T.
Mocek
, and B.
Rus
, “Measuring the electron density gradients of dense plasmas by deflectometry using short-wavelength probe
,” Phys. Plasmas
17
, 122705
(2010
).8.
M.
Valdivia
, D.
Stutman
, and M.
Finkenthal
, “Talbot–Lau based Moiré deflectometry with non-coherent sources as potential high energy density plasma diagnostic
,” J. Appl. Phys.
114
, 163302
(2013
).9.
M.
Valdivia
, D.
Stutman
, and M.
Finkenthal
, “Moire deflectometry using the Talbot–Lau interferometer as refraction diagnostic for high energy density plasmas at energies below 10 keV
,” Rev. Sci. Instrum.
85
, 073702
(2014
).10.
M.
Valdivia
, D.
Stutman
, and M.
Finkenthal
, “Single-shot z eff dense plasma diagnostic through simultaneous refraction and attenuation measurements with a Talbot–Lau x-ray moiré deflectometer
,” Appl. Opt.
54
, 2577
–2583
(2015
).11.
M.
Valdivia
, D.
Stutman
, C.
Stoeckl
, C.
Mileham
, J.
Zou
, S.
Muller
, K.
Kaiser
, C.
Sorce
, P.
Keiter
, J.
Fein
, M.
Trantham
, R. P.
Drake
, and S. P.
Regan
, “Implementation of a Talbot–Lau x-ray deflectometer diagnostic platform for the OMEGA EP laser
,” Rev. Sci. Instrum.
91
, 023511
(2020
).12.
M. P.
Valdivia
, F.
Veloso
, D.
Stutman
, C.
Stoeckl
, C.
Mileham
, I. A.
Begishev
, W.
Theobald
, M.
Vescovi
, W.
Useche
, S. P.
Regan
, B.
Albertazzi
, G.
Rigon
, P.
Mabey
, T.
Michel
, S. A.
Pikuz
, M.
Koenig
, and A.
Casner
, “X-ray backlighter requirements for refraction-based electron density diagnostics through Talbot–Lau deflectometry
,” Rev. Sci. Instrum.
89
, 10G127
(2018
).13.
G.P.-C. wishes to mention that the name of the TIA code is intended as an homage to the work of Francisco Ibáñez.
14.
A.
Momose
, S.
Kawamoto
, I.
Koyama
, Y.
Hamaishi
, K.
Takai
, and Y.
Suzuki
, “Demonstration of x-ray Talbot interferometry
,” Jpn. J. Appl. Phys., Part 2
42
, L866
(2003
).15.
T.
Weitkamp
, A.
Diaz
, C.
David
, F.
Pfeiffer
, M.
Stampanoni
, P.
Cloetens
, and E.
Ziegler
, “X-ray phase imaging with a grating interferometer
,” Opt. Express
13
, 6296
–6304
(2005
).16.
T.
Weitkamp
, C.
David
, C.
Kottler
, O.
Bunk
, and F.
Pfeiffer
, “Tomography with grating interferometers at low-brilliance sources
,” Proc. SPIE
6318
, 63180S
(2006
).17.
F.
Pfeiffer
, T.
Weitkamp
, O.
Bunk
, and C.
David
, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources
,” Nat. Phys.
2
, 258
–261
(2006
).18.
F.
Pfeiffer
, M.
Bech
, O.
Bunk
, P.
Kraft
, E. F.
Eikenberry
, C.
Brönnimann
, C.
Grünzweig
, and C.
David
, “Hard-x-ray dark-field imaging using a grating interferometer
,” Nat. Mater.
7
, 134
–137
(2008
).19.
J.
Krasinski
, D. F.
Heller
, and O.
Kafri
, “Phase object microscopy using moire deflectometry
,” Appl. Opt.
24
, 3032
–3036
(1985
).20.
B.
Moosman
, V.
Bystritskii
, C.
Boswell
, and F.
Wessel
, “Moire deflectometry diagnostic for transient plasma, using a multipulse N2 laser
,” Rev. Sci. Instrum.
67
, 170
–177
(1996
).21.
J.
Ruiz-Camacho
, F.
Beg
, and P.
Lee
, “Comparison of sensitivities of moire deflectometry and interferometry to measure electron densities in z-pinch plasmas
,” J. Phys. D
40
, 2026
(2007
).22.
J.
Valenzuela
, E.
Wyndham
, H.
Chuaqui
, D.
Cortes
, M.
Favre
, and H.
Bhuyan
, “Implementation of moiré-schlieren deflectometry on a small scale fast capillary plasma discharge
,” J. Appl. Phys.
111
, 103301
(2012
).23.
D.
Stutman
, M. P.
Valdivia
, and M.
Finkenthal
, “X-ray Moiré deflectometry using synthetic reference images
,” Appl. Opt.
54
, 5956
–5961
(2015
).24.
J.
Valenzuela
, E.
Wyndham
, and M.
Favre
, “Time-resolved study of the extreme-ultraviolet emission and plasma dynamics of a sub-joule, fast capillary discharge
,” Phys. Plasmas
22
, 083501
(2015
).25.
S.
Bachche
, M.
Nonoguchi
, K.
Kato
, M.
Kageyama
, T.
Koike
, M.
Kuribayashi
, and A.
Momose
, “Laboratory-based x-ray phase-imaging scanner using Talbot–Lau interferometer for non-destructive testing
,” Sci. Rep.
7
, 6711
(2017
).26.
M.
Seifert
, M.
Gallersdörfer
, V.
Ludwig
, M.
Schuster
, F.
Horn
, G.
Pelzer
, J.
Rieger
, T.
Michel
, and G.
Anton
, “Improved reconstruction technique for moire imaging using an x-ray phase-contrast Talbot–Lau interferometer
,” J. Imaging
4
, 62
(2018
).27.
S.
Balovsiak
, S.
Novikov
, I.
Fodchuk
, and I.
Yaremchuk
, “Analysis of moiré x-ray images of deformed crystals using radial distribution of the Fourier energy spectrum
,” Metallophys. Adv. Technol.
41
, 389
–402
(2019
).28.
H.
Lee
, D.
Jeon
, H.
Lim
, H.
Cho
, M.
Park
, and W.
Youn
, “Quantification of the effects of grid angulation on image quality in single-grid-based phase-contrast x-ray imaging
,” J. Opt.
23
, 105605
(2021
).29.
T.
Tschentscher
, M.
Altarelli
, R.
Brinkmann
, T.
Delissen
, A.
Schwarz
, and K.
Witte
, “Technical report: The European x-ray free-electron laser facility: A new infrastructure for research using ultrashort, coherent x-ray pulses of extreme brightness
,” Synchrotron Radiat. News
19
, 13
–19
(2006
).30.
G.
Geloni
, E.
Saldin
, L.
Samoylova
, E.
Schneidmiller
, H.
Sinn
, T.
Tschentscher
, and M.
Yurkov
, “Coherence properties of the European XFEL
,” New J. Phys.
12
, 035021
(2010
).31.
D.
Pile
, “First light from SACLA
,” Nat. Photonics
5
, 456
–457
(2011
).32.
J.
Arthur
, G.
Materlik
, R.
Tatchyn
, and H.
Winick
, “The LCLS: A fourth generation light source using the SLAC linac
,” Rev. Sci. Instrum.
66
, 1987
–1989
(1995
).33.
E.
Saldin
, E.
Schneidmiller
, and M.
Yurkov
, “Coherence properties of the radiation from SASE FEL
,” Nucl. Instrum. Methods Phys. Res., Sect. A
507
, 106
–109
(2003
).34.
J.
Jahns
and A. W.
Lohmann
, “The Lau effect (a diffraction experiment with incoherent illumination)
,” Opt. Commun.
28
, 263
–267
(1979
).35.
B.
Fryxell
, K.
Olson
, P.
Ricker
, F.
Timmes
, M.
Zingale
, D.
Lamb
, P.
MacNeice
, R.
Rosner
, J.
Truran
, and H.
Tufo
, “Flash: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes
,” Astrophys. J. Suppl. Ser.
131
, 273
(2000
).36.
A.
Dubey
, K.
Antypas
, M. K.
Ganapathy
, L. B.
Reid
, K.
Riley
, D.
Sheeler
, A.
Siegel
, and K.
Weide
, “Extensible component-based architecture for flash, a massively parallel, multiphysics simulation code
,” Parallel Comput.
35
, 512
–522
(2009
).37.
P.
Tzeferacos
, M.
Fatenejad
, N.
Flocke
, C.
Graziani
, G.
Gregori
, D.
Lamb
, D.
Lee
, J.
Meinecke
, A.
Scopatz
, and K.
Weide
, “Flash mhd simulations of experiments that study shock-generated magnetic fields
,” High Energy Density Phys.
17
, 24
–31
(2015
).38.
G.
Rigon
, A.
Casner
, B.
Albertazzi
, T.
Michel
, P.
Mabey
, E.
Falize
, J.
Ballet
, L.
Van Box Som
, S.
Pikuz
, Y.
Sakawa
, T.
Sano
, A.
Faenov
, T.
Pikuz
, N.
Ozaki
, Y.
Kuramitsu
, M. P.
Valdivia
, P.
Tzeferacos
, D.
Lamb
, and M.
Koenig
, “Rayleigh-Taylor instability experiments on the LULI2000 laser in scaled conditions for young supernova remnants
,” Phys. Rev. E
100
, 021201
(2019
).39.
P.
Tzeferacos
, A.
Rigby
, A. F. A.
Bott
, A. R.
Bell
, R.
Bingham
, A.
Casner
, F.
Cattaneo
, E. M.
Churazov
, J.
Emig
, F.
Fiuza
, C. B.
Forest
, J.
Foster
, C.
Graziani
, J.
Katz
, M.
Koenig
, C.-K.
Li
, J.
Meinecke
, R.
Petrasso
, H.-S.
Park
, B. A.
Remington
, J. S.
Ross
, D.
Ryu
, D.
Ryutov
, T. G.
White
, B.
Reville
, F.
Miniati
, A. A.
Schekochihin
, D. Q.
Lamb
, D. H.
Froula
, and G.
Gregori
, “Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma
,” Nat. Commun.
9
, 591
(2018
).40.
J.
Nilsen
and J. H.
Scofield
, “Plasmas with an index of refraction greater than 1
,” Opt. Lett.
29
, 2677
–2679
(2004
).41.
F. F.
Chen
, Introduction to Plasma Physics and Controlled Fusion
(Springer
, 2016
).42.
43.
G.
Williams
, H.-K.
Chung
, S.
Vinko
, S.
Künzel
, A.
Sardinha
, P.
Zeitoun
, and M.
Fajardo
, “Method of time resolved refractive index measurements of x-ray laser heated solids
,” Phys. Plasmas
20
, 042701
(2013
).44.
K.
Wieseman
, “A short introduction to plasma physics
,” in CAS-CERN Accelerator School: Ion Sources
, 2014
.45.
L.
Rayleigh
, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith
,” London, Edinburgh, Dublin Philos. Mag. J. Sci.
11
, 196
–205
(1881
).46.
J.
Li
, Z.
Peng
, and Y.
Fu
, “Diffraction transfer function and its calculation of classic diffraction formula
,” Opt. Commun.
280
, 243
–248
(2007
).47.
M.
Engelhardt
, C.
Kottler
, O.
Bunk
, C.
David
, C.
Schroer
, J.
Baumann
, M.
Schuster
, and F.
Pfeiffer
, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources
,” J. Microsc.
232
, 145
–157
(2008
).48.
N.
Bevins
, J.
Zambelli
, K.
Li
, Z.
Qi
, and G.-H.
Chen
, “Multicontrast x-ray computed tomography imaging using Talbot–Lau interferometry without phase stepping
,” Med. Phys.
39
, 424
–428
(2012
).49.
A.
Malecki
, G.
Potdevin
, and F.
Pfeiffer
, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based x-ray interferometry
,” Europhys. Lett.
99
, 48001
(2012
).50.
S.
Gkoumas
, P.
Villanueva-Perez
, Z.
Wang
, L.
Romano
, M.
Abis
, and M.
Stampanoni
, “A generalized quantitative interpretation of dark-field contrast for highly concentrated microsphere suspensions
,” Sci. Rep.
6
, 3529
(2016
).51.
V.
Bouffetier
, L.
Ceurvorst
, M.
Valdivia
, F.
Dorchies
, S.
Hulin
, T.
Goudal
, D.
Stutman
, and A.
Casner
, “Proof-of-concept Talbot–Lau x-ray interferometry with a high-intensity, high-repetition-rate, laser-driven K-alpha source
,” Appl. Opt.
59
, 8380
–8387
(2020
).52.
D. C.
Ghiglia
and L. A.
Romero
, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods
,” J. Opt. Soc. Am. A
11
, 107
–117
(1994
).53.
Y.
Yang
and X.
Tang
, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry
,” Med. Phys.
39
, 7237
–7253
(2012
).54.
C. C.
Kuranz
, H.-S.
Park
, C. M.
Huntington
, A. R.
Miles
, B. A.
Remington
, T.
Plewa
, M.
Trantham
, H.
Robey
, D.
Shvarts
, A.
Shimony
et al., “How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants
,” Nat. Commun.
9
, 1564
(2018
).55.
A.
Casner
, “Recent progress in quantifying hydrodynamics instabilities and turbulence in inertial confinement fusion and high-energy-density experiments
,” Philos. Trans. R. Soc. A
379
, 20200021
(2021
).56.
A.
Do
, A.
Angulo
, G.
Hall
, S.
Nagel
, N.
Izumi
, B.
Kozioziemski
, T.
McCarville
, J.
Ayers
, and D.
Bradley
, “X-ray imaging of Rayleigh–Taylor instabilities using Fresnel zone plate at the national ignition facility
,” Rev. Sci. Instrum.
92
, 053511
(2021
).57.
A.
Casner
, C.
Mailliet
, G.
Rigon
, S.
Khan
, D.
Martinez
, B.
Albertazzi
, T.
Michel
, T.
Sano
, Y.
Sakawa
, P.
Tzeferacos
et al., “From ICF to laboratory astrophysics: Ablative and classical Rayleigh–Taylor instability experiments in turbulent-like regimes
,” Nucl. Fusion
59
, 032002
(2018
).58.
G.
Malamud
, L.
Elgin
, T.
Handy
, C.
Huntington
, R.
Drake
, D.
Shvarts
, A.
Shimony
, and C.
Kuranz
, “Design of a single-mode Rayleigh-Taylor instability experiment in the highly nonlinear regime
,” High Energy Density Phys.
32
, 18
–30
(2019
).59.
G.
Rigon
, B.
Albertazzi
, T.
Pikuz
, P.
Mabey
, V.
Bouffetier
, N.
Ozaki
, T.
Vinci
, F.
Barbato
, E.
Falize
, Y.
Inubushi
et al., “Micron-scale phenomena observed in a turbulent laser-produced plasma
,” Nat. Commun.
12
, 2679
(2021
).60.
T.
Kameshima
, A.
Takeuchi
, K.
Uesugi
, T.
Kudo
, Y.
Kohmura
, K.
Tamasaku
, K.
Muramatsu
, T.
Yanagitani
, M.
Yabashi
, and T.
Hatsui
, “Development of an x-ray imaging detector to resolve 200 nm line-and-space patterns by using transparent ceramics layers bonded by solid-state diffusion
,” Opt. Lett.
44
, 1403
–1406
(2019
).61.
Y.
Ping
, O.
Landen
, D.
Hicks
, J.
Koch
, R.
Wallace
, C.
Sorce
, B.
Hammel
, and G.
Collins
, “Refraction-enhanced x-ray radiography for density profile measurements at CH/Be interface
,” J. Instrum.
6
, P09004
(2011
).62.
J. A.
Koch
, O. L.
Landen
, L. J.
Suter
, and L. P.
Masse
, “Simple solution to the Fresnel–Kirchoff diffraction integral for application to refraction-enhanced radiography
,” J. Opt. Soc. Am. A
30
, 1460
–1463
(2013
).63.
B.
Kozioziemski
, J.
Koch
, A.
Barty
, H.
Martz
, Jr, W.-K.
Lee
, and K.
Fezzaa
, “Quantitative characterization of inertial confinement fusion capsules using phase contrast enhanced x-ray imaging
,” J. Appl. Phys.
97
, 063103
(2005
).64.
J. A.
Koch
, O. L.
Landen
, B. J.
Kozioziemski
, N.
Izumi
, E. L.
Dewald
, J. D.
Salmonson
, and B. A.
Hammel
, “Refraction-enhanced x-ray radiography for inertial confinement fusion and laser-produced plasma applications
,” J. Appl. Phys.
105
, 113112
(2009
).65.
J. A.
Koch
, O. L.
Landen
, L. J.
Suter
, L. P.
Masse
, D. S.
Clark
, J. S.
Ross
, A. J.
Mackinnon
, N. B.
Meezan
, C. A.
Thomas
, and Y.
Ping
, “Refraction-enhanced backlit imaging of axially symmetric inertial confinement fusion plasmas
,” Appl. Opt.
52
, 3538
–3556
(2013
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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