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

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 (CT2), 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.