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    Journals >High Power Laser Science and Engineering >Volume 11 >Issue 4 >Page 04000e49 > Article
    • High Power Laser Science and Engineering
    • Vol. 11, Issue 4, 04000e49 (2023)
    Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry
    G. Pérez-Callejo1、2、*, V. Bouffetier2、3, L. Ceurvorst2、4, T. Goudal2、5, S. R. Klein6, D. Svyatskiy7, M. Holec8, P. Perez-Martin9、10, K. Falk9、10、11, A. Casner2、12, T. E. Weber7, G. Kagan13、*, and M. P. Valdivia14、15、*
    Author Affiliations
  • 1Departamento de Física Teórica Atómica y Óptica, Universidad de Valladolid, Valladolid, Spain
  • 2Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications (CELIA), UMR 5107, Talence, France
  • 3European XFEL GmbH, Schenefeld, Germany
  • 4Laboratory for Laser Energetics, Rochester, New York, USA
  • 5CEA-DAM, DIF, Arpajon, France
  • 6University of Michigan, Ann Arbor, Michigan, USA
  • 7Los Alamos National Laboratory, Los Alamos, New Mexico, USA
  • 8Lawrence Livermore National Laboratory, Livermore, California, USA
  • 9Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
  • 10Technische Universität Dresden, Dresden, Germany
  • 11Institute of Physics of the ASCR, Prague, Czech Republic
  • 12CEA-CESTA, CS 60001, Le Barp Cedex, France
  • 13Blackett Laboratory, Imperial College London, London, UK
  • 14Department of Astrophysics and Astronomy, The Johns Hopkins University, Baltimore, Maryland, USA
  • 15Center for Energy Research, University of California San Diego, San Diego, California, USA
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    DOI: 10.1017/hpl.2023.44 Cite this Article Set citation alerts
    G. Pérez-Callejo, V. Bouffetier, L. Ceurvorst, T. Goudal, S. R. Klein, D. Svyatskiy, M. Holec, P. Perez-Martin, K. Falk, A. Casner, T. E. Weber, G. Kagan, M. P. Valdivia. Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry[J]. High Power Laser Science and Engineering, 2023, 11(4): 04000e49 Copy Citation Text show less

    Abstract

    Diagnosing the evolution of laser-generated high energy density (HED) systems is fundamental to develop a correct understanding of the behavior of matter under extreme conditions. Talbot–Lau interferometry constitutes a promising tool, since it permits simultaneous single-shot X-ray radiography and phase-contrast imaging of dense plasmas. We present the results of an experiment at OMEGA EP that aims to probe the ablation front of a laser-irradiated foil using a Talbot–Lau X-ray interferometer. A polystyrene (CH) foil was irradiated by a laser of 133 J, 1 ns and probed with 8 keV laser-produced backlighter radiation from Cu foils driven by a short-pulse laser (153 J, 11 ps). The ablation front interferograms were processed in combination with a set of reference images obtained ex situ using phase-stepping. We managed to obtain attenuation and phase-shift images of a laser-irradiated foil for electron densities above ${10}^{22}\;{\mathrm{cm}}^{-3}$ . These results showcase the capabilities of Talbot–Lau X-ray diagnostic methods to diagnose HED laser-generated plasmas through high-resolution imaging.

    Keywords

    $$ \begin{align}{I}_{\mathrm{obj}}\left(\mathbf{r}\right)={A}_{\mathrm{obj}}\left(\mathbf{r}\right)+{B}_{\mathrm{obj}}\left(\mathbf{r}\right){e}^{i\left[{\mathbf{k}}_{\mathrm{f}}\cdot \mathbf{r}+{\phi}_{\mathrm{obj}}\left(\mathbf{r}\right)\right]},\end{align}$$ ((1))

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    $$\begin{align}{I}_{\mathrm{ref}}\left(\mathbf{r},n\right)={A}_{\mathrm{ref}}\left(\mathbf{r}\right)+{B}_{\mathrm{ref}}\left(\mathbf{r}\right){e}^{i\left[{\mathbf{k}}_{\mathrm{f}}\cdot \mathbf{r}+{\phi}_{\mathrm{ref}}\left(\mathbf{r}\right)+\frac{2\pi n}{T}\right]},\end{align}$$ ((2))

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    $$\begin{align}\mathrm{Attenuation}\left(\mathbf{r}\right)=\frac{A_{\mathrm{obj}}\left(\mathbf{r}\right)}{A_{\mathrm{ref}}\left(\mathbf{r}\right)}.\end{align}$$ ((3))

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    $$\begin{align}\phi \left(\mathbf{r}\right)={\phi}_{\mathrm{obj}}\left(\mathbf{r}\right)-{\phi}_{\mathrm{ref}}\left(\mathbf{r}\right).\end{align}$$ ((4))

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    $$\begin{align}{I}_{\mathrm{obj}}\left(\mathbf{r}\right)={\int}_{-\infty}^{\infty }F\left(\mathbf{k}\right){e}^{i\mathbf{k}\cdot \mathbf{r}}\mathrm{d}\mathbf{k},\end{align}$$ ((5))

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    $$\begin{align}{F}_1\left(\mathbf{k}\right)=\left\{\begin{array}{ll}F\left(\mathbf{k}\right),& \left|\mathbf{k}-{\mathbf{k}}_{\mathrm{f}}\right|>\delta, \\ {}0,& \left|\mathbf{k}-{\mathbf{k}}_{\mathrm{f}}\right|<\delta, \end{array}\right.\end{align}$$ ((6))

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    $$\begin{align}{F}_2\left(\mathbf{k}\right)=F\left(\mathbf{k}\right)-{F}_1\left(\mathbf{k}\right),\end{align}$$ ((7))

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    $$\begin{align}{A}_{\mathrm{obj}}\left(\mathbf{r}\right)={\mathrm{\mathcal{F}}}^{-1}\left({F}_1\right),\end{align}$$ ((8))

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    $$\begin{align}{B}_{\mathrm{obj}}\left(\mathbf{r}\right){e}^{i\left[{\mathbf{k}}_{\mathrm{f}}\cdot \mathbf{r}+{\phi}_{\mathrm{obj}}\left(\mathbf{r}\right)\right]}={\mathrm{\mathcal{F}}}^{-1}\left({F}_2\right),\end{align}$$ ((9))

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    $$\begin{align}\log \left[{B}_{\mathrm{obj}}\left(\mathbf{r}\right)\right]=\operatorname{Re}\left\{\log \left[{\mathrm{\mathcal{F}}}^{-1}\left({F}_2\right)\right]\right\},\end{align}$$ ((10))

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    $$\begin{align}{\mathbf{k}}_{\mathrm{f}}\cdot \mathbf{r}+{\phi}_{\mathrm{obj}}\left(\mathbf{r}\right)=\operatorname{Im}\left\{\log \left[{\mathrm{\mathcal{F}}}^{-1}\left({F}_2\right)\right]\right\}.\end{align}$$ ((11))

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    $$\begin{align}{I}_{\mathrm{ref}}\left(\mathbf{r},n\right)=\sum \limits_{j=-\infty}^{\infty }{Q}_j\left(\mathbf{r}\right){e}^{i\frac{2\pi j}{T}n},\end{align}$$ ((12))

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    $$\begin{align}{Q}_0\left(\mathbf{r}\right)={A}_{\mathrm{ref}}\left(\mathbf{r}\right),\end{align}$$ ((13))

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    $$\begin{align}{Q}_1\left(\mathbf{r}\right)={B}_{\mathrm{ref}}\left(\mathbf{r}\right){e}^{i\left[{\mathbf{k}}_{\mathrm{f}}\cdot \mathbf{r}+{\phi}_{\mathrm{ref}}\left(\mathbf{r}\right)\right]}.\end{align}$$ ((14))

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    $$\begin{align}\frac{\partial }{\partial x}\left(\int {n}_{\mathrm{e}} \mathrm{d}z\right)=\frac{\phi \left(\mathbf{r}\right)}{\lambda^2{r}_{\mathrm{e}}}\cdot \frac{p_0}{d_0},\end{align}$$ ((15))

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    $$\begin{align}\alpha =\frac{\phi \left(\mathbf{r}\right)}{2\pi}\cdot \frac{p_0}{d_0}=F\left(\mathbf{r}\right)\cdot {W}_{\mathrm{eff}},\end{align}$$ ((16))

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    G. Pérez-Callejo, V. Bouffetier, L. Ceurvorst, T. Goudal, S. R. Klein, D. Svyatskiy, M. Holec, P. Perez-Martin, K. Falk, A. Casner, T. E. Weber, G. Kagan, M. P. Valdivia. Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry[J]. High Power Laser Science and Engineering, 2023, 11(4): 04000e49
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