Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method
The accurate calculation of the angle of refraction of X-rays passing through an object is essential in X-ray phase-contrast imaging. While the wave optics-based method is commonly employed to calculate the angle of refraction, it presents several limitations. First, in cases where the object induce...
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MDPI AG
2025-05-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/12/5/442 |
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| author | Jun Yang Fangke Zong Haoqi Tang Yang Du Rongchang Chen |
| author_facet | Jun Yang Fangke Zong Haoqi Tang Yang Du Rongchang Chen |
| author_sort | Jun Yang |
| collection | DOAJ |
| description | The accurate calculation of the angle of refraction of X-rays passing through an object is essential in X-ray phase-contrast imaging. While the wave optics-based method is commonly employed to calculate the angle of refraction, it presents several limitations. First, in cases where the object induces significant phase variations, the angle of refraction becomes divergent. Second, the method fails to adequately account for point-source illumination conditions, particularly the influence of the finite X-ray source size on the angle of refraction. In this study, we demonstrate that a geometric optics-based method can effectively simulate propagation-based X-ray phase-contrast imaging with a low-brilliance X-ray source and compute the angle of refraction more accurately than the wave optics-based method. Our studies reveal that the geometric optics-based method can robustly determine the angle of refraction, even under conditions of substantial phase variations within the object. Furthermore, we show that reducing both the X-ray source size and the detector pixel size increases the angle of refraction in both simulations and experiments. Additionally, our results highlight that the angle of refraction is not invariant. Instead, it increases with the system’s total length and as the object moves closer to the light source. For systems with a Fresnel number of N ≥ 1, our method exhibits full compatibility with wave optics methods and can be extended to grating-based X-ray interferometry. The approach offers a robust alternative for calculating the angle of refraction under diverse imaging conditions. |
| format | Article |
| id | doaj-art-278d8f0be80446ff833d5a691d4b4bc8 |
| institution | DOAJ |
| issn | 2304-6732 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Photonics |
| spelling | doaj-art-278d8f0be80446ff833d5a691d4b4bc82025-08-20T03:14:39ZengMDPI AGPhotonics2304-67322025-05-0112544210.3390/photonics12050442Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics MethodJun Yang0Fangke Zong1Haoqi Tang2Yang Du3Rongchang Chen4Institute of Advanced Light Source Facilities, Shenzhen 518107, ChinaInstitute of Advanced Light Source Facilities, Shenzhen 518107, ChinaInstitute of Advanced Light Source Facilities, Shenzhen 518107, ChinaInstitute of Advanced Light Source Facilities, Shenzhen 518107, ChinaInstitute of Advanced Light Source Facilities, Shenzhen 518107, ChinaThe accurate calculation of the angle of refraction of X-rays passing through an object is essential in X-ray phase-contrast imaging. While the wave optics-based method is commonly employed to calculate the angle of refraction, it presents several limitations. First, in cases where the object induces significant phase variations, the angle of refraction becomes divergent. Second, the method fails to adequately account for point-source illumination conditions, particularly the influence of the finite X-ray source size on the angle of refraction. In this study, we demonstrate that a geometric optics-based method can effectively simulate propagation-based X-ray phase-contrast imaging with a low-brilliance X-ray source and compute the angle of refraction more accurately than the wave optics-based method. Our studies reveal that the geometric optics-based method can robustly determine the angle of refraction, even under conditions of substantial phase variations within the object. Furthermore, we show that reducing both the X-ray source size and the detector pixel size increases the angle of refraction in both simulations and experiments. Additionally, our results highlight that the angle of refraction is not invariant. Instead, it increases with the system’s total length and as the object moves closer to the light source. For systems with a Fresnel number of N ≥ 1, our method exhibits full compatibility with wave optics methods and can be extended to grating-based X-ray interferometry. The approach offers a robust alternative for calculating the angle of refraction under diverse imaging conditions.https://www.mdpi.com/2304-6732/12/5/442X-ray phase-contrast imagingangle of refractionfocal spot size |
| spellingShingle | Jun Yang Fangke Zong Haoqi Tang Yang Du Rongchang Chen Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method Photonics X-ray phase-contrast imaging angle of refraction focal spot size |
| title | Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method |
| title_full | Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method |
| title_fullStr | Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method |
| title_full_unstemmed | Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method |
| title_short | Determination of Angle of Refraction in X-Ray Phase-Contrast Imaging Using Geometric Optics Method |
| title_sort | determination of angle of refraction in x ray phase contrast imaging using geometric optics method |
| topic | X-ray phase-contrast imaging angle of refraction focal spot size |
| url | https://www.mdpi.com/2304-6732/12/5/442 |
| work_keys_str_mv | AT junyang determinationofangleofrefractioninxrayphasecontrastimagingusinggeometricopticsmethod AT fangkezong determinationofangleofrefractioninxrayphasecontrastimagingusinggeometricopticsmethod AT haoqitang determinationofangleofrefractioninxrayphasecontrastimagingusinggeometricopticsmethod AT yangdu determinationofangleofrefractioninxrayphasecontrastimagingusinggeometricopticsmethod AT rongchangchen determinationofangleofrefractioninxrayphasecontrastimagingusinggeometricopticsmethod |