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A new method for deconvolution of one-dimensional and multidimensional data is suggested. The proposed algorithm is local in the sense that the deconvolved data at a given point depend only on the value of the experimental data and their derivatives at the same point. In a regularized version of the algorithm the deconvolution is constructed iteratively with the help of an approximate deconvolution operator that requires only the low-order derivatives of the data and low-order integral moments of the point-spread function. This algorithm is expected to be particularly useful in applications in which only partial knowledge of the point-spread function is available. We tested and compared the proposed method with some of the popular deconvolution algorithms using simulated data with various levels of noise.

We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin-image problem of in-line holography and is capable of analysing data obtained using X-ray microscopy, electron microscopy, neutron microscopy or visible-light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non-iterative and computationally efficient method is applied to data obtained using an X-ray phase contrast ultramicroscope.

This review provides a brief overview, albeit from a somewhat personal perspective, of the evolution and key features of various hard X-ray phase-contrast imaging (PCI) methods of current interest in connection with translation to a wide range of imaging applications. Although such methods have already found wide-ranging applications using synchrotron sources, application to dynamic studies in a laboratory/clinical context, for example for in vivo imaging, has been slow due to the current limitations in the brilliance of compact laboratory sources and the availability of suitable high-performance X-ray detectors. On the theoretical side, promising new PCI methods are evolving which can record both components of the phase gradient in a single exposure and which can accept a relatively large spectral bandpass. In order to help to identify the most promising paths forward, we make some suggestions as to how the various PCI methods might be compared for performance with a particular view to identifying those which are the most efficient, given the fact that source performance is currently a key limiting factor on the improved performance and applicability of PCI systems, especially in the context of dynamic sample studies. The rapid ongoing development of both suitable improved sources and detectors gives strong encouragement to the view that hard X-ray PCI methods are poised for improved performance and an even wider range of applications in the near future.

We present a new method for quantitative nondestructive characterization of objects by x-ray phase-contrast imaging. Spatial distributions of the projected values of the complex refractive index in the sample are reconstructed by processing near-field images collected at a fixed sample-to-detector distance using a polychromatic incident beam and an energy-sensitive area detector, such as a CCD used in the photon-counting spectroscopy mode. The method has the potential advantages of decreased radiation dose and increased accuracy compared to conventional techniques of x-ray imaging.

We report the results of quantitative hard X-ray phase- contrast microscopy and tomography using synchrotron radiation, in-line imaging geometry and a non-interferometric phase retrieval technique based on the Transport of Intensity equation. This quantitative imaging method is fast, simple, robust, does not require sophisticated X-ray optical elements and can potentially provide submicron spatial resolution over a field of view of the order of centimeters. In the present experiment a spatial resolution of approximately 0.8 micron has been achieved in images of a polystyrene sphere using 19.6 keV X-rays. We demonstrate that appropriate processing of phase-contrast images obtained in the in-line geometry can reveal important new information about the internal structure of weakly absorbing organic samples. We present some preliminary results of a phase-contrast tomographic reconstruction with and without phase retrieval in each X-ray projection. We believe that this method of quantitative X-ray phase-contrast imaging will find applications in biology and medicine, particularly for high-contrast imaging of soft tissues.

Conventional radiography is based on absorption contrast and geometrical (ray) optics. After an outline of the relevant theory, this article reports results displaying both phase- and absorption-contrast, collected with a technique which utilizes a micro-focus x-ray source to achieve a high degree of spatial coherence, and relatively large object-to-image distances to enable (wave) interference effects (Fresnel diffraction) to occur and manifest themselves as phase contrast in the image plane. Both soft tissue (chicken knee) and hard tissue (finger bone) samples are investigated for a range of source sizes and object-to-image distances, encompassing conditions somewhat analogous to conventional radiography. Variation in image contrast and resolution as a function of these variables is observed and discussed.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Since Rontgen’s discovery of X rays in 1895 the vast majority of radiographs have been collected and interpreted on the basis of absorption contrast and geometrical (ray) optics. In recent years the possibility of utilizing phase-contrast effects has received considerable attention, much of this activity stemming from the possibility of producing X-ray beams of suitably high coherence at synchrotron sources (1). A description of a phase-contrast imaging (PCI) technique which utilizes a laboratory-based microfocus X-ray source to achieve the required spatial coherence, and does not rely on there being a high degree of chromatic coherence, will be described (2). The method employs a relatively large object-to-image distance to allow wave interference (Fresnel diffraction) to occur and manifest itself as contrast formation in the intensity distribution recorded at the image plane. PCI is particularly relevant to the nondestructive characterization of materials and this will be demonstrated by way of some exa...

Extended abstract of a paper presented at Microscopy and Microanalysis 2006 in Chicago, Illinois, USA, July 30 – August 3, 2005

Three phase-retrieval algorithms, based on the transport-of-intensity equation and on the contrast transfer function for propagation-based imaging, and on the linearized geometrical optics approximation for analyser-based imaging, are investigated. The algorithms are compared in terms of their effect on propagation of noise from projection images to the corresponding phase-retrieved images and further to the computed tomography (CT) images/slices of a monomorphous object reconstructed using filtered backprojection algorithm. The comparison is carried out in terms of an integral noise characteristic, the variance, as well as in terms of a simple figure-of-merit, i.e. signal-to-noise ratio per unit dose. A gain factor is introduced that quantitatively characterizes the effect of phase retrieval on the variance of noise in the reconstructed projection images and in the axial slices of the object. Simple analytical expressions are derived for the gain factor and the signal-to-noise ratio, which indicate that the application of phase-retrieval algorithms can increase these parameters by up to two orders of magnitude compared to raw projection images and conventional CT, thus allowing significant improvement in the image quality and/or reduction of the x-ray dose delivered to the patient.

The quantitative imaging of phase object using 16 keV x-rays is reported. The theoretical basis of the techniques is presented along with its implementation using a synchrotron x-ray source. We find that our phase image is in quantitative agreement with independent measurements of the object.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A dedicated micro-CT beamline is planned for the Australian Synchrotron which will extend the synchrotron's imaging and tomography capability down to the smaller scale, incorporating phase-contrast and absorption-contrast, and an additional focussing-based mode for high-resolution. The beamline will use multi-layer mirror monochromators for enhanced flux, and will focus particularly on dynamic and high throughput studies in both monochromatic and pink-beam mode. Together with the existing Imaging and Medical beamline, this beamline will produce numerous large datasets of 10 GB or more, providing a significant data-processing challenge. The Remote-CT project addresses this by combining the MASSIVE supercomputing GPU cluster with XLI / X-TRACT software, developed at CSIRO. This software has extensive functionality for both processing and simulation of absorption and phase-contrast tomography data and has now been modified for parallel operation on a GPU cluster to take maximum advantage of the speed-up this enables.

We investigate the quantitative accuracy and noise sensitivity of reconstruction of the 3D distribution of complex refractive index, n(r)=1−δ(r)+iβ(r), in samples containing materials with different refractive indices using propagation-based phase-contrast computed tomography (PB-CT). Our present study is limited to the case of parallel-beam geometry with monochromatic synchrotron radiation, but can be readily extended to cone-beam CT and partially coherent polychromatic X-rays at least in the case of weakly absorbing samples. We demonstrate that, except for regions near the interfaces between distinct materials, the distribution of imaginary part of the refractive index, β(r), can be accurately reconstructed from a single projection image per view angle using phase retrieval based on the so-called homogeneous version of the Transport of Intensity equation (TIE-Hom) in combination with conventional CT reconstruction. In contrast, the accuracy of reconstruction of δ(r) depends strongly on the choice of the...

This paper presents a summary and overview of heterogeneous algorithms and applications developed by the Commonwealth Scientific and Industrial Research Organisation CSIRO for solving practical and challenging science problems such as: 1 high-content analysis of brain cell images for medical research and drug discovery; 2 genetic analysis of complex experimental designs for crop breeding; 3 solving computational fluid dynamics problems; 4 deconvolving 3D images from microscopy and medical imaging; 5 reconstructing large 3D computed tomography CT images from medical and materials science; 6 quantifying uncertainty in complex environmental models. Applications discussed utilise GPUs and multicore CPUs on a scale ranging from single desktop workstations through to large GPU clusters. Results demonstrate that both types of system can successfully accelerate a variety of practical science applications. We have seen significant gains in productivity and opportunity as a result of leveraging GPUs, tackling computational problems in which execution time was previously infeasible.

The three-dimensional distribution of the materials composing a sample is reconstructed using multiple-energy computed tomography techniques. The a priori knowledge about the specific materials that are present in the sample is used for decomposing the measured intensity projections into projected thicknesses of each component material. Those decomposed projections are then processed using iterative reconstruction algorithms to separately obtain the three-dimensional distribution of each material. A new iterative reconstruction algorithm has been implemented and its performance is compared to the standard filtered back projection and to another existing iterative algorithm based on histogram manipulation. The method is first tested with simulations on data for a realistic, three-materials' numerical sample and then applied to experimental micro-tomography data. The accuracy of the reconstruction from experimental data is tested by means of an energy dispersive x-ray spectroscopy scan of the sample.

We investigate a variant of the reconstruction technique for the in-line X-ray phase-contrast tomography data. This technique uses a newly introduced quantity, which represents a particular combination of the real and imaginary parts of the complex refractive index n. This quantity coincides with the real part of (1-n) in the case of objects having negligible absorption. The advantage of the proposed approach is in the significantly simplified form of the reconstruction algorithm for the introduced quantity. As demonstrated by our numerical experiments, the newly introduced quantity can be predictably associated with a particular refractive index.

Microstructures are critical for defining material characteristics such as permeability, mechanical, electrical and other physical properties. However, the available techniques for determining compositional microstructures through segmentation of x-ray computed tomography (CT) images are inadequate when there are finer structures than the CT spatial resolution, i.e. when there is more than one material in each voxel. This is the case for CT imaging of geomaterials characterized with submicron porosity and clay coating that control petrophysical properties of rock. This note outlines our data-constrained modelling (DCM) approach for prediction of compositional microstructures, and our investigation of the feasibility of determining sandstone microstructures using multiple CT data sets with different x-ray beam energies. In the DCM approach, each voxel is assumed to contain a mixture of multiple materials, optionally including voids. Our preliminary comparisons using model samples indicate that the DCM-predicted compositional microstructure is consistent with the known original microstructure under low noise conditions. The approach is quite generic and is applicable to predictions of microstructure of various materials.

We present a method for tomographic reconstruction of objects containing several distinct materials, which is capable of accurately reconstructing a sample from vastly fewer angular projections than required by conventional algorithms. The algorithm is more general than many previous discrete tomography methods, as: (i) a priori knowledge of the exact number of materials is not required; (ii) the linear attenuation coefficient of each constituent material may assume a small range of a priori unknown values. We present reconstructions from an experimental x-ray computed tomography scan of cortical bone acquired at the SPring-8 synchrotron.

Absorption-contrast x-ray imaging serves to visualize the variation in x-ray attenuation within the volume of a given sample, whereas phase contrast allows one to visualize variations in x-ray refractive index. The former imaging mechanism has been well known and widely utilized since the time of Rontgen’s Nobel prize winning work, whereas the latter mechanism—sought for, but not found, by Rontgen himself—has laid the foundation for a revolution in x-ray imaging which is the central topic of this review. We consider the physical imaging mechanisms underlying both absorption contrast and phase contrast, together with the associated inverse problem of how one may obtain quantitative two- or three-dimensional information regarding a sample, given one or more phase-contrast images of the same. Practical questions are considered, regarding optimized phase-contrast imaging geometries as a function of detector resolution, source size, x-ray spectrum, and dose. Experimental examples pertaining to biomedical appli...

A method is presented for quantitative polychromatic cone-beam phase-contrast tomographic imaging of a single-material object from few projections. This algorithm exploits the natural combination of binary tomography with a phase-retrieval method that makes explicit use of the single-material nature of the sample. Such consistent use of a priori knowledge reduces the number of required projections, implying significantly reduced dose and scanning time when compared to existing phase-contrast tomography methods. Reconstructions from simulated data sets are used to investigate the effects of noise and establish a minimum required number of projections. An experimental demonstration is then given, using data from a point-projection X-ray microscope. Here, the complex distribution of refractive index in a sample containing several nylon fibers with diameters between 100 microm and 420 microm is reconstructed at a spatial resolution of approximately 4 microm from 20 polychromatic phase-contrast projection images with a mean photon energy of 8.4 keV.

General formulas are derived for computed tomography reconstruction in analyzer-based imaging. Two image acquisition geometries are investigated. In the first geometry, which is widely used, the rotation axis of the object is perpendicular to that of the analyzer crystal. In the second geometry, in which the rotation axes are parallel, the reconstruction formulas are shown to be significantly simpler and more stable with respect to noise in experimental data.

Effects of incident illumination on phase-contrast images obtained by means of free-space propagation are investigated under the "transport-of-intensity" approximation. Analytical expressions for image intensity distribution are derived in the cases of coherent quasi-plane and quasi-spherical incident waves, as well as for spatially incoherent and quasi-homogeneous sources and some other types of sources. Practical methods for measuring the relevant parameters of the incident radiation are discussed together with formulas allowing one to calculate the effect of these parameters on the image intensity distribution. The results are expected to be useful in quantitative in-line imaging, phase retrieval, and tomography with polychromatic and spatially partially coherent radiation. As an application we present a method for simultaneous "automatic" phase retrieval and spatial deconvolution in in-line imaging of homogeneous objects using extended polychromatic x-ray sources.

General principles and results for the optimization of the performance of x-ray in-line phase-contrast imaging systems for spatially incoherent sources are investigated. In particular, formulas expressing the dependence of image contrast, spatial resolution, and signal-to-noise ratio on instrumental parameters including source size, detector resolution, geometrical factors, x-ray energy as well as sample properties are derived for different models of sample features. The results for some special cases of interest are presented. Optimization procedures are proposed that are expected to be useful in the design of imaging systems seeking to exploit x-ray in-line phase contrast.

The first Born and Rytov approximations of scattering theory are introduced in their less familiar near-field versions. Two algorithms for phase retrieval based on these approximations are then described. It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields. The algorithms are applied to derive explicit solutions to four phase-retrieval problems of practical relevance to quantitative phase-contrast imaging and tomography. An example of successful phase reconstruction by use of the Born-type algorithm with an experimental x-ray image is presented.

Conventional X-ray radiography is based on absorption contrast and assumes geome trical optics. An “in-line” method and theory of hard X-ray phase-contrast ima ging were introduced. The differences between the conventional X-ray absorption contrast image and the phase contrast image were distinguished by using radiogra phs of biological samples. The effect of X-ray source size on the image contrast was investigated. Moreover, the key parameters of absorption contrast image and phase contrast image were simulated theoretically and discussed.

In a previous paper [ J. Opt. Soc. Am. A12, 1932 ( 1995)] we presented a method for phase recovery with the transport-of-intensity equation by use of a series expansion. Here we develop a different method for the solution of this equation, which allows recovery of the phase in the case of nonuniform illumination. Though also based on the orthogonal series expansion, the new method does not require any separate boundary conditions and can be more easily adjusted for apertures of various shapes. The discussion is primarily for the case of a circular aperture and Zernike polynomials, but we also outline the solution for a rectangular aperture and Fourier harmonics. The latter example may have some substantial advantages, given the availability of the fast Fourier transform.

Recent papers have shown that there are different coherent and partially coherent fields that may have identical intensity distributions throughout space. On the other hand, the well-known transport-of-intensity equation allows the phase of a coherent field to be recovered from intensity measurements, and the solution is widely held to be unique. A discussion is given on the recovery of the structure of both coherent and partially coherent fields from intensity measurements, and we reconcile the uniqueness question by showing that the transport-of-intensity equation has a unique solution for the phase only if the intensity distribution has no zeros.

A new technique is proposed for the recovery of optical phase from intensity information. The method is based on the decomposition of the transport-of-intensity equation into a series of Zernike polynomials. An explicit matrix formula is derived, expressing the Zernike coefficients of the phase as functions of the Zernike coefficients of the wave-front curvature inside the aperture and the Fourier coefficients of the wave-front boundary slopes. Analytical expressions are given, as well as a numerical example of the corresponding phase retrieval matrix. This work lays the basis for an effective algorithm for fast and accurate phase retrieval.

The quantitative imaging of a phase object using 16 keV x rays is reported. The theoretical basis of the techniques is presented along with its implementation using a synchrotron x-ray source. We find that our phase image is in quantitative agreement with independent measurements of the object.

A new method for extracting quantitative information from phase-contrast x-ray images obtained with microfocus x-ray sources is presented. The proposed technique allows rapid noninvasive characterization of the internal structure of thick optically opaque organic samples. The method does not generally involve any sample preparation and does not need any x-ray optical elements (such as monochromators, zone plates, or interferometers). As a consequence, samples can be imaged in vivo or in vitro, and the images are free from optical aberrations. While alternative techniques of x-ray phase-contrast imaging usually require expensive synchrotron radiation sources, our method can be implemented with conventional, albeit microfocus, x-ray tubes, which greatly enhances its practicality. In the present work, we develop the theoretical framework, perform numerical simulations, and present the first experimental results, demonstrating the viability of the proposed approach. We believe that this method should find wide-ranging applications in clinical radiology and medical research.