Directional dark-field implicit x-ray speckle tracking using an anisotropic-diffusion Fokker-Planck equation

When a macroscopic-sized non-crystalline sample is illuminated using coherent x-ray radiation, a bifurcation of photon energy flow may occur. The coarse-grained complex refractive index of the sample may be considered to attenuate and refract the incident coherent beam, leading to a coherent component of the transmitted beam. Spatially-unresolved sample microstructure, associated with the fine-grained components of the complex refractive index, introduces a diffuse component to the transmitted beam. This diffuse photon-scattering channel may be viewed in terms of position-dependent fans of ultra-small-angle x-ray scatter. These position-dependent fans, at the exit surface of the object, may under certain circumstances be approximated as having a locally-elliptical shape. By using an anisotropic-diffusion Fokker-Planck approach to model this bifurcated x-ray energy flow, we show how all three components (attenuation, refraction and locally-elliptical diffuse scatter) may be recovered. This is done via x-ray speckle tracking, in which the sample is illuminated with spatially-random x-ray fields generated by coherent illumination of a spatially-random membrane. The theory is developed, and then successfully applied to experimental x-ray data

X-ray multi-modal intrinsic-speckle-tracking

We develop x-ray multi-modal intrinsic-speckle-tracking (MIST), a form of x-ray speckle-tracking that is able to recover both the position-dependent phase shift and the position-dependent small-angle x-ray scattering (SAXS) signal of a phase object. MIST is based on combining a Fokker-Planck description of paraxial x-ray optics, with an optical-flow formalism for x-ray speckle-tracking. Only two images need to be taken in the presence of the sample, corresponding to two different transverse positions of the speckle-generating membrane, in order to recover both the refractive and local-SAXS properties of the sample. Like the optical-flow x-ray phase-retrieval method which it generalises, the MIST method implicitly rather than explicitly tracks both the transverse motion and the diffusion of speckles that is induced by the presence of a sample. Application to x-ray synchrotron data shows the method to be efficient, rapid and stable

Single-shot x-ray speckle-based imaging of a single-material object

We develop a means for speckle-based phase imaging of the projected thickness of a single-material object, under the assumption of illumination by spatially random time-independent x-ray speckles. These speckles are generated by passing x rays through a suitable spatially random mask. The method makes use of a single image obtained in the presence of the object, which serves to deform the illuminating speckle field relative to a reference speckle field (which need only be measured once) obtained in the presence of the mask and the absence of the object. The method implicitly rather than explicitly tracks speckles, and utilizes the transport-of-intensity equation to give a closed-form solution to the inverse problem of determining the complex transmission function of the object. Application to x-ray synchrotron data shows the method to be robust and efficient with respect to noise. Applications include x-ray phase--amplitude radiography and tomography, as well as time-dependent imaging of dynamic and radiation-sensitive samples using low-flux sources

X-ray speckle-based imaging of a single-material object.Beyond the geometric-flow formalism.

We develop a means for a single-shot speckle-based phase-contrast imaging of the projected thickness of a single material object, under the assumption of illumination by spatially random time-independent x-ray speckles. The method implicitly rather than explicitly tracks speckles, and utilises the Transport-of-Intensity Equation (TIE) to give a closed-form solution to the inverse problem of determining the complex transmission function of the object. The application to x-ray synchrotron data demonstrates that the method is robust and efficient with respect to noise. The CT reconstructions show image quality improvements in comparison to a geometric-flow approach demonstrated in D. M. Paganin, H. Labriet, E. Brun, and S. Berujon, Phys. Rev. A 98, 053813 (2018)

High energy X-ray phase and dark-field imaging using a random absorption mask

High energy X-ray imaging has unique advantage over conventional X-ray imaging, since it enables higher penetration into materials with significantly reduced radiation damage. However, the absorption contrast in high energy region is considerably low due to the reduced X-ray absorption cross section for most materials. Even though the X-ray phase and dark-field imaging techniques can provide substantially increased contrast and complementary information, fabricating dedicated optics for high energies still remain a challenge. To address this issue, we present an alternative X-ray imaging approach to produce transmission, phase and scattering signals at high X-ray energies by using a random absorption mask. Importantly, in addition to the synchrotron radiation source, this approach has been demonstrated for practical imaging application with a laboratory-based microfocus X-ray source. This new imaging method could be potentially useful for studying thick samples or heavy materials for advanced research in materials science

Directional dark-field implicit x-ray speckle tracking using an anisotropic-diffusion Fokker-Planck equation

International audienceWhen a macroscopic-sized noncrystalline sample is illuminated using coherent x-ray radiation, a bifurcation of photon energy flow may occur. The coarse-grained complex refractive index of the sample may be considered to attenuate and refract the incident coherent beam, leading to a coherent component of the transmitted beam. Spatially unresolved sample microstructure, associated with the fine-grained components of the complex refractive index, introduces a diffuse component to the transmitted beam. This diffuse photon-scattering channel may be viewed in terms of position-dependent fans of ultrasmall-angle x-ray scatter. These position-dependent fans, at the exit surface of the object, may under certain circumstances be approximated as having a locally elliptical shape. By using an anisotropic-diffusion Fokker-Planck approach to model this bifurcated x-ray energy flow, we show how all three components (attenuation, refraction, and locally elliptical diffuse scatter) may be recovered. This is done via x-ray speckle tracking, in which the sample is illuminated with spatially random x-ray fields generated by coherent illumination of a spatially random membrane. The theory is developed and then successfully applied to experimental x-ray data