Wire, hybrid, and laser-cut X-pinches as Talbot–Lau backlighters for electron density diagnostics

Valdivia, M. P.; Collins, IV, G. W.; Conti, F.; Beg, F. N.

doi:10.1088/1361-6587/ac4b95

Title: Wire, hybrid, and laser-cut X-pinches as Talbot–Lau backlighters for electron density diagnostics

Journal Article · 27 January 2022 · Plasma Physics and Controlled Fusion

DOI: https://doi.org/10.1088/1361-6587/ac4b95 · OSTI ID:1887288

^[1]; Collins, IV, G. W. ^[2]; Conti, F. ^[3]; Beg, F. N. ^[3]

Univ. of California San Diego, La Jolla, CA (United States); Johns Hopkins Univ., Baltimore, MD (United States); UCSD
Univ. of California San Diego, La Jolla, CA (United States); General Atomics, San Diego, CA (United States)
Univ. of California San Diego, La Jolla, CA (United States)

Talbot–Lau x-ray deflectometry (TXD) enables refraction-based imaging for high-energy-density physics experiments, and thus, it has been studied and developed with the goal of diagnosing plasmas relevant to inertial confinement and magnetic liner inertial fusion. X-pinches, known for reliably generating fast (~1 ns), small (~1 µm) x-ray sources, were driven on the compact current driver generator for ablation structure and implosion studies (~200 kA, 150 ns) as a potential backlighter source for TXD. Considering that different X-pinch configurations have characteristic advantages and drawbacks as x-ray generating loads, three distinct copper X-pinch configurations were studied: the wire X-pinch, the hybrid X-pinch, and the laser-cut X-pinch. Furthermore, the Cu K-shell emission from each configuration was characterized and analyzed regarding the specific backlighter requirements for an 8 keV TXD system: spatial and temporal resolution, number of sources, time of emission, spectrum, and reproducibility. Recommendations for future experimental improvements and applications are presented. The electron density of static objects was retrieved from Moiré images obtained through TXD. This allowed to calculate the mass density of static samples within 4% of the expected value for laser-cut X-pinches, which were found to be the optimal X-pinch configuration for TXD due to their high reproducibility, small source size (≤5 µm), short duration (~1 ns), and up to 106 W peak power near 8 keV photon energy. Plasma loads were imaged through TXD for the first-time using laser-cut X-pinch backlighting. Experimental images were compared with simulations from the x-ray wave-front propagation code, demonstrating that TXD can be a powerful x-ray refraction-based diagnostic for dense Z-pinch loads. Future plans for Talbot–Lau interferometry diagnostics in the pulsed-power environment are described.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of California San Diego, La Jolla, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003882; NA0004028

OSTI ID:: 1887288

Journal Information:: Plasma Physics and Controlled Fusion, Journal Name: Plasma Physics and Controlled Fusion Journal Issue: 3 Vol. 64; ISSN 0741-3335

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (93)

The Lau effect (a diffraction experiment with incoherent illumination) Jahns, J.; Lohmann, A. W. Optics Communications, Vol. 28, Issue 3 https://doi.org/10.1016/0030-4018(79)90316-X	journal	March 1979
Time-resolved spectroscopy of Al, Ti, and Mo X pinch radiation using an X-ray streak camera Sinars, D. B.; Pikuz, S. A.; Shelkovenko, T. A. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 78, Issue 1 https://doi.org/10.1016/S0022-4073(02)00180-2	journal	April 2003
Experimental investigations of X-pinch backlighters on QiangGuang-1 generator Wu, J.; Wang, L.; Qiu, A. Laser and Particle Beams, Vol. 29, Issue 2 https://doi.org/10.1017/S0263034611000024	journal	March 2011
Short-pulse laser-driven x-ray radiography Brambrink, E.; Baton, S.; Koenig, M. High Power Laser Science and Engineering, Vol. 4 https://doi.org/10.1017/hpl.2016.31	journal	January 2016
Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources Pfeiffer, Franz; Weitkamp, Timm; Bunk, Oliver Nature Physics, Vol. 2, Issue 4, p. 258-261 https://doi.org/10.1038/nphys265	journal	March 2006
Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing Bachche, Shivaji; Nonoguchi, Masahiro; Kato, Koichi Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-07032-y	journal	July 2017
Advanced high resolution x-ray diagnostic for HEDP experiments Faenov, A. Y.; Pikuz, T. A.; Mabey, P. Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-34717-9	journal	November 2018
The x ‐pinch as a point source of x rays for backlighting Kalantar, D. H.; Hammer, D. A. Review of Scientific Instruments, Vol. 66, Issue 1 https://doi.org/10.1063/1.1146219	journal	January 1995
Moiré deflectometry diagnostic for transient plasma, using a multipulse N ₂ laser Moosman, B.; Bystritskii, V. M.; Boswell, C. J. Review of Scientific Instruments, Vol. 67, Issue 1 https://doi.org/10.1063/1.1146566	journal	January 1996
High-luminosity monochromatic x-ray backlighting using an incoherent plasma source to study extremely dense plasmas (invited) Pikuz, S. A.; Shelkovenko, T. A.; Romanova, V. M. Review of Scientific Instruments, Vol. 68, Issue 1 https://doi.org/10.1063/1.1147689	journal	January 1997
X-ray backlighting for the National Ignition Facility (invited) Landen, O. L.; Farley, D. R.; Glendinning, S. G. Review of Scientific Instruments, Vol. 72, Issue 1 https://doi.org/10.1063/1.1315641	journal	January 2001
X-ray backlighting of wire array Z -pinch implosions using X pinch Lebedev, S. V.; Beg, F. N.; Bland, S. N. Review of Scientific Instruments, Vol. 72, Issue 1 https://doi.org/10.1063/1.1315647	journal	January 2001
Hot electron diagnostic in a solid laser target by K -shell lines measurement from ultraintense laser–plasma interactions (3×1020 W/cm2,⩽400 J) Yasuike, K.; Key, M. H.; Hatchett, S. P. Review of Scientific Instruments, Vol. 72, Issue 1 https://doi.org/10.1063/1.1319373	journal	January 2001
Point-projection x-ray radiography using an X pinch as the radiation source Shelkovenko, T. A.; Sinars, D. B.; Pikuz, S. A. Review of Scientific Instruments, Vol. 72, Issue 1 https://doi.org/10.1063/1.1323252	journal	January 2001
Slit-wire camera, a new diagnostics method for measurement of small scale high-energy density structures in hot plasmas Choi, P.; Dumitrescu, C.; Wyndham, E. Review of Scientific Instruments, Vol. 73, Issue 6 https://doi.org/10.1063/1.1480462	journal	June 2002
Experimental Study Of Wire Array Implosion In Presence Of Prolonged Plasma Production On Angara-5-1 Facility Alexandrov, V. V. AIP Conference Proceedings https://doi.org/10.1063/1.1531288	conference	January 2002
Table-top X-pinch for x-ray radiography Beg, F. N.; Krushelnick, K.; Lichtsteiner, P. Applied Physics Letters, Vol. 82, Issue 25 https://doi.org/10.1063/1.1584782	journal	June 2003
Cross calibration of new x-ray films against direct exposure film from 1 to 8keV using the X-pinch x-ray source Chandler, K. M.; Pikuz, S. A.; Shelkovenko, T. A. Review of Scientific Instruments, Vol. 76, Issue 11 https://doi.org/10.1063/1.2135276	journal	November 2005
The Imaging of Z-Pinches Using X-Pinch Backlighting Douglass, J. D. DENSE Z-PINCHES: 6th International Conference on Dense Z-Pinches, AIP Conference Proceedings https://doi.org/10.1063/1.2159336	conference	January 2006
Characterization and cross calibration of Agfa D4, D7, and D8 and Kodak SR45 x-ray films against direct exposure film at 4.0–5.5keV Lanier, N. E.; Cowan, J. S.; Workman, J. Review of Scientific Instruments, Vol. 77, Issue 4 https://doi.org/10.1063/1.2194509	journal	April 2006
Cross calibration of AGFA-D7 x-ray film against direct exposure film from 2to8.5keV using laser generated x-rays Kyrala, George A. Review of Scientific Instruments, Vol. 77, Issue 5 https://doi.org/10.1063/1.2194787	journal	May 2006
Response model for Kodak Biomax-MS film to x rays Knauer, J. P.; Marshall, F. J.; Yaakobi, B. Review of Scientific Instruments, Vol. 77, Issue 10 https://doi.org/10.1063/1.2220046	journal	October 2006
Absolute calibration of Kodak Biomax-MS film response to x rays in the 1.5- to 8-keV energy range Marshall, F. J.; Knauer, J. P.; Anderson, D. Review of Scientific Instruments, Vol. 77, Issue 10 https://doi.org/10.1063/1.2221698	journal	October 2006
Compact X-pinch based point x-ray source for phase contrast imaging of inertial confinement fusion capsules Beg, F. N.; Stephens, R. B.; Xu, H. -W. Applied Physics Letters, Vol. 89, Issue 10 https://doi.org/10.1063/1.2335959	journal	September 2006
COBRA-STAR, a five frame point-projection x-ray imaging system for 1MA scale wire-array Z pinches Douglass, J. D.; Hammer, D. A. Review of Scientific Instruments, Vol. 79, Issue 3 https://doi.org/10.1063/1.2884707	journal	March 2008
Absolute calibration of image plates for electrons at energy between 100keV and 4MeV Chen, Hui; Back, Norman L.; Bartal, Teresa Review of Scientific Instruments, Vol. 79, Issue 3 https://doi.org/10.1063/1.2885045	journal	March 2008
Hard x-ray radiography for density measurement in shock compressed matter Ravasio, A.; Koenig, M.; Le Pape, S. Physics of Plasmas, Vol. 15, Issue 6 https://doi.org/10.1063/1.2928156	journal	June 2008
Development of backlighting sources for a Compton radiography diagnostic of inertial confinement fusion targets (invited) Tommasini, R.; MacPhee, A.; Hey, D. Review of Scientific Instruments, Vol. 79, Issue 10 https://doi.org/10.1063/1.2953593	journal	October 2008
The National Ignition Facility: Ushering in a new age for high energy density science Moses, E. I.; Boyd, R. N.; Remington, B. A. Physics of Plasmas, Vol. 16, Issue 4 https://doi.org/10.1063/1.3116505	journal	April 2009
Inverse geometry for grating-based x-ray phase-contrast imaging Donath, Tilman; Chabior, Michael; Pfeiffer, Franz Journal of Applied Physics, Vol. 106, Issue 5, Article No. 054703 https://doi.org/10.1063/1.3208052	journal	September 2009
Characterization of laser‐produced plasma x‐ray sources for use in x‐ray radiography Matthews, D. L.; Campbell, E. M.; Ceglio, N. M. Journal of Applied Physics, Vol. 54, Issue 8 https://doi.org/10.1063/1.332680	journal	August 1983
Hybrid X-pinch with conical electrodes Shelkovenko, T. A.; Pikuz, S. A.; Cahill, A. D. Physics of Plasmas, Vol. 17, Issue 11 https://doi.org/10.1063/1.3504226	journal	November 2010
Talbot-Lau x-ray interferometry for high energy density plasma diagnostic Stutman, D.; Finkenthal, M. Review of Scientific Instruments, Vol. 82, Issue 11 https://doi.org/10.1063/1.3660808	journal	November 2011
A spherical crystal imager for OMEGA EP Stoeckl, C.; Fiksel, G.; Guy, D. Review of Scientific Instruments, Vol. 83, Issue 3 https://doi.org/10.1063/1.3693348	journal	March 2012
Beryllium liner implosion experiments on the Z accelerator in preparation for magnetized liner inertial fusion McBride, R. D.; Martin, M. R.; Lemke, R. W. Physics of Plasmas, Vol. 20, Issue 5 https://doi.org/10.1063/1.4803079	journal	May 2013
Talbot-Lau based Moiré deflectometry with non-coherent sources as potential High Energy Density plasma diagnostic Valdivia, M. P.; Stutman, D.; Finkenthal, M. Journal of Applied Physics, Vol. 114, Issue 16 https://doi.org/10.1063/1.4827186	journal	October 2013
Moiré deflectometry using the Talbot-Lau interferometer as refraction diagnostic for High Energy Density plasmas at energies below 10 keV Valdivia, M. P.; Stutman, D.; Finkenthal, M. Review of Scientific Instruments, Vol. 85, Issue 7 https://doi.org/10.1063/1.4885467	journal	July 2014
A Kirkpatrick-Baez microscope for the National Ignition Facility Pickworth, L. A.; McCarville, T.; Decker, T. Review of Scientific Instruments, Vol. 85, Issue 11 https://doi.org/10.1063/1.4886433	journal	November 2014
Investigation into the dynamics of laser-cut foil X-pinches and their potential use for high repetition rate operation Collins, G. W.; Valdivia, M. P.; Zick, T. O. Applied Physics Letters, Vol. 105, Issue 2 https://doi.org/10.1063/1.4889748	journal	July 2014
An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the National Ignition Facility Raman, K. S.; Smalyuk, V. A.; Casey, D. T. Physics of Plasmas, Vol. 21, Issue 7 https://doi.org/10.1063/1.4890570	journal	July 2014
Development of x-ray radiography for high energy density physics Morace, A.; Fedeli, L.; Batani, D. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4900867	journal	October 2014
An x-ray backlit Talbot-Lau deflectometer for high-energy-density electron density diagnostics Valdivia, M. P.; Stutman, D.; Stoeckl, C. Review of Scientific Instruments, Vol. 87, Issue 2 https://doi.org/10.1063/1.4941441	journal	February 2016
Characterization of laser-cut copper foil X-pinches Collins, G. W.; Valenzuela, J. C.; Hansen, S. B. Physics of Plasmas, Vol. 23, Issue 10 https://doi.org/10.1063/1.4965238	journal	October 2016
An oil-free compact X-pinch plasma radiation source: Design and radiation performance Shapovalov, Roman V.; Spielman, Rick B.; Imel, George R. Review of Scientific Instruments, Vol. 88, Issue 6 https://doi.org/10.1063/1.4986460	journal	June 2017
A 7.2 keV spherical x-ray crystal backlighter for two-frame, two-color backlighting at Sandia’s Z Pulsed Power Facility Schollmeier, M. S.; Knapp, P. F.; Ampleford, D. J. Review of Scientific Instruments, Vol. 88, Issue 10 https://doi.org/10.1063/1.4994566	journal	October 2017
X-pinch X-ray emission on a portable low-current, fast rise-time generator Shelkovenko, T. A.; Pikuz, S. A.; Tilikin, I. N. Journal of Applied Physics, Vol. 124, Issue 8 https://doi.org/10.1063/1.5032112	journal	August 2018
X-ray backlighter requirements for refraction-based electron density diagnostics through Talbot-Lau deflectometry Valdivia, M. P.; Veloso, F.; Stutman, D. Review of Scientific Instruments, Vol. 89, Issue 10 https://doi.org/10.1063/1.5039342	journal	October 2018
On the system stability and calibration of the image plate/scanner system for plasma diagnosis at the National Ignition Facility Holder, J. P.; Izumi, N.; Beach, M. Review of Scientific Instruments, Vol. 89, Issue 10 https://doi.org/10.1063/1.5039363	journal	October 2018
A study of picosecond laser–solid interactions up to 10 ¹⁹ W cm ⁻² Beg, F. N.; Bell, A. R.; Dangor, A. E. Physics of Plasmas, Vol. 4, Issue 2 https://doi.org/10.1063/1.872103	journal	February 1997
Evolution of the structure of the dense plasma near the cross point in exploding wire X pinches Shelkovenko, T. A.; Pikuz, S. A.; Hammer, D. A. Physics of Plasmas, Vol. 6, Issue 7 https://doi.org/10.1063/1.873241	journal	July 1999
Implementation of Talbot–Lau x-ray deflectometry in the pulsed power environment using a copper X-pinch backlighter Vescovi, Milenko; Valdivia, Maria Pia; Veloso, Felipe Journal of Applied Physics, Vol. 127, Issue 20 https://doi.org/10.1063/5.0001910	journal	May 2020
High-resolution x-ray radiography with Fresnel zone plates on the University of Rochester’s OMEGA Laser Systems Marshall, F. J.; Ivancic, S. T.; Mileham, C. Review of Scientific Instruments, Vol. 92, Issue 3 https://doi.org/10.1063/5.0034903	journal	March 2021
Direct comparison of wire, foil, and hybrid X-pinches on a 200 kA, 150 ns current driver Collins, G. W.; Valdivia, M. P.; Hansen, S. B. Journal of Applied Physics, Vol. 129, Issue 7 https://doi.org/10.1063/5.0035587	journal	February 2021
Talbot-Lau x-ray deflectometer: Refraction-based HEDP imaging diagnostic Valdivia, M. P.; Stutman, D.; Stoeckl, C. Review of Scientific Instruments, Vol. 92, Issue 6 https://doi.org/10.1063/5.0043655	journal	June 2021
Spectra of multiply charged nickel and copper ions in an X-pinch plasma Mingaleev, A. R.; Pikuz, S. A.; Romanova, V. M. Quantum Electronics, Vol. 23, Issue 5 https://doi.org/10.1070/qe1993v023n05abeh003061	journal	May 1993
Incoherent Superposition of Multiple Self-imaging Lau Effect and Moiré Fringe Explanation Patorski, K. Optica Acta: International Journal of Optics, Vol. 30, Issue 6 https://doi.org/10.1080/713821267	journal	June 1983
Comparison of sensitivities of Moiré deflectometry and interferometry to measure electron densities in z -pinch plasmas Ruiz-Camacho, J.; Beg, F. N.; Lee, P. Journal of Physics D: Applied Physics, Vol. 40, Issue 7 https://doi.org/10.1088/0022-3727/40/7/026	journal	March 2007
A review of the dense Z -pinch Haines, M. G. Plasma Physics and Controlled Fusion, Vol. 53, Issue 9 https://doi.org/10.1088/0741-3335/53/9/093001	journal	June 2011
Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry Yashiro, Wataru; Harasse, Sébastien; Kawabata, Katsuyuki Physical Review B, Vol. 84, Issue 9 https://doi.org/10.1103/PhysRevB.84.094106	journal	September 2011
Efficient K α x-ray source from femtosecond laser-produced plasmas Rousse, A.; Audebert, P.; Geindre, J. P. Physical Review E, Vol. 50, Issue 3 https://doi.org/10.1103/PhysRevE.50.2200	journal	September 1994
High-Gain Magnetized Inertial Fusion Slutz, Stephen A.; Vesey, Roger A. Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.025003	journal	January 2012
Observation of a stable dense core within an unstable coronal plasma in wire-initiated dense Z -pinch experiments Kalantar, D. H.; Hammer, D. A. Physical Review Letters, Vol. 71, Issue 23 https://doi.org/10.1103/PhysRevLett.71.3806	journal	December 1993
Experimental Measurements of Hot Electrons Generated by Ultraintense ( > 10 19 W / cm 2 ) Laser-Plasma Interactions on Solid-Density Targets Wharton, K. B.; Hatchett, S. P.; Wilks, S. C. Physical Review Letters, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevLett.81.822	journal	July 1998
250 kA compact linear transformer driver for wire array z -pinch loads Bott, S. C.; Haas, D. M.; Madden, R. E. Physical Review Special Topics - Accelerators and Beams, Vol. 14, Issue 5 https://doi.org/10.1103/PhysRevSTAB.14.050401	journal	May 2011
Ablation Studies of Low-Number Wire Arrays at 200 kA Using A Linear Transformer Driver Bott, Simon C.; Haas, David M.; Eshaq, Yossof IEEE Transactions on Plasma Science, Vol. 38, Issue 4 https://doi.org/10.1109/TPS.2009.2034166	journal	April 2010
The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources Engelhardt, M.; Kottler, C.; Bunk, O. Journal of Microscopy, Vol. 232, Issue 1, p. 145-157 https://doi.org/10.1111/j.1365-2818.2008.02072.x	journal	October 2008
Calibrating image plate sensitivity in the 700 to 5000 eV spectral energy range Haugh, Michael J.; Lee, Joshua; Romano, Edward SPIE Optical Engineering + Applications, SPIE Proceedings https://doi.org/10.1117/12.2024889	conference	September 2013
XWFP: an x-ray wavefront propagation software package for the IDL computer language Weitkamp, Timm; Sanchez del Rio, Manuel https://doi.org/10.1117/12.569642	conference	October 2004
Tomography with grating interferometers at low-brilliance sources Weitkamp, Timm; David, Christian; Kottler, Christian https://doi.org/10.1117/12.683851	conference	August 2006
Moire Deflectometry: A Ray Deflection Approach To Optical Testing Kafri, O.; Glatt, I. Optical Engineering, Vol. 24, Issue 6 https://doi.org/10.1117/12.7973607	journal	December 1985
A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging : Single-shot x-ray phase contrast and diffraction method Bennett, Eric E.; Kopace, Rael; Stein, Ashley F. Medical Physics, Vol. 37, Issue 11 https://doi.org/10.1118/1.3501311	journal	October 2010
Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping: Single-shot phase contrast CT Bevins, Nicholas; Zambelli, Joseph; Li, Ke Medical Physics, Vol. 39, Issue 1 https://doi.org/10.1118/1.3672163	journal	December 2011
Measurement of Laser-Plasma Electron Density with a Soft X-ray Laser Deflectometer Ress, D.; DaSilva, L. B.; London, R. A. Science, Vol. 265, Issue 5171 https://doi.org/10.1126/science.265.5171.514	journal	July 1994
Accelerated electrons and hard X-ray emission from X-pinches Shelkovenko, T. A.; Pikuz, S. A.; Mingaleev, A. R. Plasma Physics Reports, Vol. 34, Issue 9 https://doi.org/10.1134/S1063780X08090109	journal	September 2008
Dynamics of hybrid X-pinches Shelkovenko, T. A.; Tilikin, I. N.; Ivanenkov, G. V. Plasma Physics Reports, Vol. 41, Issue 1 https://doi.org/10.1134/S1063780X15010031	journal	January 2015
X-pinch. Part I Pikuz, S. A.; Shelkovenko, T. A.; Hammer, D. A. Plasma Physics Reports, Vol. 41, Issue 4 https://doi.org/10.1134/S1063780X15040054	journal	April 2015
X-pinch. Part II Pikuz, S. A.; Shelkovenko, T. A.; Hammer, D. A. Plasma Physics Reports, Vol. 41, Issue 6 https://doi.org/10.1134/S1063780X15060045	journal	June 2015
A review of projection radiography of plasma and biological objects in X-Pinch radiation Shelkovenko, T. A.; Pikuz, S. A.; Hammer, D. A. Plasma Physics Reports, Vol. 42, Issue 3 https://doi.org/10.1134/S1063780X16030065	journal	March 2016
Differential Phase X-ray Imaging Microscopy with X-ray Talbot Interferometer Takeda, Yoshihiro; Yashiro, Wataru; Hattori, Tadashi Applied Physics Express, Vol. 1 https://doi.org/10.1143/APEX.1.117002	journal	October 2008
Demonstration of X-Ray Talbot Interferometry Momose, Atsushi; Kawamoto, Shinya; Koyama, Ichiro Japanese Journal of Applied Physics, Vol. 42, Issue Part 2, No. 7B https://doi.org/10.1143/JJAP.42.L866	journal	July 2003
Phase Tomography by X-ray Talbot Interferometry for Biological Imaging Momose, Atsushi; Yashiro, Wataru; Takeda, Yoshihiro Japanese Journal of Applied Physics, Vol. 45, Issue 6A, p. 5254-5262 https://doi.org/10.1143/JJAP.45.5254	journal	June 2006
Single-shot Z_eff dense plasma diagnostic through simultaneous refraction and attenuation measurements with a Talbot–Lau x-ray moiré deflectometer Valdivia, M. P.; Stutman, D.; Finkenthal, M. Applied Optics, Vol. 54, Issue 10 https://doi.org/10.1364/AO.54.002577	journal	January 2015
Talbot–Lau x-ray deflectometry phase-retrieval methods for electron density diagnostics in high-energy density experiments Valdivia, Maria Pia; Stutman, Dan; Stoeckl, Christian Applied Optics, Vol. 57, Issue 2 https://doi.org/10.1364/AO.57.000138	journal	January 2018
Formation of Optical Images by X-Rays Kirkpatrick, Paul; Baez, A. V. Journal of the Optical Society of America, Vol. 38, Issue 9 https://doi.org/10.1364/JOSA.38.000766	journal	January 1948
Analysis of the Lau effect and generalized grating imaging Swanson, G. J.; Leith, E. N. Journal of the Optical Society of America A, Vol. 2, Issue 6 https://doi.org/10.1364/JOSAA.2.000789	journal	June 1985
Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments Chen, Guang-Hong; Bevins, Nicholas; Zambelli, Joseph Optics Express, Vol. 18, Issue 12 https://doi.org/10.1364/OE.18.012960	journal	January 2010
On the origin of visibility contrast in x-ray Talbot interferometry Yashiro, W.; Terui, Y.; Kawabata, K. Optics Express, Vol. 18, Issue 16 https://doi.org/10.1364/OE.18.016890	journal	January 2010
Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube Sato, Genta; Kondoh, Takeshi; Itoh, Hidenosuke Optics Letters, Vol. 36, Issue 18 https://doi.org/10.1364/OL.36.003551	journal	September 2011
Fresnel zone plate development for x-ray radiography of hydrodynamic instabilities at the National Ignition Facility Do, Alexandre; Pickworth, Louisa A.; Kozioziemski, Bernard J. Applied Optics, Vol. 59, Issue 34 https://doi.org/10.1364/ao.408569	journal	January 2020
A New Method of Spectroscopy for Faint X-Radiations Ross, P. A. Journal of the Optical Society of America, Vol. 16, Issue 6 https://doi.org/10.1364/josa.16.000433	journal	January 1928
Partially coherent diffraction effect between Lau and Talbot effects Liu, Liren Journal of the Optical Society of America A, Vol. 5, Issue 10 https://doi.org/10.1364/josaa.5.001709	journal	January 1988
High spectral resolution x-ray optics with highly oriented pyrolytic graphite Legall, H.; Stiel, H.; Arkadiev, V. Optics Express, Vol. 14, Issue 10 https://doi.org/10.1364/oe.14.004570	journal	January 2006
Efficient, 1–100-keV x-ray radiography with high spatial and temporal resolution Bradley, D. K.; Landen, O. L.; Bullock, A. B. Optics Letters, Vol. 27, Issue 2 https://doi.org/10.1364/ol.27.000134	journal	January 2002