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Paganin's method for image reconstruction in propagation-based phase-contrast X-ray imaging and tomography has enjoyed broad acceptance in recent years, with over one thousand publications citing its use. The present paper discusses…

Medical Physics · Physics 2026-01-13 Timur E. Gureyev , David M. Paganin , Ashkan Pakzad , Harry M. Quiney

In the first part of this paper, quantitative aspects of propagation-based phase-contrast imaging (PBI) were investigated using theoretical and numerical approaches, as well as experimental two-dimensional PBI images collected with plane…

Medical Physics · Physics 2025-07-08 T. E. Gureyev , D. M. Paganin , K. M. Pavlov , A. Maksimenko , H. M. Quiney

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to…

Medical Physics · Physics 2023-12-20 T. E. Gureyev , D. M. Paganin , H. M. Quiney

A simple coherent-imaging method due to Paganin et al. is widely employed for phase-amplitude reconstruction of samples using a single paraxial x-ray propagation-based phase-contrast image. The method assumes that the sample-to-detector…

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…

Image and Video Processing · Electrical Eng. & Systems 2022-09-21 J. A. Pollock , K. S. Morgan , L. C. P. Croton , M. K. Croughan , G. Ruben , N. Yagi , H. Sekiguchi , M. J. Kitchen

X-ray phase-contrast imaging has the potential to improve image contrast with lower dose by probing an object's refractive properties as well as its absorptive properties. To reconstruct a phase-contrast image from a raw dataset, a phase…

Medical Physics · Physics 2025-08-19 Giavanna Jadick , Patrick La Rivière

These tutorials introduce some basics of imaging with coherent X-rays, focusing on phase contrast. We consider the transport-of-intensity equation, as one particular method for X-ray phase contrast imaging among many, before passing on to…

Image and Video Processing · Electrical Eng. & Systems 2019-02-28 David M. Paganin , Daniele Pelliccia

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear…

Numerical Analysis · Mathematics 2016-04-07 Simon Maretzke , Matthias Bartels , Martin Krenkel , Tim Salditt , Thorsten Hohage

Multi-energy CT has long demonstrated its ability to enhance image quality with material decomposition. Yet, it has largely been limited to applications that already have high contrast. More recently, x-ray phase-contrast (XPC) imaging has…

Medical Physics · Physics 2025-08-19 Giavanna Jadick , Patrick La Rivière

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…

Image and Video Processing · Electrical Eng. & Systems 2021-11-16 David M. Paganin , Daniele Pelliccia

Imaging with hard x-rays is an invaluable tool in medicine, biology, materials science, and cultural heritage. Propagation-based x-ray phase-contrast imaging and tomography have been mostly used to resolve micrometer-scale structures inside…

Image and Video Processing · Electrical Eng. & Systems 2025-06-02 Margie P. Olbinado , David M. Paganin , Yin Cheng , Alexander Rack

We use the parabolic wave equation to study the propagation of x-rays in tapered waveguides by numercial simulation and optimization. The goal of the study is to elucidate how beam concentration can be best achieved in x-ray optical…

Materials Science · Physics 2009-11-13 Sebastian Panknin , Alexander K. Hartmann , Tim Salditt

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real…

Medical Physics · Physics 2021-11-16 T. E. Gureyev , D. M. Paganin , B. Arhatari , S. T. Taba , S. Lewis , P. C. Brennan , H. M. Quiney

Quantitative phase imaging has become a topic of considerable interest in the microscopy community. We have recently described one such technique based on the use of a partitioned detection aperture, which can be operated in a single shot…

Optics · Physics 2015-10-20 Roman Barankov , Jean-Charles Baritaux , Jerome Mertz

We present a multi-aperture analyser set-up for performing X-ray phase contrast imaging in planar and three-dimensional modalities. A multi-slice representation of the sample is used to establish a quantitative relation between projection…

Instrumentation and Detectors · Physics 2017-06-21 M. Endrizzi , F. A. Vittoria , L. Rigon , D. Dreossi , A. Olivo

Spectral imaging is a method in medical x-ray imaging to extract information about the object constituents by the material-specific energy dependence of x-ray attenuation. Contrast-enhanced spectral imaging has been thoroughly investigated,…

Medical Physics · Physics 2021-01-26 Erik Fredenberg , Magnus Aslund , Bjorn Cederstrom , Mats Lundqvist , Mats Danielsson

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel…

Optics · Physics 2019-11-19 Mario A. Beltran , David M. Paganin , Daniele Pelliccia

Imaging is an important means by which information is gathered regarding the physical world. Spatial resolution and signal-to-noise ratio are underpinning concepts. There is a paucity of rigorous definitions for these quantities, which are…

Optics · Physics 2019-09-27 David M. Paganin , Alexander Kozlov , Timur E. Gureyev

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser

Phase contrast imaging seeks to reconstruct the complex refractive index of an unknown sample from scattering intensities, measured for example under illumination with coherent X-rays. By incorporating refraction, this method yields…

Numerical Analysis · Mathematics 2018-11-06 Simon Maretzke
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