Because the refractive index for hard x rays is slightly different from unity, the optical phase of a beam is affected by transmission through an object. Phase images can be obtained with extreme instrumental simplicity by simple propagation provided the beam is coherent. But, unlike absorption, the phase is not simply related to image brightness. A holographic reconstruction procedure combining images taken at different distances from the specimen was developed. It results in quantitative phase mapping and, through association with three-dimensional reconstruction, in holotomography, the complete three-dimensional mapping of the density in a sample. This tool in the characterization of materials at the micrometer scale is uniquely suited to samples with low absorption contrast and radiation-sensitive systems.
Phase objects are readily imaged through Fresnel diffraction in the hard x-ray beams of third-generation synchrotron radiation sources such as the ESRF, due essentially to the very small angular size of the source. Phase objects can lead to spurious contrast in x-ray diffraction images (topographs) of crystals. It is shown that this contrast can be eliminated through random phase plates, which provide an effective way of tailoring the angular size of the source. The possibilities of this very simple technique for imaging phase objects in the hard x-ray range are explored experimentally and discussed. They appear very promising, as shown in particular by the example of a piece of human vertebra, and could be extended to phase tomography.
The novel possibilities of phase feature detection in radiography at a third generation synchrotron radiation source are used to image, both in projection and in computed tomography, a cracked silicon single crystal and metal matrix composites strained in tension. Through an instrumentally very simple technique, based on Fresnel diffraction, phase jumps related to the interface between the matrix and the reinforcing phases of the composites are detected even when these phases show very similar x-ray attenuation. Strain-induced cracks with openings below the micrometer range are also visible through the phase modulation they introduce, illustrating the potential of the technique for assessing damage in materials with improved resolution and sensitivity.
X-ray computed microtomography is particularly well suited for studying trabecular bone architecture, which requires three-dimensional (3-D) images with high spatial resolution. For this purpose, we describe a three-dimensional computed microtomography (microCT) system using synchrotron radiation, developed at ESRF. Since synchrotron radiation provides a monochromatic and high photon flux x-ray beam, it allows high resolution and a high signal-to-noise ratio imaging. The principle of the system is based on truly three-dimensional parallel tomographic acquisition. It uses a two-dimensional (2-D) CCD-based detector to record 2-D radiographs of the transmitted beam through the sample under different angles of view. The 3-D tomographic reconstruction, performed by an exact 3-D filtered backprojection algorithm, yields 3-D images with cubic voxels. The spatial resolution of the detector was experimentally measured. For the application to bone investigation, the voxel size was set to 6.65 microm, and the experimental spatial resolution was found to be 11 microm. The reconstructed linear attenuation coefficient was calibrated from hydroxyapatite phantoms. Image processing tools are being developed to extract structural parameters quantifying trabecular bone architecture from the 3-D microCT images. First results on human trabecular bone samples are presented.
The availability of three-dimensional measuring techniques coupled to specific image processing methods opens new opportunities for the analysis of bone structure. In particular, synchrotron radiation microtomography may provide three-dimensional images with spatial resolution as high as one micrometer. Moreover, the use of a monoenergetic synchrotron beam, which avoids beam-hardening effects, allows quantitative measurements of the degree of mineralization in bone samples. Indeed, the reconstructed gray levels of tomographic images correspond directly to a map of the linear attenuation coefficient within the sample. Since the absorption depends on the amount of mineral content, we proposed a calibration method to evaluate the three-dimensional distribution of the degree of mineralization within the sample. First a theoretical linear relationship modeling the linear attenuation coefficient as a function of the hydroxyapatite concentrations was derived. Then, an experimental validation on phantoms confirmed both the accuracy of the image processing tools and the experimental setup used. Finally, the analysis of the degree of mineralization in four iliac crest bone biopsy samples was reported. Our method was compared to the reference microradiography technique, currently used for this quantification in two dimensions. The concentration values of the degree of mineralization were found with both techniques in the range 0.5-1.6 g of mineral per cubic centimeter of bone, both in cortical and in trabecular region. The mean difference between the two techniques was around 4.7%, and was slightly higher in trabecular region than in cortical bone.
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