Abstract
The task of determining the geometry of a cone-beam CT scanner with flat panel detector and circular/spiral source trajectory is considered. Accomplishing this task implies analyzing projections of a set of points referred to as calibrating set or calibrating phantom. We take advantage of the fact that observed coordinates of a point’s projection are rational functions of the point’s location. Unknown coefficients of these functions can be recovered exactly from six projections of the point. Location of the source as well as position and orientation of the detector are determined in the scanner reference frame, which is constituted by rotation axis and central plane of the scanner. Two different projections of a calibrating set are enough to solve the task if the source trajectory is a circle. In applications where a shift of an object transversally to the central plane is required, two additional projections have to be collected in order to identify the direction of the shift. The developed formalism becomes especially simple when the detector is aligned with the rotation axis. In this case four projections of a single calibrating point rotated successfully about the rotation axis are sufficient. The error analysis carried out in the paper shows that the magnitude of deviation from the true values is of the order of the magnitude of measurement errors.
Highlights
In the computer tomography data are collected in form of integrals of a quantity of interest, e.g. the attenuation coefficient, measured over rays crossing an investigated object
The scanner reference frame Oxyz was defined as the one with the z-axis being rotation axis
The displacement of the detector consists of two successive steps: 1) parallel carry in which the reference point of the detector is moved to location R = (Rx, Ry, Rz ); 2) rotation at angles β and γ about the u-axis and the w-axis respectively, where the w-axis is normal to the detector
Summary
In the computer tomography data are collected in form of integrals of a quantity of interest, e.g. the attenuation coefficient, measured over rays crossing an investigated object. Correct associating the collected data with rays is crucial for the quality of the reconstruction and is possible only if a scanner’s geometry is known. As scanner’s geometry one refers to a set of system parameters describing a spatial configuration of the scanner’s essential components which are a source focus, a detector and a rotation stage designed for rotating an object under study. Relative to the rotation stage a cone beam CT scanner, regarded as a mechanical system, has nine degrees of freedom, three for the source location, three for the detector position, and three for the angular orientation of the detector. There are seven kinematically independent system parameters which have to be estimated
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