The X-ray microtomography system which is operated at the Hamburger Synchrotronstrahlungslabor HASYLAB of the Deutsches Elektronen-Synchrotron DESY in Hamburg, Germany, is presented. At the DORIS storage ring synchrotron radiation at the wiggler beamlines BW2, W2, and BW5 was used to run the microtomography apparatus as a user experiment. The development of tomography scanning techniques to investigate samples which are larger than the field of view of the X-ray detector is demonstrated for dental implants using the photon energy of 90 keV at the high energy beamline BW5. In cooperation with DESY the GKSS Research Center is setting up the high energy beamline HARWI-2 at the DORIS storage ring of DESY. This beamline will allow for tomography experiments using monochromatic X-rays from 20 to 200 keV with a beam size of 70•10 mm². Furthermore the GKSS is operating a neutron radiography facility GENRA at the research reactor Geesthacht FRG, Geesthacht, Germany. It is intended to extend this facility by a tomography station. The combination of synchrotron radiation based microtomography with neutron tomography will allow for the development of new techniques to give new insight in the 3-dim. behavior of samples especially in materials science.

Sea urchins employ as wide a range of composite reinforcement strategies as are seen in engineering composites. Besides tailoring reinforcement morphology and alignment to the functional demands of position, solid solution strengthening (high Mg calcite), inclusion toughening (macromolecules), functional gradients in mineral reinforcement morphology, composition and dimensions and mineral interface tailoring are other tactics important to achieving high toughness and high strength in sea urchin teeth. Teeth from different echinoid families illustrate combinations of reinforcement parameters and toughening mechanisms providing good functionality, a virtual probe of the available design space. This paper focuses on a multi-mode x-ray investigation of sea urchin teeth studied on scales approaching 1 µm in millimeter-sized samples, in particular mapping 3-D microarchitecture with synchrotron and laboratory microCT and mapping Ca_1-xMg_xCO₃ crystal composition x and microstrain and crystallite size via microbeam diffraction.

The detailed analysis of the fuel sprays has been well recognized as an important step for optimizing the operation of internal-combustion engines to improve efficiency and reduce emissions. However, the structure and dynamics of highly transient fuel sprays have never been visualized or reconstructed in three dimensions (3D) previously due to numerous technical difficulties. By using an ultrafast x-ray detector and intense monochromatic x-ray beams from synchrotron radiation, the fine structures and dynamics of 1-ms direct-injection gasoline fuel sprays were elucidated for the first time by a newly developed, ultrafast computed microtomography technique. Due to the time-resolved nature and the intensive data analysis, the Fourier transform algorithm was used to achieve an efficient reconstruction process. The temporal and spatial resolutions of the current measurement are 5.1 μs and 150 μm, respectively. Many features associated with the transient liquid flows are readily observable in the reconstructed spray. Furthermore, an accurate 3D fuel density distribution was obtained as the result of the computed tomography in a time-resolved manner. These results not only reveal the characteristics of automotive fuel sprays with unprecedented details, but will also facilitate realistic computational fluid dynamic simulations in highly transient, multiphase systems.

In various scientific fields -- such as materials sciences, biology or even astrophysics -- the relation between morphology and the chemical composition is a key for the understanding of structures and their function. Hard x-ray tomography is a suitable tool for structural analyzes on the micrometer scale and can give additional chemical information by combining this imaging technique with spectroscopic methods. In chemistry, X-ray absorption near-edge spectroscopy (XANES) is a well-known and established technique. By scanning the X-ray energy in the vicinity (50-100 eV) of the absorption edge of an element, information can be obtained about the oxidation state of the probed atoms. We used a fast read-out and low noise detector for XANES imaging and were able to distinguish different oxidation states in three dimension performing tomographic scans at different characteristic energies of the probed atom.

To show the feasibility of a combined micro-CT and micro-SPECT scanner based on use of polycapillary optics we inserted an optic between the radio-labeled specimen and our micro-CT scanner's imaging system. The micro-CT x-ray focal spot was placed at the focal point of the optic so that x-ray micro-CT of the specimen could also be performed without having to move the specimen. Using this set-up we scanned a 2 cm diameter Plexiglas cylinder with three (177 μCi) prostate brachytherapy seeds embedded in it. Each seed was 0.5 mm diameter, 4 mm long and filled with 0.4 mm diameter ceramic beads coated with ¹²⁵Iodine. The SPECT images clearly resolve the layer of ¹²⁵Iodine on the beads. That the SPECT image is spatially correct was cofirmed by the concurrent CT image. We also used a parallel polycapillary optic to scan a 1.5 cm Plexiglas cylinder with holes (2, 1, and 0.5 mm diameter, parallel to the cylinder axis) filled with a solution containing 11.56μCi/mm³ of ¹²⁵Iodine. These data indicate a spatial resolution of 5 line pairs per mm at 10% modulation. Based on these results we propose a design that is more efficient at acquiring the scintigraphic image data.

We have been acquiring respiratory-gated micro-CT images of live mice and rats for over a year with our General Electric (formerly Enhanced Vision Systems) hybrid scanner. This technique is especially well suited for the lung due to the inherent high tissue contrast. Our current studies focus on the assessment of lung tumors and their response to experimental agents, and the assessment of lung damage due to chemotherapy agents. We have recently installed a custom-built dual flat-panel cone-beam CT scanner with the ability to scan laboratory animals that vary in size from mice to large dogs. A breath-hold technique is used in place of respiratory gating on this scanner. The objective of this pilot study was to converge on scan acquisition parameters and optimize the visualization of lung damage in a mouse model of fibrosis. Example images from both the micro-CT scanner and the flat-panel CT scanner will be presented, as well as preliminary data describing spatial resolution, low contrast resolution, and radiation dose parameters.

Micro-computed tomography (micro-CT) provides a means for obtaining a detailed three-dimensional description of the structure of micro-vasculature in whole organs. This whole organ description allows for the examination of flow models and self similarity relationships that would otherwise be inaccessible using conventional sampling based descriptions of the microvasculature. The number of vessels that compose the micro-vasculature in a whole organ is so large, however, that such analysis is only feasible using automated image processing techniques. In this paper, the segmentation and data representation challenges of such analysis are examined with reference to mouse kidney vasculature. A semi-automated analysis method is described and is applied to a set of mouse kidneys to assess the feasibility and reproducibility of population studies. This analysis includes a new method to separate parallel arterial and venous vessels that are distinct but touching at the resolution of the micro-CT scan. Also described is a new formalism for representing the derived vessel structure that lends itself to regularization. Distributions of arterial and venous structural parameter are presented for six kidneys (three of each) taken from age matched animals of the CD1 strain. These results show a high degree of similarity among specimens and suggest that population studies to examine the influence of subtle disease or genetic factors are feasible.

A wide range of disorders are associated with alterations of the central and peripheral vascular system. Modified vascular corrosion casting using a newly developed polymer, allows for the first time hierarchical assessment of 3D vessel data in animals down to the level of capillaries. Imaging of large volumes of vasculature at intermediate resolution (16 μm) was performed using a desktop micro-computed tomography system. Subsequently regions of interest were identified for additional high resolution imaging (1.4 μm) at the X-ray Tomographic Microscopy (XTM) station of the Swiss Light Source (SLS). A framework for systematic hierarchical imaging and quantification was developed. Issues addressed included enhanced XTM data acquisition, introduction of local tomography, sample navigation, advanced post processing, and data combination. In addition to visual assessment of qualitative changes, morphometrical and architectural indices were determined using direct 3D morphometry software developed in house. Vessel specific parameters included thickness, surface, connectivity, and vessel length. Reconstructions of cerebral vasculature in mutant mice modeling Alzheimer's disease revealed significant changes in vessel architecture and morphology. In the future, a combination of these techniques may support drug discovery. Additionally, future ultra-high-resolution in vivo systems may even allow non-invasive tracking of temporal alterations in vascular morphology.

The fast scanning speed of current slip-ring CT scanners has enabled the development of perfusion imaging techniques with intravenous injection of contrast medium. In a typical CT perfusion study, contrast medium is injected and rapid scanning at a frequency of 1-2 Hz is used to monitor the first circulation of the injected contrast medium through a 1-2 cm thick slab of tissue. From the acquired time-series of CT images, arteries can be identified within the tissue slab to derive the arterial contrast concentration curve, C_a(t) while each individual voxel produces a tissue residue curve, Q(t) for the corresponding tissue region. Deconvolution between the measured C_a(t) and Q(t) leads to the determination of cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) in brain studies. In this presentation, an important application of CT perfusion in acute stroke studies -- the identification of the ischemic penumbra via the CBF/CBV mismatch and factors affecting the quantitative accuracy of deconvolution, including partial volume averaging, arterial delay and dispersion are discussed.

The feasibility of making regional perfusion measurements using a tomosynthetic digital subtraction angiography (TDSA) acquisition has been demonstrated. The study of tomosynthetic perfusion measurements was motivated by the clinical desire for perfusion measurements in an interventional angiography suite. These pilot studies were performed using the scanning-beam digital x-ray (SBDX) system which is an inverse-geometry imaging device which utilizes an electromagnetically-scanned x-ray source, and a small CdTe direct conversion photon counting detector. The scanning electron source was used to acquire planar-tomographic images of a 12.5 x 12.5 cm field of view at a frame rate of 15 frames/sec during dynamic contrast injection. A beagle animal model was used to evaluate the tomosynthetic perfusion measurements. A manual bolus injection of iodinated contrast solution was used in order to resolve the parameters of the contrast pass curve. The acquired planar tomosynthetic dataset was reconstructed with a simple back-projection algorithm. Digital subtraction techniques were used to visualize the change in contrast agent intensity in each reconstructed plane. Given the TDSA images, region of interest based analysis was used in the selection of the image pixels corresponding to the artery and tissue bed. The mean transit time (MTT), regional cerebral blood volume (rCBV) and regional cerebral blood flow (rCBF) were extracted from the tomosynthetic data for selected regions in each of the desired reconstructed planes. For the purpose of this study, the arterial contrast enhancement curve was fit with a combination of gamma variate terms, and the MTT was calculated using a deconvolution based on the singular value decomposition (SVD). The results of the contrast pass curves derived with TDSA were consistent with the results from perfusion measurements as implemented with CT acquisition.

The entrapment of nonwetting phase fluids in unconsolidated porous media systems is strongly dependent on the pore-scale geometry and topology. Synchrotron X-ray tomography allows us to nondestructively obtain high-resolution (on the order of 1-10 micron), three-dimensional images of multiphase porous media systems. Over the past year, a number of multiphase porous media systems have been imaged using the synchrotron X-ray tomography station at the GeoSoilEnviroCARS beamline at the Advanced Photon Source. For each of these systems, we are able to: (1) obtain the physically-representative network structure of the void space including the pore body and throat distribution, coordination number, and aspect ratio; (2) characterize the individual nonwetting phase blobs/ganglia (e.g., volume, sphericity, orientation, surface area); and (3) correlate the porous media and fluid properties. The images, data, and network structure obtained from these experiments provide us with a better understanding of the processes and phenomena associated with the entrapment of nonwetting phase fluids. Results from these experiments will also be extremely useful for researchers interested in interphase mass transfer and those utilizing network models to study the flow of multiphase fluids in porous media systems.

In current biological and biomedical research, quantitative endpoints have become an important factor of success. Classically, such endpoints were investigated with 2D imaging, which is usually destructive and the 3D character of tissue gets lost. 3D imaging has gained in importance as a tool for both, qualitative and quantitative assessment of biological systems. In this context synchrotron radiation based tomography has become a very effective tool for opaque 3D tissue systems. Cell cultures and adherent scaffolds are visualized in 3D in a hydrated environment, even uncovering the shape of individual cells. Advanced morphometry allows to characterize the differences between the cell cultures of two distinct phenotypes. Moreover, a new device is presented enabling the 3D investigation of trabecular bone under mechanical load in a time-lapsed fashion. Using the highly brilliant X-rays from a synchrotron radiation source, bone microcracks and an indication for un-cracked ligament bridging are uncovered. 3D microcrack analysis proves that the classification of microcracks from 2D images is ambiguous. Fatigued bone was found to fail in burst-like fashion, whereas non-fatigued bone exhibited a distinct failure band. Additionally, a higher increase in microcrack volume was detected in fatigued in comparison to non-fatigued bone. The developed technologies prove to be very effective tools for advanced 3D imaging of both hard and soft tissue.

At the ESRF Micro-Fluorescence, Imaging and Diffraction beamline ID22, X-Ray micro-tomography is a routine technique proposed to users for 3D microanalysis of various samples. The purpose of this work is to extend 3D micro-tomography in order to obtain in-situ 3D information about samples at increasing pure axial loads. We developed a new device that allows one to combine mechanical testing and micro-tomography. The device is optimised for low Gpa Young moduli like plastics or bone but can easily be adapted to higher values. In this paper we present first results obtained with animal and human bone samples to gain insight into the bone microcrack problem.

Material properties of bone are crucial for studies regarding the mechanical behavior of bone. The mechanical behavior depends on the macro- and micro-architecture as well as the organic and mineral content of bone. The marco-architecture of bone is normally analyzed by plane radiographs. The micro-architecture of the trabecular bone can be imaged by high resolution CT imaging techniques using conventional x-ray tubes. However, fine structures in bone architecture cannot be sufficiently analyzed by this technique due to its limited resolution. High resolution CT imaging technique using synchrotron radiation generates images with a high spatial resolution of bone structures on a micron scale. Additionally, this imaging technique provides superior determination of local differences in the bone mineral density. Two microtomography techniques, first: based on conventional x-ray tubes and second: based on synchrotron radiation were compared in this study to detect fine bone structures such as inner trabecular channels. In two red howler monkeys (Alouatta seniculus) femora channel structures were found inside the trabecular bone by both techniques. Only synchrotron-based microtomography was able to detect layers of lower mineral density in the channel walls. The found structures in trabecular bone are normally expected in the Haversian channel walls of the cortical bone. However, the origin of the trabecular channel structure is not fully understood. We found, that synchrotron-based microtomography is a very valuable technique in the research of fine bone structures. Further research should focus on the impact of these findings on the mechanical properties of trabecular bone.

Osteons are longitudinally arranged cylindrical structures, which form the structural units of cortical bone. Cortical bone remodeling is closely related to the osteonal organization as newly formed osteons continuously replace older ones. The degree of mineralization in these new osteons is initially lower than in the existing bone as it takes time before osteons mature. Synchrotron radiation-based computed microtomography (μCT) and scanning acoustic microscopy (SAM) are two techniques, which have both sufficient spatial resolution and sensitivity to detect local variations in bone density. The aim of this study was therefore to compare both techniques for the analysis of osteonal mineralization. Eight human cortical bone samples were scanned with both techniques and the corresponding images were matched. Synchrotron-based μCT is not affected by beam hardening and the gray values in the reconstructed images are directly related to the local mineral density. For cortical bone this means that immature osteons appear darker than their surrounding. In SAM-images the gray values are a measure of the acoustic impedance, which is a function of the local stiffness and the density. Comparison of the μCT and the SAM images of the cortical samples shows a good correspondence in the gray values of the individual osteons.

The main use of micro-CT is to analyze bone structure, and values of the linear attenuation coefficients μ at every voxel position in the scanned volume are only used for the analysis of bone structure by establishing a threshold that separates bone from non-bone material. To additionally quantify the degree of mineralization of bone (DMB) from μ in multi-component samples, we corrected for beam hardening and its associated errors in DMB quantification caused by the polychromatic spectra of X-ray tubes used in bench-top micro-CT devices. The correction was implemented by simulating the difference of mono-chromatic and poly-chromatic X-ray sources and adding these differences to the original image in an iterative fashion. When applied to simple cylinders containing a single material, improvement on the constancy of the reconstructed voxel values could be observed to over 90% accuracy.

Fluorescence microtomography is a hard x-ray scanning microscopy technique that has been developed at synchrotron radiation sources in recent years. It allows one to reconstruct non-destructively the element distribution on a virtual section inside a sample. The spatial resolution of this microbeam technique is limited by the lateral size of the microbeam. Since recently, nanofocusing refractive x-ray lenses (NFLs) are under development that were shown to produce hard x-ray microbeams with lateral resolution in the range of 100nm. Future improvements of these optics might reduce the microbeam size down to below 20nm. Using nanofocusing lenses, fluorescence microtomography with sub-micrometer resolution was performed. As an example, the element distribution inside a small cosmic dust particle is given. Tomographic reconstruction was done using a refined model including absorption effects inside the sample.

State-of-the-art synchrotron-based microtomography devices have nowadays to fulfill very stringent requirements in term of spatial resolution, detection efficiency and data throughput. The most used detection system is based on collecting the light produced by a thin scintillation screen with microscope optics and conveying it to a high-performance charge coupled device (CCD) camera. With the chip-size of currently available CCDs installed at high brilliance sources like the Swiss Light Source (SLS) raw data are produced at rate of gigabyte/minute. It is crucial therefore to provide the necessary infrastructure to be able to post-process the data in real time, and provide to the user 3D information immediately after the end of the scan. The visible-light-based detection system is intrinsically limited by scintillation properties, optical coupling and CCD granularity to a practical limit of about 1 micron spatial resolution and efficiency of a few percent. A novel detector, called Bragg magnifier, is one of the techniques recently proposed to efficiently trespass the micrometer barrier. It exploits two-dimensional asymmetric Bragg diffraction from flat crystals to produce X-ray images with magnification factors up to 150x150 and pixel sizes less than 100x100 nm². The infrastructure devoted to microtomography at the SLS is described, as well as some very promising experiments. The layout of a novel, tomography dedicated beamline is also presented.

We have developed a high definition X-ray microtomography scanner using time-delay integration CCD readout mode, whereby the camera is moved through the X-ray “shadow” during simultaneous readout. This method eliminates ring artefacts in the reconstructed image and allows the recorded image to be larger than the CCD itself. To maximise dynamic range, the reflective coated scintillator was lens coupled (two back-to-back 50mm f1.2 camera lenses). Equivalent X-ray photons per pixel were derived from noise measurements in specimen-absent projections. This was typically 600,000 for a 10 second exposure (90kV, 200μA, 25 cm source to camera). To quantify relay lens efficiency, this was re-measured at aperture settings from f1.2 to f11. The results closely fitted a model based on two noise sources (one from finite X-ray photons and one from finite light photons per X-ray photon), yielding an efficiency of 60% at f1.2. Although higher efficiency is desirable, this is a good compromise that avoids CCD saturation. This suggests that when using the more efficient direct fibre-optic coupling, a reflective scintillator coating may be undesirable, as the marginal increase in efficiency would not justify any loss of resolution or dynamic range. Correction for beam hardening is currently carried out using a 7 step Al wedge to measure experimental attenuation vs theoretical attenuation for monochromatic radiation. We intend to modify this method to improve accuracy in a more diverse range of materials. Dishing artefacts were decreased further by using a moving X-ray aperture to reduce scattered radiation.

Estimate of sorption of liquid materials inside porous stones and wood is an important parameter in industrial material testing and cultural heritage conservation. In the latter case, a suitable polymer can be used for both consolidation and conservation, it being applied either in the final form or as its parent monomer, which is subsequently allowed to polymerize in situ by the classical method or by frontal polymerization. In this paper a recently developed methodology based of X-ray tomography is presented. This technique has been applied to different types of wood and stone. The gradient of penetration has also been studied. Some of the results obtained are reported and discussed.

A compact laboratory x-ray "nano-CT" scanner has been created for 3D non-invasive imaging with 150-200 nanometers 3D spatial resolution, using advanced x-ray technologies and specific physical phenomena for signal detection. This spatial resolution in volume terms is 3 orders better than can be achieved in synchrotron tomography, 5 orders better then in existing laboratory micro-CT instruments and 10-12 orders better in comparison to clinical CT. The instrument employs an x-ray source with a 300-400nm x-ray spot size and uses small-angle scattering to attain a detail detectability of 150-200nm. An object manipulator allows positioning and rotation with an accuracy of 150nm. The x-ray detector is based on an intensified CCD with single-photon sensitivity. A typical acquisition cycle for 3D reconstruction of the full object volume takes from 10 to 60 minutes, with the collection of several hundred angular views. Subsequent volumetric reconstruction produces results as a set of cross sections with isotropic voxel size down to 140 x 140 x 140nm, or as a 3D-model, which can be virtually manipulated and measured. This unique spatial resolution in non-invasive investigations gives previously unattainable 3D images in several application areas, such as composite materials, paper and wood microstructure, biomedical applications and others.

The most important task for bioluminescence imaging is to identify the emission source from the captured bioluminescent signal on the surface of a small tested animal. Quantitative information on the source location, geometry and intensity serves for in-vivo monitoring of infectious diseases, tumor growth, metastases in the small animal. In this paper, we present a point-spread function-based method for reconstructing the internal bioluminescent source from the surface light output flux signal. The method is evaluated for sensing the internal emission sources in nylon phantoms and within a live mouse. The surface bioluminescent signal is taken with a highly sensitive CCD camera. The results show the feasibility and efficiency of the proposed point-spread function-based method.

This work illustrates the development of X-ray fluorescence tomography and polycapillary based confocal imaging towards a three-dimensional (3D), quantitative analytical method with lateral resolution levels down to the 2-20 μm scale. Detailed analytical characterization is given for polycapillary based confocal XRF imaging, which is a new variant of the 3D micro-XRF technique. Applications for 2D/3D micro-XRF are illustrated for the analysis of biological (zooplankton) and geological samples (microscopic inclusions in natural diamonds and fluid inclusions in quartz). Based on confocal imaging, fully three-dimensional distributions of trace elements could be obtained, representing a significant generalization of the regular 2D scanning technique for micro-XRF spectroscopy. The experimental work described in this paper has been carried out at the ESRF ID18F microfluorescence end-station and at HASYLAB Beam Line L.

Since 1998 we have developed X-Ray fluorescence tomography for microanalysis. All aspects were tackled starting with the reconstruction performed by FBP or ART methods. Self-absorption corrections were added and combined with Compton, transmission and fluorescence tomographies to obtain fully quantitative results. Automatic "smart scans" minimized overhead time scanning/aligning non-cylindrical objects. The scans were performed step-by-step or continuously with no overhead time. Focusing went from 5 to 1 micron range, using FZP or CRL lenses, and finally KB bent mirrors which yield sub-micron high intensity beams. Recently, we have performed the first quantitative 3D fluo-tomography by helical scanning. We are now studying energy dependent fluo-tomography for chemically-sensitive imaging of the internal structure of samples. This chronology yielded the present level of sophistication for both experiments and data treatment and finally a method ready for wide dissemination among scientists.

X-ray fluorescence computed tomography (XFCT) allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. This is challenging because the attenuation map is, in general, known only at the stimulating beam energy and not at the various fluorescence energies of interest. We make use of empirically fit analytic expressions for x-ray attenuation coefficients to express the unknown attenuation maps as linear combinations of known quantities and the unknown elemental concentrations of interest. We develop an alternating-update iterative reconstruction algorithm based on maximizing a penalized Poisson likelihood objective function. Studies with numerical phantoms indicate that the approach is able to produce qualitatively and quantitatively accurate reconstructed images of numerical phantoms even in the face of severe attenuation.

Plate-like samples are particularly challenging to reconstruct with computed tomography (CT) while preserving sensitivity to very small features within the sample. Specifically, quantifying fatigue crack openings of ≤ 2.5 μm in compact tension samples with maximum cross-sections of 25 mm is impractical with conventional microCT. If one is constrained to use plate-like samples, then an alternative approach to conventional microCT is needed. Imaging with X-ray phase contrast offers increased sensitivity compared to X-ray absorption-based techniques. Synchrotron X-ray phase contrast microradiographs (propagation method) coupled with multiple-angle stereometry are used to map the 3D position of fatigue crack surfaces within aluminum samples. The method is briefly outlined, and crack positions obtained with phase stereometry are found to agree with those determined from absorption microCT. Preliminary calculations of phase contrast derived from a sample fractured in fatigue are compared with phase micrographs of the same sample: at present agreement is only approximate.

Recently an algebraic reconstruction method, 2D-ART, has been presented for generation of three-dimensional maps of the grain boundaries within polycrystals. The grains are mapped layer-by-layer in a non-destructive way by diffraction with hard x-rays. Here we optimize the algorithm by means of simulations and discuss ways to automate the analysis. The use of generalized Kaiser-Bessel functions as basis functions is shown to be superior to a conventional discretization in terms of square pixels. The algorithm is reformulated as a block-iterative method in order to incorporate the instrumental point-spread-function and, at the same time, to avoid the need to store the set of equations. The first reconstruction of a full layer from experimental data is demonstrated.

During grain growth, larger grains tend to grow at the expense of their smaller neighbors, resulting in a steady increase in the average crystallite size. Because the growth rate of any given grain is affected by that of its neighbors, the manner in which growth occurs is determined to a large extent by correlations in the sizes of neighboring grains. Quantitative information concerning these correlations can be extracted only from a truly three-dimensional characterization of the sample microstructure. We have used x-ray microtomography to measure the nearest-neighbor size correlations in a polycrystalline specimen of Al alloyed with 2 at.% Sn. The tin atoms segregate to the grain boundaries, where they impart a strong contrast in x-ray attenuation that can be reconstructed tomographically. From such reconstructions, we measured the size, topology and local connectivity of nearly 5000 contiguous Al grains and subsequently computed the size correlations in this material. The resulting information was incorporated into a non-mean-field theory for grain growth, the accuracy of which could be evaluated by comparing its predictions to the observed microstructure of the Al-Sn samples.

The conversion of 3D data sets of x-ray absorption images into 3D composition maps requires accurate mass absorption values, high-quality images, and a robust fitting algorithm. We evaluate the status of convenient x-ray absorption databases, the impact of various CCD parameters and imaging strategies (minimal vs over-determined), and styles of least-squares fits of the images (optionally including volume constraints). Concerns raised include the impact of NEXAFS features and limited CCD dynamic range. In the absence of these effects, the reduction of images to composition is fast and robust, as tested with simulations based on element-labeled Shepp-Logan phantoms. These studies allow one to evaluate a recent experiment in which synchrotron X-ray tomography is used to image a multicomponent sample. Those samples consisted of a mixture containing high-impact polystyrene (HIPS) and a two-component flame retardant, a brominated phthalimide dimer and a synergist, antimony oxide (Sb₂O₃). Complete tomography data sets were acquired at 3.34 micron spatial resolution using seven X-ray energies in the range of 12 to 40 keV, closely spanning Br and Sb 1s electron binding energies at 13.474 and 30.491 keV, respectively.

In this article we consider cone-beam CT projections along a nonstandard 3-D spiral with variable radius and variable pitch. Specifically, we generalize an exact image reconstruction formula by Zou and Pan (2004a) and (2004b) to the case of nonstandard spirals, by giving a new, analytic proof of the reconstruction formula. Our proof is independent of the shape of the spiral, as long as the object is contained in a region inside the spiral, where there is a PI line passing through any interior point. Our generalized reconstruction formula can also be applied to much more general situations, including cone-beam scanning along standard (Pack, et al. 2004) and nonstandard saddle curves, and any smooth curve from one endpoint of a line segment to the other endpoint, for image reconstruction of that line segment. In other words, our results can be regarded as a generalization of Orlov's classical papers (1975) to cone-beam scanning.

The general goal of this paper is to extend the parallel-beam projection-slice theorem to the divergent fan-beam and cone-beam projections without rebinning the divergent fan-beam and cone-beam projections into parallel-beam projections directly. The basic idea is to establish a novel link between the local Fourier transform of the projection data and the Fourier transform of the image object. Analogous to the two- and three-dimensional parallel-beam cases, the measured projection data are backprojected along the projection direction and then a local Fourier transform is taken for the backprojected data array. However, due to the loss of the shift-invariance of the image object in a single view of the divergent-beam projections, the measured projection data is weighted by a distance dependent weight w(r) before the local Fourier transform is performed. The variable r in the weighting function w(r) is the distance from the backprojected point to the X-ray source position. It is shown that a special choice of the weighting function, w(r) = 1/r, will facilitate the calculations and a simple relation can be established between the Fourier transform of the image function and the local Fourier transform of the l/r -- weighted backprojection data array. Unlike the parallel-beam cases, a one-to-one correspondence does not exist for a local Fourier transform of the backprojected data array and a single line in the 2D case or a single slice in the 3D case of the Fourier transform of the image function. However, the Fourier space of the image object can be built up after the local Fourier transforms of the l/r -- weighted backprojection data arrays are shifted and added up in a laboratory frame. Thus the established relations Eq. (19) and Eq. (21) between the Fourier space of the image object and the Fourier transforms of the backprojected data arrays can be viewed as a generalized projection-slice theorem for divergent fan-beam and cone-beam projections. Once the Fourier space of the image function is built up, an inverse Fourier transform could be performed to reconstruct tomographic images from the divergent beam projections.

Propagation-based phase-contrast tomography is a non-interferometric imaging technique that can reconstruct the complex refractive index distribution of an object. To accomplish such a reconstruction, however, the measured phase-contrast projections must be untruncated. We have demonstrated recently that the mathematical theory of local computed tomography (CT), which was originally developed for absorption CT, can be applied naturally for understanding the problem of reconstructing the location of image boundaries from truncated phase-contrast projections. In this work, we reveal that, for two-dimensional objects, the magnitude of refractive index discontinuities can be reconstructed from truncated phase-contrast projections acquired in the near-Fresnel zone. We show that these magnitudes can be reliably reconstructed using algorithms that were developed originally for local absorption CT.

In this article, we unify several recently developed analytic algorithms for spiral cone-beam computed tomography (CT), including both the filtered-backprojection algorithm and the backprojected-filtration algorithms in the cases of standard spiral, nonstandard spiral, and more general scanning loci. Using Tuy's inversion scheme, we give concise proofs of these reconstruction formulas for cone-beam CT. While a similar proof of the Katsevich algorithm was previously reported, our proof of the Zou-Pan algorithm is new. More importantly, our formulation is generally valid for nonstandard spiral loci and other curves, in agreement with another paper from our group. Furthermore, two sets of simulation results are presented, showing both filtered-backprojection reconstruction using asymmetric filtering lines and backprojected-filtration reconstruction using a saddle curve.

In 1997 we presented some correction techniques for image intensifier images. In the mean time flat panel detectors are often used instead of. The visible contrast of the 16bit flat panel is much higher then with the same digitisation from intensifier images. This misleads users of CT-systems with flat panel detectors to expect far better results. Nevertheless all of the previously described corrections have to be done here too, if an artefact free image is the aim. This gets most important, if an automated evaluation shall be used to extract features from CT images. The main advantage of the new proposed correction technique is that the detector intrinsic scattered radiation (stray light) is corrected with a fast two dimensional filter. Also the right interaction with other corrections like beam hardening and object-scattered radiation is of importance, examples will be shown. The corrected 2D detector images enhances the quality of cone beam CT results in respect to their geometrical distinctness so that geometrical measurements and reverse engineering results get comparable with 2D CT measurements. Results are shown on the µ-CT scanner for bigger objects or for objects with higher X-ray absorption which was set up at BAM. The system is equipped with a bipolar 320kV micro focus tube and a flat panel detector of amorphous Si with 400mm side length, room and system temperatures are regulated.

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed by our group. While the forward imaging model is described by the diffusion approximation, BLT is the inverse problem to recover an internal bioluminescent source distribution subject to Cauchy data for the diffusion equation. This inverse source problem is ill-posed and does not yield the unique solution in the general case. The uniqueness problem under practical constraints was recently studied by our group. It was found that all the inverse source solutions can be expressed as the unique minimal energy source solution plus a nonradiating source. We demonstrate that the minimal energy source solution is not physically favorable for bioluminescence tomography, although the minimal energy constraint is utilized in other applications. To find a physically meaningful unique solution, adequate prior knowledge must be utilized. Here we propose two iterative approaches in this work. The first one is a variant of the well-known EM algorithm. The second one is based on the Landweber scheme. Either of the methods is suitable for incorporating knowledge-based constraints. We discuss several issues related to the implementation of these methods, including the initial guess and stopping criteria. Also, we report our numerical simulation results to demonstrate the feasibility of bioluminescence tomography.

X-ray phase tomography with X-ray Talbot interferometry (XTI) is reported. XTI employs two transmission gratings and generates a contrast corresponding to the differential phase shift caused by a sample. Quantitative phase measurement and tomographic image reconstruction with XTI are demonstrated for biological samples. Finally, the possibility of medical applications of XTI is discussed, based on the advantage of XTI that divergent and polychromatic X-rays are available.

Diffraction tomography (DT) is a well-known method for reconstructing the complex-valued refractive index distribution of weakly scattering objects. A reconstruction theory of intensity DT (I-DT) has been proposed [Gbur and Wolf, JOSA A, 2002] that can accomplish such a reconstruction from knowledge of only the wavefield intensities on two different transverse planes at each tomographic view angle. In this work, we elucidate the relationship between I-DT and phase-contrast tomography and demonstrate that I-DT reconstruction theory contains some of the existing reconstruction algorithms for phase-contrast tomography as special cases.

In conventional computed tomography (CT) a single volumetric image representing the linear attenuation coefficient of an object is produced. For weakly absorbing tissues, the attenuation of the X-ray beam may not be the best description of disease-related information. In this work we present a new volumetric imaging method, called multiple-image computed tomography (MICT), that can concurrently produce several images from a set of measurements made with a single X-ray beam. MICT produces three volumetric images that represent the attenuation, refraction, ultra-small-angle scattering properties of an object. The MICT method is implemented to reconstruct images of a physical phantom and a biological object from measurement data produced by a synchroton light source. An iterative reconstruction method is employed for reconstruction of MICT images from experimental data sets that contains enhanced Poisson noise levels that are representative of future benchtop implementations of MICT. We also demonstrated that images produced by the DEI-CT method (the predecessor of MICT) can contain significant artifacts due to ultra-small-angle scattering effects while the corresponding MICT images do not.

New synchrotron x-ray CT system with phase-contrast and fluorescent techniques are being developed for biomedical researches with the high-contrast and high-spatial resolution. We have applied these techniques for in-vivo and ex-vivo imaging. The phase-contrast x-ray CT (PCCT) was a highly sensitive imaging technique to depict the morphological information of the soft tissue in biological object, whereas fluorescent x-ray CT (FXCT) could depict the functional information concerning to specific heavy atomic number elements at very low content. Thus, the success of in-vivo imaging by PCCT and FXCT allows starting new approach to bio-imaging researches.

Two shearing X-ray interferometers and reconstruction of refractive index distribution from their data are described. The first interferometer is made of a silicon single crystal consisting of two pairs of blades. It can be used with an incoherent x-ray source such as a usual X-ray tube. Simple experiments are made with the interferometer. An algorithm for reconstructing refractive index distribution from the shearing data is described and refractive index distribution on a section of an acrylic cylinder is reconstructed experimentally with the algorithm. Features of the interferometer are discussed. On the basis of the discussion an grooved grating shearing interferometer that can be used with an ordinary X-ray tube is proposed and its performance is estimated.

C-arm CT first emerged as a useful high-contrast imaging modality in the late 1990s, using an XRII as the large area x-ray detector. To date, the C-arm approach to intra-procedural 3D imaging has primarily been used for high-contrast imaging tasks. The emerging goal for these systems is to extend the imaging range into the area of soft-tissue, and it is thought that digital flat-panel detectors may help. Flat panels replace the analog image intensifier, the camera optics, the pickup tube and the analog-to-digital converter with an all-digital detector. Flat panel detectors have a linear response, do not require distortion correction, do not suffer from veiling glare or blooming, and have higher dynamic range that current XRIIs. On the other hand, XRIIs have greater flexibility in FOV, and could support higher frame rates at high resolution, thereby reducing the effects of view aliasing. We have experience with a typical XRII-based C-arm imaging system and a new high-end C-arm equipped with a large flat-panel detector. Initial investigations show that when projection pixel size, acquisition geometry and focal spot size are matched, the flat-panel-based system produces reconstructions with improved MTF, primarily due to the additional interpolation step required for XRII warp correction. Investigations of artifact levels and comparison with in vivo CT images are presented.

Energy-resolved fan beam coherent scatter computed tomography (CSCT) is a novel X-ray based imaging method revealing structural information on the molecular level of tissue or other material under investigation with high resolution of the momentum-transfer dependent coherent scatter cross-section. Since the molecular structure is the source of contrast a very good material discrimination and possibly also medical diagnosis of structural changes of tissue can be achieved with this technique. Poor spectral resolution as found in previous work due to the application of a polychromatic X-ray source can be overcome when energy-resolved detection is used. In this paper experimental results on phantoms using an energy-resolving CdTe-detector are shown. With the present setup the spatial resolution was found to be 4.5 mm (FWHM) and a spectral resolution of 6% was achieved. Applications of this technique can be found in medical imaging, material analysis and baggage inspection.

The microstructure of pathological biomineral deposits has received relatively little attention, perhaps, in part because of the difficulty preparing samples for microscopy. MicroCT avoids these difficulties, and laboratory microCT results are reviewed for aortic valve calcification (human as well as a rabbit model), for human renal calculi (stones) and for calcinoses formed in juvenile dermatomyositis (JDM). In calcified aortic valves of rabbits, numerical analysis of the data shows statistically significant correlation with diet. In a large kidney stone the pattern of mineralization is clearly revealed and may provide a temporal blueprint for stone growth. In JDM calcified deposits, very different microstructures are observed and may be related to processes unique to this disease.

Many environmental processes are controlled by the micro-scale interaction of water and air with the solid phase (soils, sediments, rock) in pore spaces within the subsurface. The distribution in time and space of fluids in pores ultimately controls subsurface flow and contaminant transport relevant to groundwater resource management, contaminant remediation, and agriculture. Many of these physical processes operative at the pore-scale cannot be directly investigated using conventional hydrologic techniques, however recent developments in synchrotron-based micro-imaging have made it possible to observe and quantify pore-scale processes non-invasively. Micron-scale resolution makes it possible to track fluid flow within individual pores and therefore facilitates previously unattainable measurements. We report on experiments performed at the GSECARS** (Advanced Photon Source) microtomography facility and have measured properties such as porosity, fluid saturation and distribution within the pore space, as well as interfacial characteristics of the fluids involved (air, water, contaminant). Different image processing techniques were applied following mathematical reconstruction to produce accurate measurements of the physical flow properties. These new micron-scale measurements make it possible to test existing and new theory, as well as emerging numerical modeling schemes aimed at the pore scale.

Sulfate ions present in soil, groundwater, seawater, decaying organic matter, acid rain, and industrial effluent adversely affect the long-term durability of portland cement concrete, but lack of complete understanding of the nature and consequences of sulfate attack hamper our ability to accurately predict performance of concrete in sulfate-rich environments. One impediment to improved understanding of sulfate deterioration of cement-based materials has been the lack of appropriate non-destructive characterization techniques. Laboratory x-ray microtomography affords an opportunity to study in situ the evolution of physical manifestations of damage due to sulfate exposure. The influence of materials selection and mixture parameters -- including water-to-cement ratio, cement type, and presence or absence of aggregate, as well as the influence of sulfate exposure conditions, including sulfate and cation type (i.e., Na₂SO₄ and MgSO₄) and concentration -- have been examined by microtomography to determine their influence on the rate and character of the sulfate-induced deterioration.

The paper presents the three dimensional analysis of the geometric structure of different aluminium foams by means of micro tomography at spatial resolutions of 10 μm using a synchrotron radiation based setup, and 100 μm using a tabletop cone beam setup, repectively. The most important methods for the calculation of foam structure parameters by means of 3D image processing methods like feature segmentation and labelling as well as granulometry are described and applied to different closed-cell Al-foams produced by a powder-metallurgical processing route. The analysis steps can be used as a standard procedure to characterize the structure of closed as well as open cell foams or other kind of porous materials like e.g. sponges. As an example, the temporal development of foams during their ageing could be observed by ex-situ determination of the geometric structure parameters. Furthermore, the special properties of monochromatic synchrotron radiation have been used to study quantitatively not only the pore- and cell-wall space at a high resolution, but also the distribution and geometric parameters of the blowing agent TiH₂.

The application of computer tomography (CT) for non-destructive testing is of continuing interest to research and industry alike, as economic pressure is ever increasing on production processes. Three concurring goals drive the development of CT, namely: It has to be fast, cheap and precise. With a fast CT-system, the technique can not only be used for error analysis and precision measurements, but also for the application as a standard tool in the production line for the complete quality control of parts. At the Robert Bosch corporate research centre in Stuttgart, Germany, we have set up a CT-system, that allows us to conduct experiments towards these goals and to test and develop the latest software for the reconstruction of x-ray images. One of our main challenges is to use CT for reverse engineering processes and to create computer assisted design (CAD) models from measured data. For this application often a coordinate measurement machine (CMM) is used that gathers a cloud of data points by optical inspection. However, for many parts the inside of the object is relevant. Here CT has the unique advantage of delivering volumetric data. Once the process of the generation of a cloud of data points can be achieved with high precision, standard reverse engineering CAD software can be used to determine the dimensions of the interior structure of an object. This paper describes the use of CT for non-destructive testing at Robert Bosch GmbH, the accuracy limits for the measurement of volumetric data and the classification and analysis of material defects. Furthermore, it highlights the ongoing research to make CT fast, exact and cheap, and to enable its utilisation for 100% testing of parts at the end of a production line.

A fully integrated X-ray tomography facility with the ability to generate tomograms with 2048³ voxels at 2 micron spatial resolution was built to satisfy the requirements of a virtual materials testing laboratory. The instrument comprises of a continuously pumped micro-focus X-ray gun, a milli-degree rotation stage and a high resolution and large field X-ray camera, configured in a cone beam geometry with a circular trajectory. The purpose of this facility is to routinely analyse and investigate real world biological, geological and synthetic materials at a scale in which the traditional domains of physics, chemistry, biology and geology merge. During the first 2 years of operation, approximately 4 Terabytes of data have been collected, processed and analysed, both as static and in some cases as composite dynamic data sets. This incorporates over 300 tomograms with 1024³ voxels and 50 tomograms with 2048³ voxels for a wide range of research fields. Specimens analysed include sedimentary rocks, soils, bone, soft tissue, ceramics, fibre-reinforced composites, foams, wood, paper, fossils, sphere packs, bio-morphs and small animals. In this paper, the flexibility of the facility is highlighted with some prime examples.

A method for non-destructive characterization of plastic deformation in bulk materials is presented. The method is based on X-ray absorption microtomography investigations using X-rays from a synchrotron source. The method can be applied to materials that contain marker particles, which have an atomic number significantly different from that of the matrix material. Data were acquired at the dedicated microtomography instrument at beamline BW2 at HASYLAB/DESY, for a cylindrical aluminium sample containing W particles with an average particle diameter of 7 μm. The minimum detectable size of the maker particles is 1-2 μm with the present spatial resolution at HASYLAB. The position (x,y,z) of all the detected marker particles within 1 mm³ was determined as function of strain. The sample was deformed in stepwise compression along the axis of the cylinder. A tomographic scan was performed after each deformation step. After a series of image analysis steps to identify the centre of mass of individual particles and alignment of the successive tomographic reconstructions, the displacements of individual particles could be tracked as a function of external strain. The particle displacements are then used to identify local displacement gradient components, from which the local 3D plastic strain tensor can be determined. This allows us to map the strain components as a function of location inside a deforming metallic solid.

Micro-deformation and -damage processes running before the macroscopical failure of a component determine its macroscopically observable behaviour. Such processes in metal matrix composites (MMCs) can be imaged during tensile tests with high resolution microtomography utililising synchrotron radiation. To improve the understanding of the material's behaviour the microstructural changes in tensile experiments were studied by tomography and compared with FE computer simulations. Miniaturised tensile test specimens consisting of the particle reinforced MMC Al/10% TiN were manufactured on a powder metallurgic route. From a sub-volume in the gauge length of a specimen high resolution tomograms were created at different deformation stages deploying monochromatic synchrotron radiation supplied by the wiggler beamline BW2 in HASYLAB at DESY in Hamburg. After segmentation and binarization, wherein to each voxel of the 3D tomogram a phase property like e.g. surrounding air, particle or matrix is assigned, the FE-model of the area of interest was set up: Two and three dimensional micro-tomographical sections of interest were discretized using different element shapes to apply a non-linear finite-element method on the real microstructure. The ductile metal matrix was modelled using von Mises flow theory with isotropic hardening. Displacements computed by iterative matching of the tomograms of different deformation states were applied to the FE-model as boundary conditions. The FE-simulations show the appearance and development of plastic zones in the metal matrix as well as high stress concentrations on particles' surfaces, which are areas of crack initiation as the experiments reveal. In future work, criteria for micro-damaging like particle or matrix cracking and delamination can be derived from the comparison of the real with the computer experiments.

Three silicate glasses were hydrated at high pressure and then heated at atmospheric pressure to exsolve the water into bubbles and create foams. The bubble size distribution in these foams was measured by x-ray microtomography on the GSECARS BM-13 beamline at the Advanced Photon Source. The bubble area distributions were measured in two dimensions using the image slices produced from the microtomography and the software ImageJ. The bubble volume distributions were measured from the three-dimensional tomographic images with the BLOB3D software. We found that careful analysis of the microtomography data in both two and three dimensions was necessary to avoid the physically unrealistic, experimental artifact of identifying and counting many small bubbles whose surfaces were not defined by a septum of glass. When this artifact was avoided the foams demonstrated power-law distributions of bubble sizes in both two and three dimensions. Conversion of the power-law exponents for bubble areas measured in two dimensions to exponents for bubble volumes usually agreed with the measured three dimensional volume exponents. Furthermore, the power-law distributions for bubble volumes typically agree with multiple theories of bubble growth, all of which yield an exponent of 1 for the cumulative bubble volume distribution. The measured bubble volume distributions with exponents near 0.3 can be explained by diffusive growth as proposed by other authors, but distributions with exponents near 1.4 remain to be explained and are the subject of continuing research on the effects of water concentration and melt viscosity on foaming behavior.

Digital radiographs of long large objects such as water pipelines, show radiation images which have poor contrast and low signal to noise ratio, especially in the strongly attenuated areas. The examination of the whole objects will spend much time. So, how to shorten the examination time and improve the contrast and signal to noise ratio of radiation images, is the essential problems. The images reconstructed by only a few projective images in digital Tomosynthesis, have a sensible improvement of signal to noise ratio and contrast, compared with digital radiographic images. This will be helpful to the nondestructive testing of the large objects, Therefore, the application of digital Tomosynthesis to the CT nondestructive testing of large objects will effectively improve the Examination efficiency and image quality. Firstly employ digital Tomosynthesis to obtain the axial images of large objects, for the sake of locating the suspicious defects. After indicating the ROIs of defects, radial images will be reconstructed by CT reconstruction methods. Thus the 3D regions of the defects will be rapidly located by the integration of digital Tomosynthesis and CT.

Over the past two years, we have developed a series of algorithms for Grangeat-type half-scan based reconstruction of a short object. These algorithms allow high temporal resolution and high temporal consistence, and suppress Feldkamp-type reconstruction related artifacts. Therefore, this scheme is promising for dynamic and/or quantitative imaging. In this paper, we extend our work into a solution to the long object problem. Our approach takes a temporally non-optimized pre-reconstruction step to transform the long object problem into a short object problem. The detector area is analytically classified into desirable, corrupted, and useless areas. The cone-beam data in the corrupted area are then corrected by the forward projection of the pre-reconstruction, while the data in the useless area are set to zero. A generalized Feldkamp algorithm is chosen for the pre-reconstruction. After the correction, the Grangeat-type half-scan based reconstruction of a short object is performed along with several shadow zone interpolation techniques for the final reconstruction. Numerical simulation is conducted to compare the proposed algorithm with a half-scan Feldkamp algorithm.

The Landweber method provides a framework to formulate iterative algorithms for image reconstruction problems with large, sparse and unstructured system matrices. In a previous study, the authors established the convergence conditions for a general Landweber scheme in both simultaneous and block-iterative [or ordered-subset (OS)] formats with either consistent or inconsistent data, without constraints. Constrained iterative algorithms provide a mechanism for incorporating prior knowledge such nonnegativity, bounds, finite spatial or spectral supports, etc. Hence, they have been widely used in practice. Although the simultaneous constrained (or projected) Landweber scheme was well studied, the convergence of the constrained block-iterative Landweber scheme is unknown. Block-iterative schemes are recently intensively studied theoretically and applied widely. In this paper, we report convergence conditions of a constrained block-iterative Landweber scheme. Prior knowledge is represented as convex sets in which an image of interest must stay. The constrained block-iterative Landweber scheme is constructed by alternatively performing a projection onto convex sets (POCS) and a conventional block-iterative Landweber iteration. The POCS method has been used before for constrained image reconstruction to satisfy both imaging equations and convex constraints. Our approach is different from the conventional application of the POCS method in that we use Landweber iteration for the imaging equations and perform POCS only for the convex constraints. While the conventionally applied POCS method requires Moore-Penrose inverses of matrix blocks, our constrained block-iterative method only takes transposes of such matrix blocks, and improves the computational complexity greatly.

Recently, Katsevich proposed an exact filtered backprojection (FBP) algorithm to solve the long object problem. Although the Katsevich algorithm is theoretically error-free, it may produce image artifacts if its numerical implementation is not well designed. To evaluate the Katsevich algorithm, we implement it in planar detector geometry. Then, we study four types of image artifacts associated with the numerical implementation of this algorithm, which are “texture”, “streak”, “shadow” and “winkle” artifacts. The “texture” artifacts appear if the endpoints of the PI-Line are not treated appropriately. The “streak” artifacts are caused by an inadequate number of filtering lines Q, which can be reduced by setting 0.3N<Q<0.7N. In the step of Hilbert filtering, the aliasing effect results in “shadow” artifacts if the window is not truncated properly. The “wrinkle” artifacts are due to both the interpolation and difference operators, which may be minimized using more sophisticated interpolation methods, increasing projection data and using a more accurate derivative formula. Our results should be valuable to apply the Katsevich algorithm optimally for practical spiral cone-beam CT.

To solve the long object problem, an exact and efficient algorithm has been recently developed by Katsevich. While the Katsevich algorithm only works with standard helical cone-beam scanning, there is an important need for nonstandard spiral cone-beam scanning. Specifically, we need a scanning spiral of variable radius for our newly proposed electron-beam CT/micro-CT prototype. In this paper, for variable radius spiral cone-beam CT we construct two Katsevich-type cone-beam reconstruction algorithms in the filtered backprojection (FBP) and backprojected filtration (BPF) formats, respectively. The FBP algorithm is developed based on the standard Katsevich algorithm, and consists of four steps: data differentiation, PI-line determination, slant filtration and weighted backprojection. The BPF algorithm is designed based on the scheme by Zou and Pan, and also consists four steps: data differentiation, PI-line determination, weighted backprojection and inverse Hilbert transform. Numerical experiments are conducted with mathematical phantoms.

In this paper, we perform numerical studies on Feldkamp-type and Katsevich-type algorithms for cone-beam reconstruction with a nonstandard spiral locus to develop an electron-beam micro-CT scanner. Numerical results are obtained using both the approximate and exact algorithms in terms of image quality. It is observed that the two algorithms produce similar quality if the cone angle is not large and/or there is no sharp density change along the z-direction. The Katsevich-type algorithm is generally preferred due to its nature of exactness.

Conventionally, the FDK algorithm is used to reconstruct images from cone-beam projections in many imaging systems. One advantage of this algorithm is its shift-invariant feature in the filtering process. In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory. Examples of the arc trajectory include the full circular scan mode, a short-scan mode and a super-short-scan mode depending upon the angular range of the scanning path. Since the single arc does not satisfy Tuy's data sufficiency condition, there is no mathematically exact algorithm. However, one advantage of this reconstruction is that the shift-invariance property has been preserved despite the lack of a mathematically complete data set. The new algorithm includes backprojections from three adjacent segments of the arc defined by T₁(vector x), T₂(vector x) and T₃(vector x). Each backprojection step consists of a weighted combination of 1D Hilbert filtering of the modified cone-beam data along horizontal and non-horizontal directions. The non-horizontal filtering is a new feature of this FBP algorithm. For the full circle scanning path, this algorithm reduces to the conventional FDK algorithm plus a term involving a first order derivative filter. Numerical simulations have been performed to validate the algorithm.

Although they are approximate only from the theoretical point of view, the FDK cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circular source trajectory and the general CB-FBP algorithm for other source trajectories, including a helix, have been utilized for decades in extensive applications. A common feature of these two algorithms is that the filtering operation is carried out along each horizontal detector row. Although the horizontal filtering works well for small cone angles, it has been shown that, in applications where a helical source trajectory is employed, the filtering step needs to be carried out along a direction tangential to the source helix to improve reconstruction accuracy. Furthermore, view weighting techniques have to be applied in helical CB-FBP algorithm to suppress streak artifacts caused by data inconsistency. Usually, the view weighting techniques are directly borrowed from their fan beam counterparts, which work well at relatively low helical pitch, but fail at high helical pitches. In this paper, we propose a new helical CB-FBP reconstruction algorithm. The filtering in the proposed algorithm is naturally carried out along the tangential direction of the helical source trajectory after a row-wise fan-to-parallel rebinning. A 3D weighting function (which is dependent on view angle β, ray distance t from the ISO, and cone angle α), is utilized to: (a) suppress artifact caused by data inconsistency; (b) improve noise characteristics by using redundant projection data; (c) extend field of view (FOV) at high pitches by maintaining data redundancy. Both computer simulations and real phantom scans are used to evaluate the proposed helical CB-FBP algorithm. Experimental evaluation verifies that the proposed algorithm produces excellent results from the perspective of reconstruction accuracy, noise characteristics, large FOV at high pitches, and temporal resolution.

One of the recent efforts in development of cone-beam CT is aimed at the construction of a volumetric CT apparatus with distributed X-ray sources. This new concept in 3D CT requires a CT reconstruction algorithm designed for X-ray foci uniformly distributed on a surface rather than on a curve. To research the properties of such algorithm an exact reconstruction formula is derived for a continuous distribution of sources on a surface of a sphere. The algorithm is implemented using finite number of focal spots for simulated phantom projection data. High resolution images were obtained for 100-400 focal spots for both noiseless and noisy input. The results exhibit a potential for CT image reconstruction from highly undersampled projection data.

In this paper, we propose a helical cone-beam scanning configuration of triple symmetrically located X-ray sources, and study minimum detection windows to extend the traditional Tam-Danielsson window for exact image reconstruction. For three longitudinally displaced scanning helices of the same radius and a source location on any helix, the corresponding minimum detection window is bounded by the most adjacent turns respectively selected from the other two helices. The height of our proposed minimum detector window is only 1/3 of that in the single helix case. Associated with proposed minimum detection windows, we define the inter-helix PI-line and establish its existence and uniqueness property: through any point inside the triple helices, there exists one and only one inter-helix PI-line for any pair of the helices. Furthermore, we prove that cone-beam projection data from such a triple-source helical scan are sufficient for exact image reconstruction. Although there are certain redundancies among those projection data, the redundant part cannot be removed by shrinking the detector window without violating the data sufficiency condition. Those results are important components for development of exact or quasi-exact image reconstruction algorithms in the case of triple-source helical cone-beam scanning in the future.

In this paper, a unified framework of image reconstruction from both fan-beam and cone-beam projections is formulated by using intermediate functions. The intermediate function has an imaginary part and a real part. The causality principle is used to prove that the imaginary and real part is mutually linked by a Hilbert transform. Using this link, it is shown that image can be reconstructed by using either the real part or the imaginary part of the intermediate function. Thus there exist two fundamental image reconstruction schemes in image reconstruction from divergent beam projections. One scheme only uses the imaginary part of the intermediate function, while the other scheme only uses the real part. Two schemes are dual to each other by Hilbert transform in intermediate functions. Thus this dual nature is called H-duality. One of the paired dual formulas explicitly allows data truncation, while the other one does not. However, they are equivalent in the sense that both of them are mathematically exact image reconstruction formulas provided the measured data is sufficient for both formulas and is free from noise. Practically, a fan-beam image reconstruction formula is identified to solve the fan-beam data truncation problem.

In high-resolution microtomography, the alignment of the axis of rotation with respect to the optical axis and to the rows of the detector pixel array is an important issue, misalignment being a critical source of reconstruction artifacts. A common calibration method is based on the use of small fiducial markers on a sample. However, the automatic detection and identification of such markers is difficult. Moreover, the exact determination of their positions in the radiographs is prone to errors in the presence of noise, beam-profile fluctuations or nonuniform detector response. This is largely due to the fact that the markers cover only a small number of pixels in the image, which results in poor signal statistics. We have developed a new method that overcomes this limitation. It is based on the use of a purpose-built reference sample with periodic grid structures that cover large regions of the radiographs. Straightforward Fourier analysis techniques are used to determine from the images not only the tilt angles of the rotation axis, but also the lateral position of the axis and the exact pixel size.

Theoretically, the ramp filter for filter backprojection reconstruction in X-ray computed tomography (CT) is a generalized function, expressed as |ω| in the frequency domain and -1/(2π²t²) in the real space. The traditional method for designing a practical filter is to select a curve in the frequency domain which is close to the function |Οω| in some sense. Similarly, to design a practical filter one also can select a function in the real space which approximates the function -1/(2π²t²). Several approximations are studied, leading to either known or new filters. The image reconstructed using the new filter is comparable with that using the band-limited filter.

Metal artifacts in many cases significantly limit non-invasive imaging in evaluation of cerebrovascular patients who have undergone prior aneurysm clipping or coiling. The data inconsistency due to the presence of metal produces streaks in the reconstructed CT slices, which then manifest themselves in the coronal and sagittal reprojections most often used to display CT angiographic data. In DSA, no CT reconstructions are performed and the presence of metal only produces a reduction in SNR behind the metal unless misregistration produces artifacts. In this paper, we have begun to investigate a new method to obtain DSA-like images by using a CT scanner. In this approach, sinogram data is obtained from the multi-slice scanner using the same scan parameters before and after contrast injection. These sets of data are registered, subtracted and rebinned to generate radiography-like images. This new method to form DSA-like images from a CT scanner is called Digital Subtraction Topography (DST). Importantly, CT image reconstruction procedure is not performed to obtain DST images. In principle, the disturbing metal artifacts in the CT images do not appear in the DST images. A number of topographic images representing each of the gantry angles are obtained. These images give clinical information at all angles with AP and RL resolution equivalent to that in the CT slices. Resolution in the SI direction is determined by the CT slice thickness, which can be sub millimeter. The conventional CT image reconstruction can also be applied to DST datasets to generate CT DSA images. In the absence of misregistration, the metal artifacts in the reconstructed CT DSA images could be reduced.

X-ray microtomography is rapidly becoming the tool of choice for three-dimensional (3D) imaging of thick structures at the 1-10 µm scale. The fast microtomography system developed at beamline 2-BM of the Advanced Photon Source (APS) is a new class of instrument offering near video-rate acquisition of tomographic data combined with pipelined processing, reconstruction, and visualization. This system can acquire and reconstruct 720 projections (1024x1024 pixels) at 0.25 deg angular increments in under 5 min using a dedicated 32-node computer cluster. At this throughput, hundreds of specimens can be imaged in a 24 h experiment. Alternatively, time-dependent 3D sample evolution can be studied on practical time scales. In this work, we present the current instrument status and the most recent application.

Performing computed assisted tomography (CAT) requires a perfect centering of the rotation axis with the center of the detector. This requirement is sometimes hard to obtain. Thus, a post acquisition centering correction of the acquired data is mandatory. Several correction techniques can be found in the literature. However, all of them are not completely reliable when the measure is not performed in perfect experimental condition. As matter of fact, researcher use to fit the center of rotation by a post measure visual inspection of the projections. This approach is not practical at high-throughput tomography system where hundreds of samples a day can be easily measured, moreover, the visual approach does not always give the best centering. In this paper we report a new centering technique that is more robust when the quality of the acquired data is poor due to low contrast or noisy acquisition.

Herein we present a quantitative noise analysis of diffraction enhanced imaging (DEI), an x-ray imaging method that produces absorption and refraction images, with inherent immunity to wide-angle scatter. DEI can be used for planar imaging or computed tomography. DEI produces excellent images, but requires an x-ray source of very high power; therefore, it has principally been confined to synchrotron studies. Clinical systems currently under development using conventional x-ray sources will be photon-limited. Therefore, it is important that the noise properties of DEI be understood. We derive mathematical expressions for the noise statistics of DEI images, and show that the original formulation of DEI, given by Chapman, et al, is the maximum-likelihood solution of the image-estimation problem for the case of Poisson noise. However, we find that the standard DEI solution is only unbiased under particular conditions, which must be obeyed if good results are to be achieved. We also present the results of applying various noise-reduction filters, which we found to be very effective in reducing noise variance while introducing little bias.

Optical signatures of tumor cells may be generated by expression of reporter genes encoding bioluminescent/fluorescent proteins. Bioluminescent imaging is a novel technique that identifies such light sources from the light flux detected on the surface of a small animal. This technique can effectively evaluate tumor cell growth and regression in response to various therapies in medical research, drug development and gene therapy. In this paper, the diffusion approximation is employed to describe the propagation of photons through biological tissues. Then, a practical method is proposed for localizing and quantifying bioluminescent sources from external bioluminescent signals. This method incorporates prior knowledge on permissible source regions, and transforms the inverse bioluminescent problem into a finite element-based constrained optimization procedure. This approach is validated and evaluated with ideal and noise data in numerical simulation.

White nylon material was chosen to make cylindrical tissue phantoms for development of bioluminescence tomography techniques. A low-level light source, delivered through an optic fiber of core diameter 200 μm, was placed at different locations on one phantom surface. The light travels through the phantom, reaches the external surface, and is captured by a liquid nitrogen-cooled CCD camera. The scattering, absorption, and anisotropy parameters of the phantom are obtained by matching the measured light transmission profiles to the profiles generated by the TracePro software. The perturbation analysis, with the homogeneous phantoms, demonstrated that the imaging system is sufficiently sensitive to capture intensity change of higher than 0.5nW/cm² or a location shift of the light source of more than 200 microns. It is observed that the system can distinguish two point light sources with separation of about 2 mm. The perturbation analysis is also performed with the heterogeneous phantom. Based on our data, we conclude that there is inherent tomographic information in bioluminescent measures taken on the external surface of the mouse, which suggests the feasibility of bioluminescence tomography for biomedical research using the small animals, especially the mice.

The technology for x-ray computed tomography (CT) has experienced tremendous growth in recent years. Since the introduction of 4-slice helical scanners in 1998, rapid improvement has been made on CT scanners in terms of the volume coverage, spatial resolution, scan speed, and the number of slices. These advancements not only significantly impact clinical applications, but also bring huge challenges to the CT system design. Because of the complexity of the volumetric CT (VCT) system, various strategies have to be utilized in the design process. These methodologies include theoretical analysis, computer simulation for system performance prediction, bench-top experiments for analysis confirmation, automated image analysis tools for automatically evaluating image performance, and double-blind tests with human observers for parameter optimization. In this paper, we present some of the system design considerations and optimization processes for a 64-slice scanner. These design processes ensure the optimal performance of the cone beam CT scanner. Initial clinical feedback has demonstrated the effectiveness of our approach.

In recent years, hard x-ray full field microscopy and tomography has been developed for synchrotron radiation sources based on parabolic refractive x-ray lenses. These optics are used as objective lens in a hard x-ray microscope that can image objects in transmission free of distortion. Using beryllium as lens material, an optical resolution of about 100nm has been reached in a field of view that is larger than 500 micrometers. In the future, the spatial resolution may be improved to below 50nm. Recording a large number of micrographs from different perspectives allows one to reconstruct non-destructively the 3-dimensional inner structure of an object with resolutions well below one micrometer. Different contrast mechanisms can be exploited, such as absorption and near field phase contrast. The method is demonstrated using a microchip as a test sample.

For several years efforts have been made to improve the resolution for imaging and tomography with hard X-rays. Recently we demonstrated sub-100 nm resolution at 13 keV with a microscope including a Kirkpatrick-Baez multilayer-mirror (KB) as a condenser followed by a micro-Fresnel Zone Plate (FZP) as an objective lens. We built since a new tomography station at UNICAT at the Advanced Photon Source integrating the KB-FZP microscope for 100 nm tomography.

Hard x-ray absorption spectroscopy is combined with scanning microtomography to reconstruct full near edge spectra of an elemental species at each location on an arbitrary virtual section through a sample. These spectra reveal the local concentrations of different chemical compounds of the absorbing element inside the sample and give insight into the oxidation state, the local atomic structure, and the local projected free density of states. The method is implemented by combining a quick scanning monochromator and data acquisition system with a scanning microprobe setup based on refractive x-ray lenses. The full XANES spectra reconstructed at each point of the tomographic slice allow to detect slight variations in concentrations of chemical compounds, such as metallic and monovalent copper. The method is applied to the analysis of a heterogeneous catalyst.

In this work we investigate the phase-contrast tomography reconstruction problem assuming an incident (paraxial) spherical-wave. Starting from linearized inverse scattering theory, we develop an intensity diffraction tomography (I-DT) reconstruction algorithm that is relevant to scanning geometries that have a fixed source-to-object distance. This reconstruction algorithm accounts for first-order scattering effects introduced by the object and provides a relationship between the intensity measurements made on two parallel detector planes and the desired complex refractive index distribution. A preliminary numerical investigation of the developed reconstruction algorithm is presented.

A new, ultra-fast microCT instrument with scanning+reconstruction cycle under 50 seconds for full 3D-volume has been created. The scanner based on the scanning geometry with static object and rotation of source-camera pair(s), which allows using it for industrial applications as well as for low-dose in-vivo imaging of small laboratory animals where rotation of the object is not acceptable. Acquisition part contains two pairs of x-ray sources and cameras for data collection from complementary directions simultaneously. Reconstruction engine (cone-beam reconstruction by modified Feldkamp algotithm) includes 1, 2 or 4 dual Intel-Xeon computers working in parallel under control of the host PC through local network. The instrument specifications are following: voxel size is 48 or 96 um for corresponding 1024x1024x1024 or 512x512x512 reconstruction array; scanning time with parallel reconstruction is 50 seconds for 96um resolution. X-ray sources peak energy can be adjusted in the range of 20-65kV. Typical scanning dose is 0.4Gy. The scanner itself is a compact desktop instrument, which contains all x-ray parts and necessary shielding for safe operations in the normal laboratory environments.

Micro-phase-contrast X-ray computed tomography with an X-ray interferometer (micro-phase-contrast CT) is in operation to obtain high spatial resolution images of less than 0.01 mm at the undulator beam-line 20XU of SPring-8, Japan, and we applied micro-phase-contrast CT to observe the organs of rats and hamsters. The excised kidney and spleen fixed by formalin were imaged. The fine inner-structures such as vessels, glomeruli of kidney and white and red pulps of spleen were visualized clearly about 0.01-mm spatial resolutions without using contrast agent or staining procedure. The results were very similar to those by optical microscopic images with 20-fold magnification. These results suggest that the micro-phase tomography might be a useful tool for various biomedical researches.

Newts are the most developed vertebrates which retain the ability as adults to regenerate missing limbs; they are, therefore, of great interest in terms understanding how such regeneration could be triggered in mammals. In this study, synchrotron microCT was used to study bone microstructure in control forelimbs and in forelimbs regenerated for periods from 37 to 85 days. The bone microstructure in newts has been largely neglected, and interesting patterns within the original bone and in the regenerating arm and hand are described. Periosteal bone formation in the regenerating arm and finger bones, delayed ossification of carpal (but not metacarpal) bones and the complex microstructure of the original carpal bones are areas where microCT reveals detail of particular interest.

This study explores the application of conventional micro tomography (μCT) and synchrotron radiation (SR) based μCT to evaluate the bone around titanium dental implants. The SR experiment was performed at beamline W2 of HASYLAB at DESY using a monochromatic X-ray beam of 50 keV. The testing material consisted of undecalcified bone segments harvested from the upper jaw of a macaca fascicularis monkey each containing a titanium dental implant. The results from the two different techniques were qualitatively compared with conventional histological sections examined under light microscopy. The SR-based μCT produced images that, especially at the bone-implant interface, are less noisy and sharper than the ones obtained with conventional μCT. For the proper evaluation of the implant-bone interface, only the SR-based μCT technique is able to display the areas of bony contact and visualize the true 3D structure of bone around dental implants correctly. This investigation shows that both conventional and SR-based μCT scanning techniques are non-destructive methods, which provide detailed images of bone. However with SR-based μCT it is possible to obtain an improved image quality of the bone surrounding dental implants, which display a level of detail comparable to histological sections. Therefore, SR-based μCT scanning could represent a valid, unbiased three-dimensional alternative to evaluate osseointegration of dental implants.

Beam-hardening is caused by the filtering of a polychromatic X-ray beam by the objects in the scan field. In industrial field, both the X-ray source and the attenuation characteristics of the materials are different with those in medical field. Methods that work in medical field cannot give satisfying results here. The author has developed a computer software, named simulative tomographic machine (STM) platform. STM platform is designed to simulate the procedure of high-energy ICT scanning. It is also the platform for developing data process algorithm. With the STM platform, this paper presents an efficient correction technique, which can eliminate beam-hardening artifacts efficiently in high-energy ICT. The new algorithm is based on the following facts: the attenuation coefficient of each substance is precisely known; the polychromatic spectrum of accelerator can be computed with Monte Carlo (MC) method; the total photon interaction cross-section of most inspected object can be treated as constant in the energy region between 1.5 and 9MeV. The monochromatic projection can be computed from the polychromatic projection with an iterative algorithm. So we can reconstruct perfect image from the projection made only by high-energy photons.

Synchrotron radiation based X-ray microtomography was applied for the morphometric analysis of polyurethane scaffolds (polymer foams) intended for the use as a biocompatible replacement material. The X-ray microtomography apparatus used for this study is described in detail. The full data evaluation process including X-ray image recording, tomographic reconstruction and the subsequent data reduction steps is explained. The 3-dim. segmentation of the scaffolds and the results of the morphometric analysis are presented.

A facility for x-ray computed microtomography (CMT) is operating as a national user facility for earth and environmental sciences research on the bending magnet beamline at the GeoSoilEnviroCARS sector at the Advanced Photon Source (APS). The APS bending magnet has a critical energy of 20 keV, and thus provides high flux at photon energies up to 100 keV, making it well suited to imaging a wide range of earth materials up to several cm in size. The beamline is equipped with a Si (111) double-crystal monochromator covering the energy range from 5 to 70 keV with beam sizes up to 50mm wide and 6mm high. The transmitted x-rays are imaged with a single crystal YAG scintillator, a microscope objective and a 1300x1030 pixel 12-bit 5MHz CCD detector. The maximum spatial resolution is under 2 microns in both the transmission radiographs and the reconstructed slices. Data collection times for full 3-D datasets range from 5-60 minutes. This facility has been used for a wide range of studies, including multiphase fluids in porous media, high-pressure studies, meteorites, and hyper-accumulating plants.

Maximum-likelihood estimation is an important method of inference. Recently, maximum-likelihood techniques have been successfully applied to absorption tomography of weakly as well as strongly absorbing materials. In this presentation we generalize this method to the phase contrast tomography, which combines the phase estimation and tomography. Unlike the standard phase fitting followed by the filtered back-projection, the developed procedure gives reasonable results also when applied to very noisy data or data consisting of only a few measured projections. The proposed method could therefore considerably shorten measuring times in applications involving low intensity beams, such as phase tomography with low intense X-ray beams or neutrons.

We have developed a two-grating interferometer for hard X rays that can be used for phase imaging and tomography. A silicon phase grating positioned just downstream of the object under study splits the distorted wavefront into essentially a positive and a negative first-order beam. At a given distance from this beam-splitter grating, where the two beams still mostly overlap, they form a pattern of interference fringes that is distorted according to the wavefront distortions. The fringes may be finer than the resolution of an area detector used to record the signal, but an absorption grating with suitable pitch, put in front of the detection plane, allows the detection of intensity variations that correspond to the derivative of the wavefront phase taken along the direction perpendicular to the grating lines. A combination of this technique with the phase-stepping method, in which several exposures are made which differ in the phase of the fringe pattern, allows to eliminate effects of non-uniform intensity due to inhomogeneous illumination and edge-enhancing inline phase contrast. Several examples of tomograms taken under different experimental conditions are shown, including a polychromatic "pink-beam" setup.