Вычислительная модель рентгеновской компьютерной томографии с функцией оценки плотности

A computational model of X-ray computed tomography with a density estimation function in the parallel beam geometry is proposed. The model includes blocks for simulating and correcting sinograms and reconstructing slices of test object. When generating sinograms, the parameters of the test object, source and detector of X-ray radiation are taken into account. Algorithms of simulation are implemented in the MathCad software and are tested on virtual test objects.

Effects of Misalignment of Parallel Beam Optics on Thin Film Stress Analysis

Collecting reliable data is crucial in the research of residual stresses in thin films using X-ray diffraction. The parallel beam geometry has advantage of reliability compared to focusing beam geometry. Though care must be taken to the alignment. A small alignment error may cause a significant error in the stress value. We will show the sensitivity for the misalignment of the parallel beam optics, discuss requirements on hardware alignment and demonstrate a software correction for the presence of remaining hardware errors.

An analytical iterative statistical algorithm for image reconstruction from projections

The main purpose of the paper is to present a statistical model-based iterative approach to the problem of image reconstruction from projections. This originally formulated reconstruction algorithm is based on a maximum likelihood method with an objective adjusted to the probability distribution of measured signals obtained from an x-ray computed tomograph with parallel beam geometry. Various forms of objectives are tested. Experimental results show that an objective that is exactly tailored statistically yields the best results, and that the proposed reconstruction algorithm reconstructs an image with better quality than a conventional algorithm with convolution and back-projection.

Inverse Fourier Transform in the Gamma Coordinate System

This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.

XRD total pattern fitting applied to study of microstructure of TiO2 films

New XRD total pattern fitting software MSTRUCT was used to study the microstructure of magnetron-deposited TiO2 thin films. MSTRUCT is an extension of the FOX program for structure determination from powder diffraction data. MSTRUCT makes corrections for refraction and absorption, residual stress, and preferred orientation that are necessary for thin-film analysis using the parallel-beam geometry and an asymmetric detector scan with small angles of incidence. The program also corrects for crystallite size broadening in terms of log-normal distribution, two models of strain (phenomenological and dislocation models), as well as the influence of stacking faults in the most common cubic and hexagonal structures. The microstructure results obtained by this study show that during crystallization of the amorphous TiO2 films, tensile stresses were generated resulting in anisotropic shifts of diffraction peaks. This was confirmed by in situ crystallization and direct stress measurements. The consideration of the stress effect in terms of the weighted Reuss-Voigt model improved the fits significantly. The stresses were found to depend systematically on the TiO2 film thickness, and their values determined by total pattern fitting agree well with the values measured directly by XRD stress analysis.

Application of a single-reflection collimating multilayer optic for X-ray diffraction experiments employing parallel-beam geometry

Instrumental aberrations of a parallel-beam diffractometer equipped with a rotating anode X-ray source, a single-reflection collimating multilayer optic and a parallel-plate collimator in front of the detector have been investigated on the basis of standard measurements (i.e.employing stress- and texture-free isotropic powder specimens exhibiting small or negligible structural diffraction line broadening). It has been shown that a defocusing correction, which is a major instrumental aberration for diffraction patterns collected with divergent-beam (focusing) geometries, is unnecessary for this diffractometer. The performance of the diffractometer equipped with the single-reflection collimating multilayer optic (single-reflection mirror) is compared with the performance of the diffractometer equipped with a Kirkpatrick–Baez optic (cross-coupled Göbel mirror) on the basis of experimental standard measurements and ray-tracing calculations. The results indicate that the use of the single-reflection mirror provides a significant gain in photon flux and brilliance. A high photon flux, high brilliance and minimal divergence of the incident beam make the setup based on the single-reflection mirror particularly suitable for grazing-incidence diffraction, and thus for the investigation of very thin films (yielding low diffracted intensities) and of stress and texture (requiring the acquisition of large measured data sets, corresponding to the variation of the orientation of the diffraction vector with respect to the specimen frame of reference). A comparative discussion of primary optics which can be used to realise parallel-beam geometry shows the range of possible applications of parallel-beam diffractometers and indicates the virtues and disadvantages of the different optics.

An Efficient Estimation Method for Reducing the Axial Intensity Drop in Circular Cone-Beam CT

Reconstruction algorithms for circular cone-beam (CB) scans have been extensively studied in the literature. Since insufficient data are measured, an exact reconstruction is impossible for such a geometry. If the reconstruction algorithm assumes zeros for the missing data, such as the standard FDK algorithm, a major type of resulting CB artifacts is the intensity drop along the axial direction. Many algorithms have been proposed to improve image quality when faced with this problem of data missing; however, development of an effective and computationally efficient algorithm remains a major challenge. In this work, we propose a novel method for estimating the unmeasured data and reducing the intensity drop artifacts. Each CB projection is analyzed in the Radon space via Grangeat's first derivative. Assuming the CB projection is taken from a parallel beam geometry, we extract those data that reside in the unmeasured region of the Radon space. These data are then used as in a parallel beam geometry to calculate a correction term, which is added together with Hu’s correction term to the FDK result to form a final reconstruction. More approximations are then made on the calculation of the additional term, and the final formula is implemented very efficiently. The algorithm performance is evaluated using computer simulations on analytical phantoms. The reconstruction comparison with results using other existing algorithms shows that the proposed algorithm achieves a superior performance on the reduction of axial intensity drop artifacts with a high computation efficiency.