Exact and efficient computation of noise covariance for fan-beam FBP reconstructions that use rebinning to parallel-beam geometry

2012 ◽  
Author(s):  
Adam Wunderlich ◽  
Frédéric Noo
Keyword(s):  
Efficient Computation ◽  
Parallel Beam ◽  
Beam Geometry ◽  
Noise Covariance ◽  
Parallel Beam Geometry

X-ray Diffraction Studies of Polycrystalline Thin Films Using Glancing Angle Diffractometry

1988 ◽  
Vol 32 ◽  
pp. 311-321 ◽  
Author(s):  
R.A. Larsen ◽  
T.F. McNulty ◽  
R.P. Goehner ◽  
K.R. Crystal
Keyword(s):  
Thin Films ◽  
Deep Penetration ◽  
X Ray Diffraction ◽  
Parallel Beam ◽  
X Ray ◽  
Beam Geometry ◽  
Polycrystalline Thin Films ◽  
Glancing Angle ◽  
Parallel Beam Geometry

AbstractThe use of conventional θ/2θ diffraction methods for the characterization of polycrystalline thin films is not in general a satisfactory technique due to the relatively deep penetration of x-ray photons in most materials. Glancing incidence diffraction (GID) can compensate for the penetration problems inherent in the θ/2θ geometry. Parallel beam geometry has been developed in conjunction with GID to eliminate the focusing aberrations encountered when performing these types of measurements. During the past yearwe developed a parallel beam attachment which we have successfully configured to a number of systems.

scholarly journals Inverse Fourier Transform in the Gamma Coordinate System

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Yuchuan Wei ◽  
Hengyong Yu ◽  
Ge Wang
Keyword(s):  
Fourier Transform ◽  
Coordinate System ◽  
Inverse Fourier Transform ◽  
Rotation Axis ◽  
General Scheme ◽  
Weight Functions ◽  
Projection Data ◽  
Parallel Beam ◽  
Beam Geometry ◽  
Parallel Beam Geometry

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.

D-50 Parallel Beam Geometry After the Hype

2004 ◽  
Vol 19 (2) ◽  
pp. 204-204
Author(s):  
M. Fransen
Keyword(s):  
Parallel Beam ◽  
Beam Geometry ◽  
Parallel Beam Geometry

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

2008 ◽  
Vol 41 (1) ◽  
pp. 124-133 ◽  
Author(s):  
M. Wohlschlögel ◽  
T. U. Schülli ◽  
B. Lantz ◽  
U. Welzel
Keyword(s):  
Incident Beam ◽  
Grazing Incidence ◽  
Photon Flux ◽  
Data Sets ◽  
Parallel Beam ◽  
X Ray ◽  
Beam Focusing ◽  
Beam Geometry ◽  
Parallel Beam Geometry ◽  
Diffraction Patterns

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.

The Sensitivity of Focusing, Parallel Beam and Mixed Optics to Alignment Errors in XRD Residual Stress Measurements

2005 ◽  
Vol 490-491 ◽  
pp. 131-136 ◽  
Author(s):  
Arnold C. Vermeulen
Keyword(s):  
Residual Stress ◽  
Incident Beam ◽  
Peak Position ◽  
Beam Optics ◽  
Parallel Beam ◽  
Stress Measurements ◽  
Beam Geometry ◽  
Position Sensitivity ◽  
Parallel Beam Geometry ◽  
Alignment Errors

The sensitivity of various combinations of optics to alignment errors is investigated. A large number of tests with varying specimen displacements and incident beam misalignments are performed for both line and point focus residual stress optics combinations. This investigation includes experiments with mixed combinations of typical “focusing beam optics” and “parallel beam optics”. It is verified if the peak positions are either sensitive to height errors like for the focusing beam geometry or insensitive like for the parallel beam geometry. The peak position sensitivity is classified for all combinations of incident beam and diffracted beam optics modules.

Вычислительная модель рентгеновской компьютерной томографии с функцией оценки плотности

2021 ◽  
Vol 3 ◽  
pp. 53-65
Author(s):  
С.П. Осипов ◽  
И.Г. Ядренкин ◽  
С.В. Чахлов ◽  
О.С. Осипов ◽  
Е.Ю. Усачёв
Keyword(s):  
Test Object ◽  
Parallel Beam ◽  
X Ray ◽  
Virtual Test ◽  
Beam Geometry ◽  
Estimation Function ◽  
Parallel Beam Geometry ◽  
X Ray Computed ◽  
Mathcad Software ◽  
Test Objects

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.

scholarly journals Misalignments calibration in small-animal PET scanners based on rotating planar detectors and parallel-beam geometry

2012 ◽  
Vol 57 (22) ◽  
pp. 7493-7518 ◽  
Author(s):  
M Abella ◽  
E Vicente ◽  
A Rodríguez-Ruano ◽  
S España ◽  
E Lage ◽  
...  
Keyword(s):  
Small Animal ◽  
Small Animal Pet ◽  
Parallel Beam ◽  
Animal Pet ◽  
Beam Geometry ◽  
Parallel Beam Geometry ◽  
Pet Scanners

Parallel Beam and Focusing X-ray Powder Diffractometry

1988 ◽  
Vol 32 ◽  
pp. 481-488
Author(s):  
W. Parrish ◽  
M. Hart
Keyword(s):  
Lattice Parameter ◽  
Particle Sizes ◽  
Parallel Beam ◽  
Instrument Function ◽  
X Ray ◽  
Experimental Profile ◽  
Beam Geometry ◽  
Parallel Beam Geometry ◽  
Integrated Intensities ◽  
Voigt Function

AbstractComparison of results using synchrotron radiation and X-ray tubes requires a knowledge of the fundamentally different profile shapes inherent in the methods. The varying asymmetric shapes and peak shifts in focusing geometry limit the accuracy and applications of the method and their origins are reviewed. Most o f the focusing aberrations such as specimen displacement, flat specimen and θ-2θ mis-setting do not occur in the parallel beam geometry. The X-ray optics used in synchrotron parallel beam methods produces narrow, symmetrical profiles which can be accurately fit with a pseudo-Voigt function, They have the same shape in the entire pattern. Only the width increases as tanθ due to wavelength dispersion but with higher resolution systems dispersion can be eliminated. The constant instrument function contribution to the experimental profile shape is an important advantage in studies involving profile shapes, e.g., small particle sizes and microstrains, and accurate integrated intensities. The absence of systematic errors leads to more precise lattice parameter determinations.

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