Measurement of the X-ray computed tomography instrument geometry by minimization of reprojection errors—Implementation on simulated data

Abstract

The X-ray computed tomography (CT) measurement process suffers from a variety of error sources including geometrical misalignments of the CT imaging components: X-ray source focal spot, rotation stage, and X-ray detector. Effective correction of these misalignments demands accurate measurement of the instrument geometry. A common method to measure geometrical parameters involves radiographically imaging a reference object consisting of several high X-ray absorption spheres. The resulting projection images are used to solve the CT geometry of the instrument. Geometrical parameters can be solved either analytically or by minimization of reprojection errors. In this study, the minimization technique is chosen over analytical methods due to the relative versatility in its practical implementation. Various precautions must be taken when using minimization techniques and these are discussed. Errors in the data acquisition and subsequent minimization procedure introduce errors in the measured geometry and are investigated here. The geometrical measurement procedure is performed on simulated data using the Computed Tomography Calibration Tube (CT 2), a reference object that was designed to reduce sphere overlaps in the projected images while at the same time broadening the distribution of projected spheres across the detector area. It should be noted, however, that the proposed procedure can be implemented with any reference object consisting of high X-ray absorption spheres, provided the coordinate positions of the sphere centers in a local frame are known. Residual errors between the true (simulated) and measured geometrical parameters are shown to be negligible from tomographic reconstruction of datasets acquired in the presence of these residual errors.

X-ray Computed Tomography InstrumentPerformance Evaluation, Part I: Sensitivity to Detector Geometry Errors

“…1 along with the coordinate system employed. The geometry errors considered in this paper and the coordinate system employed are based on Ferrucci et al [13]. The origin of the global coordinate system is located at the source, O.…”

Measurement of the X-ray computed tomography instrument geometry by minimization of reprojection errors—Implementation on experimental data

“…The following description of the coordinate convention is supplemented by the diagram in figure 1, which also includes the parameterization of the reference object position and orientation. Coordinate conventions in this study are chosen to correspond to previously used conventions [5]. A right-handed global Cartesian coordinate system is fixed on the X-ray source focal spot.…”

“…The reference object presented in [4] is used in this experimental study and is briefly discussed here. It should be noted that the geometrical measurement procedure, which is described in more detail in [5], can be implemented with any sphere-based reference object. The CT 2 reference object consists of = 48 high X-ray absorption spheres of 2.5 mm diameter fixed to a hollow, cylindrical carbon fiber support (figure 2).…”

“…Unlike analytical methods, minimization does not require precise a priori knowledge of the position or orientation of the reference object in the instrument coordinate frame. In this study, the global minimization technique described in [5] is applied and is briefly described below.…”

“…The geometrical measurement procedure is based on the least squares estimation of a set of geometrical parameters in a CT ray-tracing model. The development of the reference object (named the Computed Tomography Calibration Tube-CT 2 ) is presented in [4], while the geometrical measurement procedure is introduced and applied to simulated data in [5]. It should be noted that the geometrical measurement procedure can be implemented with any other sphere-based reference object, provided the sphere center positions in a local coordinate frame are known, e.g.…”