On the definition, utility, and practical implementation of X-ray omnidirectional differential phase contrast and dark-field imaging.
23 Nov 2021-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 118, Iss: 47
TL;DR: In this paper, the use of a speckle pattern in order to retrieve omnidirectional differential phase and dark-field images was investigated and the claim that a simple modulator can have distinct benefits comparted to X-ray optics was found to be inaccurate.
Abstract: The paper by Wang and Sawhney (1) describes the use of a speckle pattern in order to retrieve omnidirectional differential phase and dark-field images. Although the approach is methodologically correct and the claim that a simple modulator can have distinct benefits comparted to X-ray optics is true, there are a few passages in both the significance statement and the main text that we find to be inaccurate.
[↵][1]1To whom correspondence may be addressed. Email: mkagias{at}caltech.edu.
[1]: #xref-corresp-1-1
Citations
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TL;DR: Wang et al. as mentioned in this paper showed that the amplitude A 1 differential phase and the phase term ϕ A can be derived with fast Fourier transform (FFT) analysis.
Abstract: Kagias and Stampanoni (1) claim that there are a few passages that are inaccurate in our recent publication (2). We dispute this claim. We agree that the directional derivates can be calculated by having access to two orthogonal components; in fact, this is already described and included in our publication (2).
The multiple directional differential phase images (DDPI) can be directly measured with the method proposed (2), and the amplitude A 1 differential phase and the phase term ϕ A can be derived with fast Fourier transform (FFT) analysis. The DDPI at any angle θ can be expressed as follows (equation 4 in ref. 2): α θ = − A 1 cos ( θ + ϕ A ) = − A 1 cos θ cos ϕ A + A 1 sin θ sin ϕ A . [1]
According to equation 5 …
[↵][1]1To whom correspondence may be addressed. Email: hongchang.wang{at}diamond.ac.uk.
[1]: #xref-corresp-1-1
References
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TL;DR: An X-ray diffractive optics method is presented which enables single shot acquisition of SAXS signals in a single shot over large areas, applicable to a wide range of X-Ray sources with varying levels of spatial coherence and monochromaticity.
Abstract: Insights into the micro- and nano-architecture of materials is crucial for understanding and predicting their macroscopic behaviour. In particular, for emerging applications such as meta-materials, the micrometer scale becomes highly relevant. The micro-architecture of such materials can be tailored to exhibit specific mechanical, optical or electromagnetic behaviours. Consequently, quality control at micrometer scale must be guaranteed over extended areas. Mesoscale investigations over millimetre sized areas can be performed by scanning small angle X-ray scattering methods (SAXS). However, due to their long measurement times, real time or operando investigations are hindered. Here we present a method based on X-ray diffractive optics that enables the acquisition of SAXS signals in a single shot (few milliseconds) over extended areas. This method is applicable to a wide range of X-ray sources with varying levels of spatial coherence and monochromaticity, as demonstrated from the experimental results. This enables a scalable solution of spatially resolved SAXS.
34 citations
TL;DR: In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path.
Abstract: Ever since the discovery of X-rays, tremendous efforts have been made to develop new imaging techniques for unlocking the hidden secrets of our world and enriching our understanding of it. X-ray differential phase contrast imaging, which measures the gradient of a sample’s phase shift, can reveal more detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient’s component in two mutually orthogonal directions is measurable. In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path. The retrieved amplitude and main orientation images for differential phase yield more information than the existing imaging methods. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. The proposed method can open up new possibilities for studying a wide range of complicated samples composed of both heavy, strongly scattering atoms and light, weakly scattering atoms.
7 citations
01 Jan 1967
TL;DR: In this paper, a function F(x, y) of two variables x and y is considered, where x is a point of Euclidean space R n, x = (x1,..., x n ), and y a point in some compact topological space y.
Abstract: In this chapter we shall be concerned with a function F(x, y) of two variables x and y. x is supposed to be a point of Euclidean space R n , x = (x1, ..., x n ), and y a point of some compact topological space y. While all the considerations of this chapter are carried out for a general y, the applications made in this book have y a closed bounded set in Euclidean space, and the reader may therefore if he wishes read “closed bounded Euclidean” when he sees “compact topological.”
6 citations