Porosities in gold and the balance wheel spring

Today we focus on the focal spot and bring high resolution to the details.

High resolution in computed tomography (CT) gets achieved by a very small focal spot, a higher magnification, and a well-aligned system with a very accurate rotation axis. But then we come back to the question of having the right kV-class for the object and the material it is made of.

Even without demanding the highest resolution, heavy metals are very challenging for CT. In its extreme, heavy metals like tungsten or gold absorb 225 kV radiation quickly. Using 2 mm Cu as a beam hardening filter, just half a millimeter of tungsten or gold is enough so that 90% of the radiation is mainly absorbed as well as scattered. The 90%-absorption thickness changed dramatically by a factor of 7 to 3.5 mm with 450 kV and 3 mm Sn filter. 3d metals like iron, copper, and nickel are a little bit easier to handle, but because of the object's diameter, it becomes quickly challenging as well. Therefore, 450 kV MesoFocus will offer the perfectly flexible solution for very challenging heavy metals.

Detail detectability

The ability to detect details is often demonstrated with straight lines in a 2D image or with walls in 3D. Such details can be detected far below the spatial resolution, as these details only disappear slowly with the unsharpness of the perpendicular direction to their orientation.

In the case of porosities, detail detectability in CT gets lost near the resolution, as the blurring of three dimensions causes the contrast of a pore to fade fast and even faster in a noisy image. Then, details that should look sharp appear like homogeneous material. That can be seen particularly well when we change the resolution by the focal-spot size.

According to ASTM E2698 as well as simpler calculations, a smaller focal spot allows a higher magnification. The experience shows that you can always magnify a little more than formulas recommend, but this is normally because the focal spots or their profiles are often sharper than stated.

Usually, the magnification can be too low so that it’s going towards the detector resolution. It can be optimal to gain the maximum possible resolution, or the magnification can be too high. If it is too high, unwanted degradation of sharpness and resolution arises again.

Therefore, the optimum magnification also limits the iso-voxel size in Computed Tomography (CT). That shows again the limitation of mini-focus systems since there the voxels are often larger than the indications that can occur.

Porosities in gold

The wristwatch shows a nice example when looking at the soldered connection (lugs) from the watch to the bracelet. For some reason, a lot of porosities appear in the lugs.

Starting with the nominal 350 µm focal spot, a magnification of around 2 is recommended.

According to the nominal values, the resolution should correspond roughly to that of a mini-focus CT. But a direct comparison shows that even the 450 µm focal point of the MesoFocus achieves sharper results than the 700 W 400 µm focal point of the HP11.

Figure 1 shows a crop into the region of interest. The orientation of the cross-section is parallel to the clock face. It shows beside the lugs also a part of the bracelet. To demonstrate the influence of the voxel size, I switched off the interpolation mode of the cross-sectional view.

Fig. 1: CT with 350 µm focal spot of the 450 kV MesoFocus

With this resolution of roundabout 110 µm or 4.5 lp/mm and a voxel size of 75 µm, the image shows some porosities.

That gets a little more detailed by changing to the 250 µm focal spot. The change to 250 µm increases the magnification from 2 to 2.5 and reduces the voxel size from 75 µm to 56 µm. The non-interpolated cross-sectional view becomes subtler and the expected spatial resolution increases from 103 µm to 85 µm (6 lp/mm). Here, we enter the ASTM E2002 D10 resolution requirement of aerospace applications. At the soldering area, larger pores can now be seen with higher contrast and smaller pores become visible. But also with the bracelet mechanism, the spring can now be seen better separately, and instead of gray-on-gray in Figure 1, the movable bolt that holds the lug pen can be seen.

Fig. 2: CT with 250 µm focal spot of the 450 kV MesoFocus

Significantly more resolution and magnification can get achieved with the smallest, nominally 60 µm focal spot. 5.7 times magnification and 25 µm voxel size are so fine that the non-interpolated sectional view can no longer be distinguished from the usual interpolated view.

Here details come to light that could not even be guessed in the other two CT scans. Many small pores are between and around larger pores.

Fig. 3: CT with 60 µm focal spot of the 450 kV MesoFocus

In addition, I arranged a one-by-one comparison of the 60 µm focal spot scan with the previously shown mini-focus CT of the first part. Here, the cross-section is aligned to the soldering plane.

Fig. 4: Comparisson 400 µm 450 kV mini-focus (left) to 60 µm 450 kV MesoFocus (right)

Balance wheel

„Thinner than a human hair, but with a lot of power. “

This is the description of the fine Nivarox (“not variable, not oxidizing”) spring, which is responsible for the clock beat.

The spring appeared as another nice example to show the increase in resolution and how details appear if their size is below the spatial resolution.

Side by side, the 350 and 250 µm CT scans show an increase in sharpness but no real improvement resolving the spring in the balance wheel center.

Fig. 5: Montage 250 µm (left half) and 350 µm (right half) focal spot of 450 kV MesoFocus

That changes visibly with the smallest 60 µm focal spot. The well-winded spiral spring is now clearly visible, as well as the gaps where it is clamped. An additional montage of the cross-sectional view of the CT volume with a micro-focus 2D image shows that the Nivarox spring is even thinner than it appears in the reconstruction. Therefore, one can expect that the spring thickness is below the spatial resolution.

Fig. 6: CT with 60 µm focal spot of the 450 kV MesoFocus

Fig. 7: Montage 60 µm focal-spot CT of the 450 kV MesoFocus with µ-focus 2D insert

A similar increase in recognizability can be expected for very fine cracks, but these are usually much deeper than wide.

In the next blog post, we want to take a look at a medium-sized additive manufactured copper sample.