A straightforward and analytical method for precise X-ray CT magnification correction

Abstract

X-ray Computed Tomography (XCT) has evolved over the last two decades from a medical imaging device to an industrial tool for dimensional metrology and quality control. Employing XCT for these purposes relies on the ability to generate an accurate 3D representation of the scanned object. An essential component of this is inputting the exact geometric magnification into the reconstruction algorithm, where failure to do so results in inaccurate dimensions, distortions, and/or image artifacts. Here, we propose a simple and accurate approach to correct the magnification of a rotation stage based XCT system using a single spherical reference sphere of well-known size. The method uses geometric relationships developed between the source, rotation stage, and detector to relate the sphere's position based on projection edges at three fixed locations on the rotation stage. The typical projection edge is difficult to locate as it is obscured by the air-to-object gray value gradient. Here, the precise edge locations are found through the convergence of several geometrically derived equations describing the sphere's edges from different perspectives. The results indicate that the method repeatedly delivered micron-level determination of geometric magnification, resulting in micron-level precision in dimensional reconstruction. The method is simple and easy to employ, without the need of multiple projections with a complex phantom or the use of a secondary instrument. It is simple and rapid enough to be performed on a scan-by-scan basis for any rotation stage based XCT instrument.