# Refraction simulation for optimisation of X-Ray Phase Contrast imaging

Emilie Pietersoone, Jean Michel Létang, Simon Rit, Emmanuel Brun, Julien Bert, Max Langer

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Emilie Pietersoone, Jean Michel Létang, Simon Rit, Emmanuel Brun, Julien Bert, et al. Refraction simulation for optimisation of X-Ray Phase Contrast imaging. XRM2024, Aug 2024, Lund, Sweden. hal-04910272

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Submitted on 24 Jan 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Refraction simulation for optimisation of X-Ray Phase Contrast imaging

**Emilie Pietersoone**<sup>1)</sup>, Jean Michel Létang<sup>2)</sup>, Simon Rit<sup>2)</sup>, Emmanuel Brun<sup>3)</sup>, Julien Bert<sup>4)</sup>, Max Langer<sup>1)</sup>

(1) Univ. Grenoble Alpes, CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, F-38000 Grenoble, France

(2) INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Étienne, CNRS, Inserm, CREATIS UMR 5220, U1294, F-69373 Lyon, France

(3) Univ. Grenoble Alpes, Inserm, UA7 STROBE, F-38000 Grenoble, France

(4) LaTIM, INSERM UMR 1101, IBRBS, Faculty of Medicine, Univ Brest, F-29238, Brest, France

*Corresponding Author: emilie.pietersoone@univ-grenoble-alpes.fr (only 1)

**Keywords:** X-ray Phase Contrast Imaging, Refraction, Simulation; (maximum 4)

X-ray Phase Contrast Imaging (XPCI) is particularly advantageous when imaging materials with low X-ray absorption. This technique provides superior visualisation compared to absorption-based methods. The phase information obtained through XPCI's exploitation of refraction is highly sensitive to changes in the sample's electron density. Current XPCI simulation methods, while valuable, fail to recreate the noise present in experimental images. The current hypothesis, is that it might be due to limitations in capturing certain physical phenomena [1]. Some simulation methods combine MC and wave effects in order to include refraction [2,3]. The presented research continues this research, by testing different methods to incorporate refraction in 2D and 3D projection-based simulations.

We focus on edge detection [4] within a ray tracing projection-based simulation. The research is based on the application of Snell's law at the sample interfaces. Detection of these interfaces are done by testing both gradient calculation and application of thresholds, and use of the monogenic signal to analytically calculate the trajectory for multidimensional signals [5]. The gradient module quantifies the importance of the highlighted contour, which is the magnitude of the intensity jump observed in the image. The gradient direction determines the edge present in the image. Indeed, the gradient direction is orthogonal to that of the contour. The monogenic signal is seen as an extension of the analytic signal, transitioning from one-dimensional to high-dimensional space. It is constructed by combining the Riesz transform with the original signal, offering representations of signal features like local attenuation and the local phase vector. The movement comes from providing a framework to include incoherent scattering in XPCI simulations. The different methods that will be presented compare a theoretical result with a prism, a gradient orientation-based method, and a monogenic signal-based method. Purpose of the method, is proposing a novel manner of including refraction for voxels.

X-ray phase contrast techniques have shown promise for improving soft tissue visibility and enhancing the detection of subtle abnormalities. Simulations incorporating refraction participate in optimising the imaging setup for specific applications, contributing to the development of more effective diagnostic tools. XPCI is invaluable in material science and non-destructive testing by providing detailed information about the internal structures of materials. Refraction simulations are crucial for understanding and optimizing the imaging process for different types of materials.

**References:**

[1] Suuronen, J. P., Hesse, B., Langer, M., Bohner, M., & Villanova, J. (2022). J. Synchrotron Rad., 29(3), 843-852.

[2] Cipiccia, S., Vittoria, F. A., Weikum, M., Olivo, A., & Jaroszynski, D. A. (2014). Opt. Express, 22(19), 23480-23488.

[3] Langer, M., Cen, Z., Rit, S., & Létang, J. M. (2020). Opt. Express, 28(10), 14522-14535.

[4] Sahoo, T., & Pine, S. (2016). In SCOPES IEEE. (pp. 1224-1228).

[5] Cheng, D., & Kou, K. I. (2022). arXiv preprint arXiv:2209.08880.