# Tomography strategies dedicated to laser-based Kα X-ray source

Adrien Stolidi, Victor Bussy, Raphaël Clady, Abdessamad Boudafcha, Olivier

Uteza, Amélie Ferre

► To cite this version:

Adrien Stolidi, Victor Bussy, Raphaël Clady, Abdessamad Boudafcha, Olivier Uteza, et al. Tomography strategies dedicated to laser-based Kα X-ray source. 10th International Symposium on Digital Industrial Radiology and Computed Tomography (DIR 2025), Jul 2025, Paris, France. pp.ISSN 1435-4934, 10.58286/31379. cea-05197532

HAL Id: cea-05197532

https://cea.hal.science/cea-05197532v1

Submitted on 2 Aug 2025

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# Tomography strategies dedicated to laser-based Kα X-ray source

Adrien STOLIDI¹*, Victor BUSSY¹,
Raphaël CLADY², Abdessamad BOUDAFCHA², Olivier UTÉZA² and Amélie FERRÉ²

¹Université Paris-Saclay, CEA, List, F91120 Palaiseau, France.

²Aix-Marseille Université, CNRS, LP3 UMR 7341, 13288, Marseille, France.

*Corresponding author, E-mail: adrien.stolidi@cea.fr

## Abstract

Laser-based Kα X-ray sources offer compact and cost-effective alternatives to large-scale facilities like synchrotrons, providing high photon flux and ultrashort pulses ideal for advanced imaging. However, challenges such as flux variability, target refresh limitations and acquisition constraints hinder their use in tomography. This study presents tomographic strategies leveraging a priori knowledge of the sample and advanced denoising techniques, tested on simulated data.

**Keywords:** Laser-based X-ray source, Tomography.

## 1. Introduction

The emergence of laser-based Kα X-ray sources has provided a compact and cost-effective alternative to conventional large-scale X-ray sources, such as synchrotrons and XFELs. These sources are generated by focusing an ultrashort and intense laser pulse onto a high atomic number (Z) solid target, producing a broad X-ray spectrum consisting of Bremsstrahlung emission and prominent monochromatic Kα and Kβ lines (accounting for more than 35% [1]) related to the nature of the solid target. With a high Kα photon flux, short pulse duration and small emission volume, laser-based Kα sources are particularly attractive for advanced imaging techniques such as X-ray phase-contrast imaging [2,3]. Furthermore, their synchronization with the driving laser pulse enables time-resolved studies, offering significant advantages for dynamic imaging of materials and industrial components.

Despite their numerous benefits, several constraints limit the use of laser-based Kα sources for tomographic acquisitions. For instance, laser beam pointing fluctuations and laser energy shot to shot fluctuations can lead to a nonconstant size, position and/or flux of the X-ray source, hindering the repeatability of image quality and, consequently, the accuracy of the 3D reconstructed volume. Additionally, the limited number of laser shots on a given target, caused by the need to refresh the interaction area, poses challenges in achieving adequate data acquisition for tomographic reconstruction. These factors collectively make tomographic imaging using laser-based Kα X-ray sources a complex and challenging task.

In this work, we propose innovative tomographic strategies to address these challenges and improve the quality of reconstructions under constrained acquisition conditions.

## 2. Materials and Methods

### 2.1 Laser-based Kα X-ray source

When focused on a target, intense ultrashort laser pulses induce an abundant liberation of highly energetic (hot) electrons via various collisional and collisionless mechanisms developing during the plasma-laser interaction. With a target made of high Z material like Copper (Cu) or Molybdenum (Mo), this results in the generation of hard short-pulse X-rays in small transiently-excited volume issued from hot electron recombination and consecutive Kα fluorescence. For every laser shot the surface of the solid target is ablated. To gain in stability and reproductibility of generated X-rays, the interaction area is always refreshed inducing a limitation of the laser shots for a given target. However, this type of X-rays source offer inherent advantages, such as isotropic emission and beam divergence, which facilitate imaging over a wide field of view, unlike other nearly collimated laser plasma sources such as Inverse Compton scattering and Betatron.
By definition, these sources can provide time-resolved diagnostics and deliver a high X-ray flux (up to 1.5×10¹² X-ray photons/s [4]), excellent monochromaticity (Kα radiation) with a broad Bremsstrahlung spectrum, tunable energy from around 5 to near 100 keV (by changing the target material), and micrometric source dimensions comparable to the laser driver focused spot size [1,4]. Figure 1 present an example of a laser-based Kα X-ray source which is here the ASUR platform operated by the LP3 laboratory.

<figure><img src="image_2.png" /><figcaption>Figure 1: Picture of the ASUR platform with the two amplification chains (left) and the schematic of the interaction chamber, where the high-intensity laser is focused on the solid target (Molybdenum), inducing the production of X-rays. Diagnostics are in place to monitor the quality and stability of the X-ray source.</figcaption></figure>

## 2.2 Numerical modelisation

To evaluate our approach, a simulation study using the CIVA software suite has been conducted, implementing a designed experiment to compare reconstruction results under different strategic configurations. The object under inspection is a carbon-based sample designed via additive manufacturing techniques. To represent a Molybdenum target of the interaction chamber, the X-ray source was set at 17.48 keV, corresponding to the Mo Kα line. The X-ray peak-to-flux varied by approximately ±13% around its mean value, based on typical experimental data [1,5] (see for instance Figure 3). The acquisition trajectory consisted of 360 evenly distributed points along a circular path around the object. Taking into account the source-rotation axis distance and detector-rotation axis distance, which were fixed at 260 mm and 100 mm respectively—representing the spatial configuration of the ASUR experimental bench—this led to a magnification factor of 1.38.

<figure><img src="image_3.png" /><figcaption>Figure 2: CIVA simulation result showing one projection of the carbon-based sample (left) and a representation of the simulation scene (right), with the X-ray source set at 17.48 keV (Mo Kα), with its position shown in blue, and the square green area representing the detector.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3 [from 5]: Similar experimental data with a laser CR (Contrast Ratio) value of 3.3 10¹⁰ (green triangle) are used for the simulation. Experimental data used for the simulation: Left, the dependence of the X-ray source size on four temporal laser contrasts. The middle graph describes the relation between the Kα X-ray flux and the laser intensity on the target, again for four temporal laser contrasts. And on the right, the existing X-ray spectrum highlights the contribution of the Kα and Kβ lines of the Molybdenum target</figcaption></figure>

<figure><img src="image_5.png" /></figure>

## 2.3 Tomographic reconstruction strategies

As introduced, we tackle here two main challenges for tomographic reconstruction using laser-based Kα X-ray source: significant flux variations and a limited number of projections to preserve the target consumption. To address the latter, we adopted a view selection strategy based on the Empirical Interpolation Method (EIM). This technique is fast and allows, starting from either a CAD (Computer-Aided Design) model or a fully simulated sinogram, the identification of the most informative views [6,7]. By selecting only the most relevant projections, we significantly reduce the number of required acquisitions, thereby preserving the solid target consumption in our experimental setup. To handle the substantial flux variations, we implemented a two-step correction procedure prior to and during the reconstruction process. First, all projections were normalized to ensure that the mean flux across the images was consistent. Second, the tomographic problem was weighted according to the statistical reliability of each projection. Under the assumption of a monoenergetic beam and that the noise distributions along different paths are statistically independent, the Poisson log-likelihood function for the joint probability distribution can be expressed as [3]:

$$Y_i \sim \text{Poisson}\{\mathbf{b}_i \exp(-[A\boldsymbol{\mu}]_i) + \mathbf{r}_i\}, \quad i = 1, \dots, N \quad (1)$$

where $b_i$ is the blank scan factor, and N is the number of measured rays. The matrix A is the projection operator. The notation $[A\boldsymbol{\mu}]_i = \sum_j a_{ij}\boldsymbol{\mu}_j$ represents the ith line integral. To estimate the attenuation coefficient vector $\boldsymbol{\mu}$, we use a likelihood-based estimation approach [7]. In this framework, projections acquired under higher flux conditions contribute more significantly to the reconstruction, as they are associated with a higher signal-to-noise ratio (SNR). Conversely, projections with lower flux — and thus lower SNR — are given less weight in the reconstruction process. By defining $\hat{l}_i = \ln(\frac{b_i}{Y_i})$, the tomographic reconstruction problem can be formulated as the following weighted least-squares minimization:

$$\boldsymbol{\mu}^* = \min_{\boldsymbol{\mu}} \sum_i \frac{Y_i}{2} \left( [A\boldsymbol{\mu}]_i - \hat{l}_i \right)^2 \quad (2)$$

## 3. Results

As a first step, we investigated the impact of projection normalisation. A high-resolution reference volume of 671 × 520 × 243 voxels was reconstructed using the Feldkamp-Kress-Davis (also referred to as FDK) algorithm from the dense trajectory (360 projections). This was then compared with a reconstruction obtained from a sparse trajectory (200 projections), with and without flux normalisation. Figure 4 displays
the reconstructed central slice. The results demonstrate that flux normalisation leads to a notable improvement in image quality.

<figure><img src="image_6.png" /><figcaption>Figure 4 : Left : with normalization. Right : without normalization.</figcaption></figure>

Subsequently, we explored the effect of weighting the projections according to the number of detected photons within the tomographic inversion process. The corresponding results are presented in Table 1. We observe a further improvement in the Peak Signal to Noise Ratio (PSNR) when projection normalisation is applied. Moreover, the use of statistical weighting proves beneficial, particularly in down-weighting low-SNR projections, which might otherwise degrade the overall reconstruction quality.

<table><caption>Table 1. Results of Improvements Achieved through Flux Normalisation and Projection Weighting Strategies</caption><thead><tr><th>PSNR Reconstruction 200 projections</th><th>Without weighting</th><th>With weighting</th></tr></thead><tbody><tr><td>Without normalization</td><td>19.87</td><td>24.79</td></tr><tr><td>With normalization</td><td>29.32</td><td>30.01</td></tr></tbody></table>

Finally, we quantified the contribution of the view selection strategy to the reconstruction quality by comparing sparse reconstructions obtained using either uniformly spaced views or views selected *via* the Discrete Empirical Interpolation Method (DEIM). The results are presented in Figure 5. The optimised sampling achieved through DEIM leads to a noticeable improvement in reconstruction quality.

<figure><img src="image_7.png" /><figcaption>Figure 5 : Reconstruction quality according to the number of projections. Values undergo a moving average with a kernel size of 5.</figcaption></figure>
# 4. Conclusions

In conclusion, this study presents preliminary simulation results that demonstrate the potential of laser-based $K\alpha$ X-ray sources as a compact and cost-effective alternative to conventional large-scale X-ray sources for advanced imaging techniques. Despite challenges such as flux variations and limited projections, innovative tomographic strategies, including view selection and flux normalization, have shown promise in enhancing reconstruction quality. The use of the Empirical Interpolation Method and statistical weighting in the reconstruction process improves image quality and preserves target consumption. While these initial findings are encouraging, experimental results are currently underway to further validate and refine these approaches. These advancements pave the way for more effective dynamic imaging of materials and industrial components, highlighting the promise of laser-based $K\alpha$ X-ray sources in tomographic applications.

# Acknowledgements

This work received government funding managed by the French National Research Agency under the France 2030 program for the PEPR LUMA, referenced ANR-22-EXLU-0002 (ULTRAFAST).

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