Effect of geometric magnification on dimensional measurements with a metrology-grade X-ray computed tomography system

Abstract

This paper evaluates the dimensional accuracy of industrial X-ray computed tomography (CT) measurements as a function of the geometric magnification (Mg) used for CT scanning. Two plates of square-shaped geometry with 28 drilled holes, one made of aluminum (48 mm × 48 mm × 8 mm) and a second one made of steel (6 mm × 6 mm × 1 mm), are used as measuring workpieces to test fourteen different magnification axis positions in a metrology-grade X-ray CT system. In addition to measuring the diameter and roundness of each hole, distance measurements between the holes are evaluated—both as uni-directional (center-to-center) and bi-directional (point-to-point or edge-to-edge) lengths. The variance of CT dimensional measurements, with respect to reference data obtained from tactile coordinate measurement machines (CMMs), is studied. It is found that the measurement deviations for uni-directional distances are approximately independent of Mg and mostly within a ±4 μm range. In contrast, for measurements of diameter, roundness, and bi-directional lengths, the deviations between CT and CMM data extend outside the ±4 μm limits and strongly depend on Mg (which is a variable inversely proportional to the voxel size of CT scan, VX). More specifically, decreasing Mg or, equivalently, increasing VX, generally leads to larger deviations in the dimensional data. To include the magnification dependence on the estimations of CT measurement deviations, based on the experimental data presented throughout this paper, the authors propose that the maximum error of CT length measurements can be expressed as Emax=(A+X/B+L/K) μm, with A, B, and K being constant factors (determined for a particular CT measuring setup), L the dimension of the measuring length (in mm), and X the magnification axis position of the CT scanner (also in mm). Whereas the term “L/K” considers error influences from the size of the sample, the term “X/B” accounts for influences from magnification (and voxel size) selections during CT measurement.