Determining particle size distributions from a single projection image

Measuring grain size fractions of bidisperse granular materials using X-ray radiography

The mechanical properties of granular materials such as sand, snow and rice are inherently tied to the size of the constituent particles. When a system is composed of particles of various sizes, it is common for these particles to segregate by size when disturbed. There is therefore a need to measure the particle size distribution within granular media as it evolves over time. However, there are very few experimental techniques available which can measure the particle sizes in situ without disturbing the medium. Here we present a technique to determine the volume fractions of the grain sizes in bidisperse granular materials with the aid of dynamic X-ray radiography. As a result of the penetration of the X-rays into the medium, radiography minimises the effect of walls and boundaries on experimental measurements, which typically dominate optical measurements. The technique proposed here is based on using Fourier transforms of X-ray radiographs to extract local measurements evolving over time that can be related to the particle size distribution. For the case of bidisperse granular media, with two distinct particle sizes, we show that this technique can measure the relative concentration of the two species, which we determine via a heuristic calibration parameter. We validate this technique by comparing discrete element simulations of mixtures of known concentration with experimental measurements derived from X-ray radiography of glass beads. In the future, this technique could be used to measure the grain size distribution in systems of bidisperse dense granular media where the concentration of particles is not known a priori. Additionally, the technique can be used to analyse granular segregation as it evolves dynamically.

Determination of size distributions of non-spherical pores or particles from single x-ray phase contrast images

Although x-ray tomography is commonly used to characterize the three-dimensional structure of materials, sometimes this is impractical due either to limited time for data collection (such as in rapidly-evolving systems) or the need to limit the radiation exposure of the sample. In such situations, it is desirable to extract as much information as possible from a more limited data set. In this paper, we describe how to extract the size distribution of non-spherical pores (or, equivalently, particles) from single x-ray phase contrast imaging (XPCI). Because the pores overlap in projection, interpreting the images and extracting quantitative information about the size distribution is non-trivial. In this paper we extend a previously-developed Fourier-based framework for interpreting the speckle pattern of XPCI images from materials with spherical pores to the more challenging case of non-spherical pores. We develop an analytical expression for the XPCI image from a distribution of randomly-oriented ellipsoidal pores, and show that we can use this expression to extract quantitative information about the size distribution from single images. We discuss three approaches to evaluating this expression, corresponding to different assumptions about the nature of the size distribution, and validate our results with simulated XPCI images and experimental data from Berea sandstone.

X-ray specks: low dose in vivo imaging of lung structure and function

Respiratory health is directly linked to the structural and mechanical properties of the airways of the lungs. For studying respiratory development and pathology, the ability to quantitatively measure airway dimensions and changes in their size during respiration is highly desirable. Real-time imaging of the terminal airways with sufficient contrast and resolution during respiration is currently not possible. Herein we reveal a simple method for measuring lung airway dimensions in small animals during respiration from a single propagation-based phase contrast x-ray image, thereby requiring minimal radiation. This modality renders the lungs visible as a speckled intensity pattern. In the near-field regime, the size of the speckles is directly correlated with that of the dominant length scale of the airways. We demonstrate that Fourier space quantification of the speckle texture can be used to statistically measure regional airway dimensions at the alveolar scale, with measurement precision finer than the spatial resolution of the imaging system. Using this technique we discovered striking differences in developmental maturity in the lungs of rabbit kittens at birth.

Real-time measurement of alveolar size and population using phase contrast x-ray imaging

Herein a propagation-based phase contrast x-ray imaging technique for measuring particle size and number is presented. This is achieved with an algorithm that utilizes the Fourier space signature of the speckle pattern associated with the images of particles. We validate this algorithm using soda-lime glass particles, demonstrating its effectiveness on random and non-randomly packed particles. This technique is then applied to characterise lung alveoli, which are difficult to measure dynamically in vivo with current imaging modalities due to inadequate temporal resolution and/or depth of penetration and field-of-view. We obtain an important result in that our algorithm is able to measure changes in alveolar size on the micron scale during ventilation and shows the presence of alveolar recruitment/de-recruitment in newborn rabbit kittens. This technique will be useful for ventilation management and lung diagnostic procedures.

Measurement of absolute regional lung air volumes from near-field x-ray speckles

Propagation-based phase contrast x-ray (PBX) imaging yields high contrast images of the lung where airways that overlap in projection coherently scatter the x-rays, giving rise to a speckled intensity due to interference effects. Our previous works have shown that total and regional changes in lung air volumes can be accurately measured from two-dimensional (2D) absorption or phase contrast images when the subject is immersed in a water-filled container. In this paper we demonstrate how the phase contrast speckle patterns can be used to directly measure absolute regional lung air volumes from 2D PBX images without the need for a water-filled container. We justify this technique analytically and via simulation using the transport-of-intensity equation and calibrate the technique using our existing methods for measuring lung air volume. Finally, we show the full capabilities of this technique for measuring regional differences in lung aeration.

Decoding the structure of granular and porous materials from speckled phase contrast X-ray images

Imaging techniques for studying the structure of opaque, granular and porous materials are limited by temporal resolution and radiation dose. We present a technique for characterising the structure of such materials by decoding three dimensional structural information from single, propagation based phase contrast X-ray images. We demonstrate the technique by measuring the distribution of diameters of glass microspheres in packed samples. We also present synthetic data, which shows that our inverse method is stable and that accuracy is improved by phase contrast X-ray imaging. Compared to computed tomography, our technique has superior temporal resolution and lower radiation dose.