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ABSTRACT: The first monochromatic X-ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X-ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point-spread function for the X-ray imaging system and harmonic contamination of the X-ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X-ray spectrum prior to monochromatization, allowance for the response of the double-crystal Si monochromator used (via X-ray dynamical theory), as well as a thorough assessment of the role of X-ray phase-contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point-spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X-ray tomography data, across a wide range of disciplines, including materials and life sciences.
Journal of Synchrotron Radiation 09/2012; 19(Pt 5):728-50. · 2.73 Impact Factor
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ABSTRACT: 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.
Applied Physics Letters 01/2010; 96(2):021105-021105-3. · 3.84 Impact Factor
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ABSTRACT: Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated. The analytical expressions are compared with the results of numerical simulations using Kirchhoff diffraction theory, as well as with experimental X-ray measurements.
Optics Express 04/2008; 16(5):3223-41. · 3.59 Impact Factor
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ABSTRACT: Phase-contrast tomography (PCT) allows three-dimensional imaging of objects that display insufficient contrast for conventional absorption-based tomography. We prove that PCT is stable with respect to high-frequency noise in experimental phase-contrast data, unlike conventional tomography, which is known to be mildly unstable. We use known properties of the three-dimensional x-ray transform and transport-of-intensity equation to construct a matrix representation of the forward PCT operator. We then invert this formula to show that, under natural boundary conditions, the PCT reconstruction operator exists and leads to a unique solution. We show that the singular values s(n) of the reconstruction operator have asymptotic behavior s(n)=O(n(-3/2)), guaranteeing the mathematical stability of the reconstruction process.
Journal of the Optical Society of America A 10/2007; 24(9):2516-26. · 1.56 Impact Factor
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ABSTRACT: Optical systems capable of three-dimensional transmission imaging are considered; these systems employ a conventional tomographic setup with an added linear shift-invariant optical system between the sample and the detector. A theoretical analysis is presented of image formation and sample reconstruction in such systems, examples of which include diffraction tomography and phase-contrast tomography with the use of analyzer crystals. An example is introduced in which the image is obtained by scanning the beam along the line orthogonal to the optic axis and to the axis of rotation with a one-dimensional slit or grating parallel to the rotation axis. We show that under certain conditions the proposed system may allow quantitative local (region-of-interest) tomography.
Journal of the Optical Society of America A 09/2007; 24(8):2230-41. · 1.56 Impact Factor
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ABSTRACT: 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.
Journal of the Optical Society of America A 02/2006; 23(1):34-42. · 1.56 Impact Factor
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ABSTRACT: 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.
Applied Optics 05/2004; 43(12):2418-30. · 1.41 Impact Factor
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ABSTRACT: 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.
Applied Optics 12/2003; 42(32):6488-94. · 1.41 Impact Factor
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ABSTRACT: 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.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
05/1999;
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ABSTRACT: We consider the problem of quantitative phase retrieval from images obtained using a coherent shift-invariant linear imaging system whose associated transfer function (i.e., the Fourier transform of the complex point-spread function) is well approximated by a linear function of spatial frequency. This linear approximation to the transfer function is applicable when the spread of spatial frequencies, in a two-dimensional complex wavefield, is sufficiently narrow when compared to the characteristic length of variation of the transfer function for an imaging system taking such a wavefield as input. We give several algorithms for reconstructing both the phase and amplitude of a given two-dimensional coherent wavefield, given as input data one or more images of such a wavefield which may be formed by different states of the imaging system. When an object to be imaged consists of a single material, or of a single material embedded in a substrate of constant thickness, the phase-amplitude reconstruction can be performed using a single image. As a first application of these ideas, we write down an algorithm for using a single diffraction-enhanced image (DEI) to obtain a quantitative reconstruction of the projected thickness of a single-material sample which is embedded within a substrate of approximately constant thickness. This algorithm is used to quantitatively map inclusions in a breast phantom, from a single synchrotron DEI image of the same. In particular, the reconstructed images quantitatively represent the projected thickness in the bulk of the sample, in contrast to raw DEI images which greatly emphasise sharp edges (high spatial frequencies). Lastly, we point out that the methods presented here are also applicable to the quantitative analysis of differential interference contrast (DIC) images, obtained using both visible-light and X-ray microscopy.
Optics Communications.
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84.
