Anna Burvall

Phase retrieval in X-ray phase-contrast imaging suitable for tomography

In-line phase-contrast X-ray imaging provides images where both absorption and refraction contribute. For quantitative analysis of these images, the phase needs to be retrieved numerically. There are many phase-retrieval methods available. Those suitable for phase-contrast tomography, i.e., non-iterative phase-retrieval methods that use only one image at each projection angle, all follow the same pattern though derived in different ways. We outline this pattern and use it to compare the methods to each other, considering only phase-retrieval performance and not the additional effects of tomographic reconstruction. We also outline derivations, approximations and assumptions, and show which methods are similar or identical and how they relate to each other. A simple scheme for choosing reconstruction method is presented, and numerical phase-retrieval performed for all methods.

Axicon-the Most Important Optical Element

Last year, the optics community celebrated the 50th anniversary of the formal naming of the axicon. Long before that, however, axicons generated vivid discussions and disagreements, often of fundamental importance to our understanding of optics.

Simple lens axicon

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.

A 24 keV liquid-metal-jet x-ray source for biomedical applications.

We present a high-brightness 24-keV electron-impact microfocus x-ray source based on continuous operation of a heated liquid-indium/gallium-jet anode. The 30-70 W electron beam is magnetically focused onto the jet, producing a circular 7-13 μm full width half maximum x-ray spot. The measured spectral brightness at the 24.2 keV In K(α) line is 3 × 10(9) photons∕(s × mm(2) × mrad(2) × 0.1% BW) at 30 W electron-beam power. The high photon energy compared to existing liquid-metal-jet sources increases the penetration depth and allows imaging of thicker samples. The applicability of the source in the biomedical field is demonstrated by high-resolution imaging of a mammography phantom and a phase-contrast angiography phantom.

Linearity of the pyramid wavefront sensor.

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.

X-ray phase contrast for CO2 microangiography

We demonstrate a laboratory method for imaging small blood vessels using x-ray propagation-based phase-contrast imaging and carbon dioxide (CO(2)) gas as a contrast agent. The limited radiation dose in combination with CO(2) being clinically acceptable makes the method promising for small-diameter vascular visualization. We investigate the possibilities and limitations of the method for small-animal angiography and compare it with conventional absorption-based x-ray angiography. Photon noise in absorption-contrast imaging prevents visualization of blood vessels narrower than 50 µm at the highest radiation doses compatible with living animals, whereas our simulations and experiments indicate the possibility of visualizing 20 µm vessels at radiation doses as low as 100 mGy. Experimental computed tomography of excised rat kidney shows blood vessels of diameters down to 60 µm with improved image quality compared to absorption-based methods. With our present prototype x-ray source, the acquisition time for a tomographic dataset is approximately 1 h, which is long compared to the 1-20 min common for absorption-contrast micro-CT systems. Further development of the liquid-metal-jet microfocus x-ray sources used here and high-resolution x-ray detectors shows promise to reduce exposure times and make this high-resolution method practical for imaging of living animals.

First application of liquid‐metal‐jet sources for small‐animal imaging: High‐resolution CT and phase‐contrast tumor demarcation

PURPOSE Small-animal studies require images with high spatial resolution and high contrast due to the small scale of the structures. X-ray imaging systems for small animals are often limited by the microfocus source. Here, the authors investigate the applicability of liquid-metal-jet x-ray sources for such high-resolution small-animal imaging, both in tomography based on absorption and in soft-tissue tumor imaging based on in-line phase contrast. METHODS The experimental arrangement consists of a liquid-metal-jet x-ray source, the small-animal object on a rotating stage, and an imaging detector. The source-to-object and object-to-detector distances are adjusted for the preferred contrast mechanism. Two different liquid-metal-jet sources are used, one circulating a Ga∕In∕Sn alloy and the other an In∕Ga alloy for higher penetration through thick tissue. Both sources are operated at 40-50 W electron-beam power with ∼7 μm x-ray spots, providing high spatial resolution in absorption imaging and high spatial coherence for the phase-contrast imaging. RESULTS High-resolution absorption imaging is demonstrated on mice with CT, showing 50 μm bone details in the reconstructed slices. High-resolution phase-contrast soft-tissue imaging shows clear demarcation of mm-sized tumors at much lower dose than is required in absorption. CONCLUSIONS This is the first application of liquid-metal-jet x-ray sources for whole-body small-animal x-ray imaging. In absorption, the method allows high-resolution tomographic skeletal imaging with potential for significantly shorter exposure times due to the power scalability of liquid-metal-jet sources. In phase contrast, the authors use a simple in-line arrangement to show distinct tumor demarcation of few-mm-sized tumors. This is, to their knowledge, the first small-animal tumor visualization with a laboratory phase-contrast system.

Comparison of two x-ray phase-contrast imaging methods with a microfocus source

We present a comparison for high-resolution imaging with a laboratory source between grating-based (GBI) and propagation-based (PBI) x-ray phase-contrast imaging. The comparison is done through simulations and experiments using a liquid-metal-jet x-ray microfocus source. Radiation doses required for detection in projection images are simulated as a function of the diameter of a cylindrical sample. Using monochromatic radiation, simulations show a lower dose requirement for PBI for small object features and a lower dose for GBI for larger object features. Using polychromatic radiation, such as that from a laboratory microfocus source, experiments and simulations show a lower dose requirement for PBI for a large range of feature sizes. Tested on a biological sample, GBI shows higher noise levels than PBI, but its advantage of quantitative refractive index reconstruction for multi-material samples becomes apparent.

Lens axicons in oblique illumination

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

Speckle-based x-ray phase-contrast imaging with a laboratory source and the scanning technique

The speckle-based scanning method for x-ray phase-contrast imaging is implemented with a liquid-metal-jet source. Using the two-dimensional scanning technique, the phase shift introduced by the object is retrieved in both transverse orientations, and the limitations on spatial resolution inherent to the speckle-tracking technique are avoided. This method opens up possibilities of new high-resolution multimodal applications for lab-based phase-contrast x-ray imaging.