Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources

Abstract

X -ray radiographic absorption imaging is an invaluable tool in medical diagnostics and materials science. For biological tissue samples, polymers or fibre composites, however, the use of conventional X-ray radiography is limited due to their weak absorption. This is resolved at highly brilliant X-ray synchrotron or micro-focus sources by using phase-sensitive imaging methods to improve the contrast 1,2 . However, the requirements of the illuminating radiation mean that hard-X-ray phase-sensitive imaging has until now been impractical with more readily available X-ray sources, such as X-ray tubes. In this letter, we report how a setup consisting of three transmission gratings can efficiently yield quantitative differential phase-contrast images with conventional X-ray tubes. In contrast with existing techniques, the method requires no spatial or temporal coherence, is mechanically robust, and can be scaled up to large fields of view. Our method provides all the benefits of contrast-enhanced phase-sensitive imaging, but is also fully compatible with conventional absorption radiography. It is applicable to X-ray medical imaging, industrial non-destructive testing, and to other low-brilliance radiation, such as neutrons or atoms.In conventional X-ray imaging, contrast is obtained through the differences in the absorption cross-section of the constituents of the object. The technique yields excellent results where highly absorbing structures such as bones are embedded in a matrix of relatively weakly absorbing material, for example the surrounding tissue of the human body. However, in cases where different forms of tissue with similar absorption cross-sections are under investigation (for example, mammography or angiography), the X-ray absorption contrast is relatively poor. Consequently, differentiating pathologic from non-pathologic tissue in an absorption radiograph obtained with a current hospital-based X-ray system remains practically impossible for certain tissue compositions.To overcome these limitations, several methods to generate radiographic contrast from the phase shift of X-rays passing through the sample have been investigated 3-13 . They can be classified into interferometric methods 3,4 , techniques using an analyser 5-7 and free-space propagation methods [8][9][10][11][12][13] . These methods differ vastly in the nature of the signal recorded, the experimental setup, and the requirements on the illuminating radiation. Because of the use of crystal optics, interferometric and analyser-based methods rely on a highly parallel and monochromatic X-ray beam. The required spatial and temporal coherence lengths 14 are given by ξ s = l( α/α) −1 and ξ t = l( E/E) −1 , where l is the wavelength, α/α is the angular acceptance and E/E is the energy band pass of the crystal optics. With typical values of α/α ≤ 10 −4 and E/E ≤ 10 −4 , they range in the order of ξ s ≥ 10 −6 m and ξ t ≥ 10 −6 m. Propagation-based methods can overcome the stringent requirements on the temporal coherence, and have been demonstrated to...

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