X-ray phase-contrast imaging: a broad overview of some fundamentals

Abstract

We outline some basics of imaging using both fully-coherent and partially-coherent X-ray beams, with an emphasis on phase-contrast imaging. We open with some of the basic notions of X-ray imaging, including the vacuum wave equations and the physical meaning of the intensity and phase of complex scalar fields. The projection approximation is introduced, together with the concepts of attenuation contrast and phase contrast. We also outline the multi-slice approach to X-ray propagation through thick samples or optical elements, together with the Fresnel scaling theorem. Having introduced the fundamentals, we then consider several aspects of the forward problem, of modelling the formation of phase-contrast X-ray images. Several topics related to this forward problem are considered, including the transport-of-intensity equation, arbitrary linear imaging systems, shift-invariant linear imaging systems, the transfer-function formalism, blurring induced by finite source size, the space-frequency model for partially-coherent fields, and the Fokker-Planck equation for paraxial X-ray imaging. Having considered these means for modelling the formation of X-ray phase-contrast images, we then consider aspects of the associated inverse problem of phase retrieval. This concerns how one may decode phase-contrast images to gain information regarding the sample-induced attenuation and phase shift.

arXiv commentSome minor corrections have been made to some of the equations in the preceding version. To appear in Advances in Imaging and Electron Physics. arXiv admin note: text overlap with arXiv:1902.00364

References in corpus (17)

• Fourier-transform Ghost Imaging with Hard X-rays
• Experimental x-ray ghost imaging
• Photons that travel in free space slower than the speed of light
• On Random-Matrix Bases, Ghost Imaging and X-ray Phase Contrast Computational Ghost Imaging
• X-ray Fokker--Planck equation for paraxial imaging
• The Theory of Diffraction Tomography
• Three dimensions, two microscopes, one code: automatic differentiation for x-ray nanotomography beyond the depth of focus limit
• Dark-field signal extraction in propagation-based phase-contrast imaging
• Boosting spatial resolution by incorporating periodic boundary conditions into single-distance hard-x-ray phase retrieval
• X-ray Multimodal Intrinsic-Speckle-Tracking
• Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent X-ray radiation
• Quantum enhanced X-ray detection
• Ghost Imaging at an XUV Free-Electron Laser
• Quantum Turbulent Structure in Light
• Tutorials on X-ray Phase Contrast Imaging: Some Fundamentals and Some Conjectures on Future Developments
• Propagation of fully-coherent and partially-coherent complex scalar fields in aberration space
• Speckled cross-spectral densities and their associated correlation singularities for a modern source of partially coherent x rays

Cited by in corpus (5)

• Texture tomography, a versatile framework to study crystalline texture in 3D
• Paraxial diffusion-field retrieval
• Uniqueness Theorems for Tomographic Phase Retrieval with Few Diffraction Patterns
• Eliminating the Second-Order Time Dependence from the Time Dependent Schrödinger Equation Using Recursive Fourier Transforms
• Directional dark-field implicit x-ray speckle tracking using an anisotropic-diffusion Fokker-Planck equation