Resolution Enhancement by Variable Zoom Trajectory in X-Ray Computed Tomography

X-ray computed tomography (CT) emerged as an efficient tool for comprehensive 3D inspection of various types of samples. Due to its ability to analyze both inner and outer features of objects with high resolution down to micron and submicron scale, it has become an essential technology for non-destructive inspection of defects in various industrial fields as well as in the scientific domain. For example, Li-Ion batteries may contain various types of defects such as impurities in the cathode and anode, overhangs, or delamination which reduce the battery performance and contribute to rapid aging [1, 2]. Also, other electronic parts may suffer from defects such as voids in solder joints which may lead to component failure [3‐6].

Challenges appear when scanning complex samples of large dimensions which are difficult to fit into field of view (FOV) of CT scanner. Even if focusing only on part of the object with region of interest (ROI) scanning, available magnification and therefore spatial resolution can be limited when using standard circular trajectory, because the object could collide with CT system components, or the ROI is still too large to fit in the detector under desired magnification. For example, when scanning objects of cylindrical shape and high aspect ratio, users can decide to move the sample closer to the source to increase magnification and the resulting resolution. However only part of the sample will be scanned. Fitting the whole object in the detector FOV could on the other side decrease the resolution. Other example of challenging object are those of planar shape like electronic boards, pouch battery cells, or composite plates, which are often analyzed for the presence of various defects [7‐9]. Several techniques were already proposed to increase resolution and extend the scanning FOV in both longitudinal and lateral directions, however, their applicability depends on the overall object dimensions, position and dimension of the ROI, CT scanner’s geometry and the available degrees of freedom during acquisition.

The FOV can be extended longitudinally by stitching multiple circular scans [10], employing helical trajectory CT or similar trajectories like ellipse-line-ellipse [11‐13]. Such techniques can be used to improve the resolution and image quality of CT scans for samples like cylindrical batteries or additive manufactured components while acquiring data for the whole ROI [14, 15]. To extend the FOV laterally and improve resolution, a detector offset can be used [16‐18]. However, in many scenarios, such as analyzing defects in parts of large flat objects as electronic circuit boards, the resolution is limited mainly by the smallest achievable source-to-object distance (SOD) instead of the detector size. The sample cannot be moved close enough to the source to reach the geometrical magnification necessary for the required resolution, because the flat object would collide with the tube during 360° rotation. In such cases, limited angle tomography, laminography or tomosynthesis techniques could be used to avoid collision while utilizing higher geometrical magnification. These approaches may enhance the resolution but will lead to image artifacts due to incomplete information from some angles [19, 20]. Missing data in these types of scans can be completed by combining multiple scans with different trajectories or magnifications as proposed in [21], which may however lead to a significant increase in time costs for the whole measurement.

It is also possible to obtain projection data from all directions in a single scan and increase the information gain by changing the SOD during the object rotation to avoid collisions and increase the magnification in some of the projections. An elliptical trajectory was proposed in medical CT to allow closer following of the contours of the human body, but the effects were tested only on small simulated dataset of 64 projections and did not focus on evaluation of resolution improvement [22]. Dabravolski et al. [23] proposed moving the object as close as possible to the source for each projection while avoiding truncation of the whole object’s projection by detector edges. They computed variable zoom trajectory for a piece of pencil using an outer hull estimated from a circular CT scan reconstruction as an input and demonstrated that slightly higher level of detail can be achieved. Their study was however limited to only one real experiment with subjective evaluation of results. Proposed algorithm also does not consider focusing only on a part of an object (ROI). Nikishkov et al. [24] applied a variable zoom technique together with a modified Feldkamp-Davis-Kress (FDK) reconstruction algorithm to improve resolution of ROI (impact area with defects) in composite plates. They used an analytical formula to generate the trajectory using information about sample width and length and included the safety offset defined by a user. The formula was however derived assuming rectangular object and ROI in object’s center. It could therefore lead to unnecessary low magnification in projection from some angles in case of more complex shape and position of an object and an ROI. The performance was evaluated by measuring the sharpness of the material interface, dimensions of holes and attached wires showing improvement over conventional circular CT. Sharpness improvement was shown as well in the reconstruction of the composite plates, although part of the projections was acquired with lower magnification. Some manufacturers of CT systems offer an option to acquire data with variable zoom trajectory, determined from the user-specified boundary of the object and position of ROI [25].

In this work, we present an automatic algorithm for generating variable zoom trajectory for arbitrary position and shape of object and ROI inside to maximize magnification in each projection. We demonstrate the improvement of resolution on two realistic samples and two reference objects. Due to their flat and elongated shape, the realistic samples – printed circuit board (PCB) with a BGA (ball grid array) and rectangular prismatic cell – present a challenge for conventional circular CT measurement when high resolution is required in ROIs. They are therefore suitable for scanning with variable zoom trajectory. Because the magnification in projection is higher from some angles in variable zoom acquisition, we expect that the resulting quality and resolution have directional dependency in the reconstructed data. We quantify the anisotropic spatial resolution using modular transfer function (MTF) calculated from CT data of a precision ruby sphere, and interpolated spatial resolution (iSR_CT) values obtained using a bar pattern phantom.

A typical task for the analysis of the PCB used in this study is defect detection in BGA and in copper tracks through the board. Using a conventional circular scan, we were able to measure the board with SOD = 103 mm (CLR), corresponding to 7.5 × magnification, while the SOD for the variable zoom acquisition (VZM) varied from 28.3 to 103 mm increasing the magnification up to 27. Even with the circular trajectory, we were able to reveal many defects in the solder balls. Increasing magnification during the variable zoom scan led to improvement of resolution of these defects as is shown in Fig. 4. The improvement is demonstrated in the details of three selected defects (Fig. 5). The smallest of the selected defects (a) has dimensions of approximately 60 × 30 × 50 µm³.In the CLR, the defect is barely visible to a human observer. It is possible to distinguish a dip in a gray value line profile over the defect cross-section, but due to blurring its width appears two times larger than in the VZE scan. VZE trajectory also improved the sharpness of the copper track on the board, however, no notable defects were found (Fig. 4f, g).

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With conventional circular trajectory, we achieved 9 × magnification, while with the variable zoom trajectory the magnification in projections reached up to 24. In the circular scan we were able to distinguish layers of cathode, anode, copper current collector in anode (Fig. 6c), and some polymer separators (Fig. 6a). With the VZE2 trajectory, we observe a higher-resolved polymer separator (Fig. 6b) and we are also able to resolve the aluminum current collector inside the cathode, as it can be seen in the gray value line profiles in Fig. 6.

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Although the prismatic cell and PCB scans showed improvement by variable zoom trajectory, the evaluation is to some extent subjective, and it is difficult to quantify it on those samples. Therefore, we conducted a quantitative evaluation using two reference objects. We used the object parameters of the PCB and generated a circular trajectory with the smallest and highest SODs used in the VZM trajectory (CLR and CHR trajectory) and we also generated a variable zoom trajectory for ROI positioned closer to the edge of the sample (VZE). We applied these four trajectories for scanning the bar pattern and ruby sphere phantoms.

CT reconstructions of bar pattern phantom are visualized in Fig. 7. With the CLR trajectory, we can barely distinguish line patterns of 30 µm width, while with the VZM trajectory we can distinguish patterns down to 10 µm in y-direction oriented patterns or 20 µm in the x-direction. We quantitatively evaluated the contrast dips in the line profile through patterns which resulted in iSR_{CT, x} = 29 µm and iSR_{CT, y} = 25 µm for CLR scan, while with the VZM trajectory, the resolution was improved to iSR_{CT, x} = 21 µm and iSR_{CT, y} = 5 µm (Table 2). In this case, the line patterns in the y-direction are reconstructed using projections collected with higher magnification (up to 27 ×) while in the x-direction the magnification is lower (down to 7.5 ×) leading to the anisotropy in resolution. The situation is different when the ROI is positioned more to the edge of the object such as in the case of VZE trajectory. Here we can obtain more than 180° rotation with high magnification projections which leads to even more improvement in resolution in x-direction where iSR_{CT, x} = 5 µm. This makes the resolution from the VTE scan reach almost to level in the high-resolution circular scan although we can still observe lower resolution on the x-direction 10 µm pattern. It is visible also in the dip measurement (Fig. 8) which is 65% for CHR trajectory, 57% for VZE in the y-direction but only 39% for VZE in the x-direction and 44% for VZM in the y-direction, while for VZM in x-direction the 10 µm pattern could not be measured at all.

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We also analyzed the performance of different trajectories by evaluating the MTF on ruby sphere measurement and calculated its 10% frequency to characterize the resolution. MTF charts are shown in Fig. 9 and MTF_10% values in Fig. 10 and Table 3. The highest resolution was achieved with CHR trajectory which led to MTF_10% from 78 and 82 lp/mm. As the phantom was measured relatively close to the source, we observed an edge enhancement effect. It is assumed to be caused by phase contrast, leading to enhanced contrast in structures of certain sizes which is demonstrated in the MTF as a maximum at higher frequency instead of at zero as in other cases. The lowest resolution was obtained with the CLR scan leading to MTF_10% = 23 lp/mm. Both variable zoom scans showed improvements in resolution compared to the CLR scam. In the VZM scan the MTF_10% reached up to 56 lp/mm in Q4 and 39 lp/mm in Q2, while in Q1 and Q3 the MTF_10% was comparably lower with 28 lp/mm. Again, it showed an anisotropy due to varying magnification in this trajectory. An even higher resolution was achieved with VZE trajectory leading to MTF_10% from 54 to 69 lp/mm, demonstrating a lower difference of resolution in different directions due to a larger portion of projections being acquired with similar magnification.

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We point out that although the MTF is obtained by evaluating a large number of pixels around the sphere circumference or in our case its sections, it still can be sensitive to image noise and other influencing factors during measurement. The MTF for both the Q4 and Q2 sections of the VZM scan has a similar shape, however, it is getting almost monotonous around 10% value which leads to a significant difference (more than 25%) in the MTF_10% values. Common practice is to use this method for performance checks of CT systems to allow for the optimization of acquisition parameters and higher tube power during the measurement which reduces the noise. Here, we reduced the power to keep the spot size small enough to avoid blurring in the projected image, which would neglect the resolution gained by using higher magnification. Similarly, the evaluation of the bar pattern phantom was more challenging due to relatively noisy CT data. ASTM E2576 is designed for the characterization of detectors from radiographs. These can be more easily optimized to reduce noise by increasing exposure and averaging, which would however need to be multiplied by a number of projections used in CT scans and therefore require significantly higher time costs for CT data evaluation. Also commonly used duplex-wire type IQIs [28] use wire pairs with smaller steps between the width of different patterns, it is therefore easier to satisfy the recommendation to measure two line pairs under 20% dip to obtain the reliable value of iSR. We could not satisfy this recommendation in any of our measurements as the bar pattern used in our experiments contained line patterns in the measured range with 5 µm steps. This resulted in iSR_CT values of 5 µm, which were the closest line patterns with zero measured dip, but these values are also less than utilized voxel size. It would be beneficial to use a phantom with smaller steps between line-pair widths to be able to capture more realistic values, which in this case would probably lie between 5 and 10 µm.

All our measurements used the same total number of projections (2300) to avoid number of projections as a possible influence factor. This number was selected according to the manufacturer’s recommendation for the CHR scan. For the CLR scans with lower magnification and ROI covering a smaller portion of the detector, we however could per the manufacturer’s recommendation use a lower number of projections without significant resolution loss. We can therefore assume that the number of projections or more specifically the sampling angle between projections could be also adjusted in variable zoom scans to reduce the time cost. However, no specific recommendations for this type of trajectory exist in current literature according to our knowledge and it is therefore a suitable topic for future research. In our algorithm we also considered only simplified 2D geometry of the CT system and object. It was sufficient to demonstrate capabilities of the variable zoom trajectory, but the improvement could be made to consider 3D shape of the object and shape and real time position of CT system components, leading to more robust collision protection and to even better resolution.

In this paper, we presented an automatic algorithm to generate variable zoom trajectory to maximize magnification in X-ray projection for CT scan of ROI in the sample. The generated trajectory depends on the shape, and dimensions of the whole object, position and dimensions of ROI and CT system geometry. We measured two realistic samples which are challenging for conventional CT measurement due to their flat shape: PCB with BGA and prismatic cell focusing on ROI positioned approximately in the middle of these objects (BGA array and corner of electrode stack). In both cases we were able to achieve higher resolutions, specifically improving defect resolution in solder balls in PCB and resolution of various layers in the electrode stack of the prismatic cell.

To quantify the improvement of resolution we measured MTF from ruby sphere scan and interpolated spatial resolution using bar pattern phantom. With variable zoom trajectory, we were able to achieve up to 5 × higher iSR_CT and up to 3 × higher MTF_10% compared to conventional circular scan. The resolution in the reconstructed volume is however directionally dependent. Resolution is higher in directions, which are reconstructed using higher magnification projections. Overall, the resolution depends on the magnification, which is possible to achieve from different directions, which is related to the object’s shape and shape and position of the ROI.

Both methods of quantitative evaluation of resolution described in ASTM standard needed to be modified for the scope of this paper, especially due to challenges brought by relatively noisy CT data. There is space for further development of methods, guidelines, and reference objects to characterize spatial resolution in CT data.