Verifying the measurement accuracy for X-ray cone-beam CT scans of objects smaller than 5 mm diameter

Dimensional metrology has become an important and well-established application of industrial X-ray computed tomography (CT). Currently there is an increasing need to use CT-based metrology for objects scanned at very high resolution (< 1 µm voxel size). In order to validate the measurement accuracy of a CT scanner, calibrated length standards are required that match the range of field-of-view (FOV) sizes offered by the scanner. While there are now many lengths standards available for FOV diameters of 50 mm and above [1], so far there are few or no standards that are suitable for a small FOV diameter, and at the same time meet the requirements of guideline VDI/VDE 2617/2630 [2], dealing with CT-based metrology. In order to fit a FOV diameter of less than 5 mm, a length standard was designed in accordance with that guideline, manufactured from a support material and ruby spheres, and tactile measurements were performed with a ZEISS F25 coordinate measurement machine. CT metrology was performed using a ZEISS METROTOM 800, and the results are compared.


Length standard "METROTOM-Check nano"
The newly developed length standard consists of 22 identical ruby spheres attached to a supporting structure made of fused silica (see figs. 1 and 2).The support structure material has a low coefficient of thermal expansion of only 0.6 * 10 -6 1/K.The maximum center-to-center distance of the spheres is 3.6 mm, the height range covered by the spheres is 1.5 mm, given by the height of the central sphere above the plane of the outer sphere ring.Two prototypes were manufactured: one with 300 µm diameter ruby spheres of sphere grade 5, the other with 400 µm sphere diameter of sphere grade 10, both made by Saphirwerk AG.The total number of spheres in the standard is given by the guideline, which requires 7 different spatial directions with at least 5 different measurement lengths in each of those directions [2].Each such measurement length is implemented as the center-to-center distance of a pair of spheres.Note that for a complete determination of the length measurement error E, the probing errors for form (PF) and size (PS) must also be determined.Reference values of the sphere positions and radii were determined using a tactile probe with 300 µm probe sphere diameter.The clearance between the spheres is very small: less than 100 µm for adjacent 400 µm diameter spheres and in the presence of the probe sphere.Hence possible probing paths are severely restricted.At the same time, the force exerted by the tactile probe needs to be as small as possible, to minimize bending of the supports, and prevent breakage.The ZEISS F25 micro-CMM was capable of meeting these requirements, with a probing force of only 5 mN.

Results of CT metrology
The prototypes were scanned on a ZEISS METROTOM 800 130 kV, with a voxel size of 3.54 µm (see table 1 for complete scan parameters).Evaluation of the volumetric data was done with the ZEISS CALYPSO measurement software (see fig. 3).After trend removal (i.e.subtracting a fit line that intersects the origin), the differences between the CT values, and the reference tactile values, for the sphere center-to-center distances lie inside a +/-0.2µm corridor (see fig. 4).Trend removal was required because at this magnification the image scale had not been calibrated independently.The current prototype design yields 7x5 = 35 measurement lengths as required by the guideline, however these cluster around 4 values between 1.2 and 3.6 mm, rather than 5 values as mentioned in the guideline.
Figure 3: CALYPSO inspection plan used to evaluate the prototypes.There are 8 circular virtual probing paths per sphere, with 100 points per path (5% outlier elimination was applied to each path, no additional filtering).
Figure 4: Difference of METROTOM and F25 sphere center-to-center distances after trend removal (for prototype with 300 µm sphere diameter).

Figure 1 :
Figure 1: Model of length standard "METROTOM-Check nano", consisting of 22 spheres.Highlighted in green is a group of 4spheres that are used for 5 different measurement lengths in one spatial direction (0°), with a maximum center-to-center distance of 3.6 mm.There are 6 other, similar groups of 4 spheres each, for a total of 7 different spatial directions.

Table 1 :
Parameters of CT measurement