Electron-optical in-situ metrology for electron beam powder bed fusion: calibration and validation

Additive manufacturing and in-situ ELO monitoring were performed with the in-house developed PBF-EB system ATHENE. Its central component is a 6 kW electron beam gun by pro-beam GmbH & Co. KGaA (Gilching, Germany) that operates with an acceleration voltage of 60 kV. Using the standard configuration, the accompanying deflection system covers a build area of $130\,\times\,130$ mm² and enables deflection speeds above 1000 m s⁻¹. Feedstock material was plasma atomized Ti-6Al-4V ELI powder with particle size of 45–105 μm by Tekna Plasma Europe (Mâcon, France). The process was conducted in a controlled vacuum atmosphere of $3~\times\, 10^{-3}$ mbar helium pressure.

Parts were manufactured through layer-wise repetition of a PBF-EB build cycle that consisted of four major steps. In the first step a powder layer with a thickness of 50 μm was applied using a recoater system. The second step was preheating of the powder with a fast and defocused electron beam to maintain a process temperature of around 740 ^∘C. The third step was selective melting of the current slice cross-section with a focused beam. A standard cross-snake hatching strategy with 90^∘-rotation between layers was used for area melting. Further details on the chosen melting parameters for the two objects are given in the following sections. The fourth and last step was ELO imaging to acquire an image of the build surface before the next powder layer was applied and another run of the build cycle begun.

The ELO imaging step distinguishes the chosen build cycle from current standard PBF-EB build cycles. In this step a low-power electron beam scans linewise over a rectangular area. The kinetic energy of the beam electrons impinging the surface is not fully dissipated into heat but also converted to different kinds of secondary emission. The most important species in the current context are BSE, i.e. primary beam electrons reflected from build surface through elastic scattering with material's atom cores. These electrons may be captured with a BSE-detector and used to create an image in a similar way as performed in scanning electron microscopy. Since the number and direction of BSEs depends on material and topography of the surface, the intensity measured by the detector can be used to obtain an image contrast.

The sensor used for BSE detection was an annular copper plate which was located coaxial to the optical axis of the beam in central position above the build surface. The sensor and signal processing system was initially designed by pro-beam GmbH & Co. KGaA (Gilching, Germany) for applications in electron beam welding. In the current experiment a beam current of 3 mA was used to capture ELO images with a size of 1500×1500 px. The exposure area was set to 115 × 115 mm² for the calibration experiment and to 70 × 70 mm² for the validation experiment, leading to an instantaneous field of view of 77 and 47 μm px⁻¹, respectively. The scan time for all images was set constant at 1.8 s. These imaging parameters are again summarized in table 1.

The purpose of the calibration object was the examination and enhancement of ELO imaging accuracy. The chosen design was a disc-shaped plate with concentric circular walls that had already been used in another investigation [28]. A sketch of the object is depicted in figure 2. The disc had a diameter of 115 mm, a thickness of 1 mm and was molten with a beam current of 25 mA and deflection speed of 10 m s⁻¹. The hatch line spacing was 100 μm. Below the disc there was a columnar support structure with a height of 5 mm that connected the object to the steel base plate of the PBF-EB build job. The upper part consisted of 22 concentric circular walls and a central pin with a height of 1 mm. Between the walls there was a nominal spacing of 2.5 mm. Each circle was molten as single line with a beam current of 5 mA and a deflection speed of 1 m s⁻¹. The central pin was molten with similar beam current and a spot residence time of 1 ms.

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For calibration purposes, the final position of the circular walls in real coordinates had to be determined by external measurement. Therefore the surface topography of the calibration object was measured with an optical 3D-scanner VR-5200 by Keyence Corporation (Osaka, Japan). The scanner works on the principle of fringe projection and is equipped with a movable stage to examine objects exceeding the optical field of view (7.6 × 5.7 mm²). The 2D height profile of the calibration object was measured along x- and y-direction through the center of the object. Precise orientation of the object with respect to the scanner was achieved by using two triangular markers on the base disc indicating the main axes (see also figure 2). The instantaneous field of view of the 3D-scanner was 7.4 μm px⁻¹.

Figure 3 shows the chosen geometry for validation of the in-situ measurement approach. The specimen had a base-area of 10 × 10 mm² and a height of 20 mm. The layer cross-sections were varied every 4 mm by cutting a stepwise increasing part of the cuboid geometry leading to different cross-sections shaped like the letter 'H'. Below the specimen there was a columnar support structure with a height of 5 mm. Choosing the build area center as coordinate system origin, the validation object's xy-centroid was put at a non-central position of x = 10 mm and $y = -10$ mm. The layers of the specimen were molten with a beam current of 6.7 mA, a deflection speed of 2.67 m s⁻¹ and a hatch line spacing of 100 μm. It was manufactured in a PBF-EB build job together with a few other samples which are not relevant within the scope of this manuscript.

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To validate the in-situ determination of dimensional accuracy, the as-built object also had to be measured externally. In contrast to the calibration object where only measurement of one surface was required, the validation object had to be captured in its full three-dimensional structure. Therefore, XCT was used as external measurement method for the validation object. The XCT system was a v|tome|x m 300 by GE Sensing & Inspection Technologies GmbH (Wunstorf, Germany). The x-rays were created with an acceleration voltage of 190 kV and a current of 60 μA. The acquired 2000 x-ray projection images were then used to reconstruct the three-dimensional density distribution with a voxel size of 10.00 μm.

Validation was performed by conducting a comparison between in-situ ELO imaging, XCT slice data and the CAD model in terms of geometrical and dimensional information. Figure 4 summarizes the processing of the geometrical data prior to comparison. Since the data was intended to be compared on a layer level, selection of the correct image from the stack of acquired ELO-images was the first step in case of ELO data post-processing. The image was then calibrated by including the deflection error as determined in the calibration experiment. Thermal shrinkage was considered by adjustment of the assumed pixel size from 46.7 to 46.3 μm. The decrease of 0.77% corresponds to the thermal strain created by cooling from 740 ^∘C to 20 ^∘C as found in literature [29] for material Ti-6Al-4V. To enable a more accurate comparison, the contour of the molten area was then extracted from the image by using a marching squares algorithm which is the 2D-case of the marching cubes algorithm [30]. The calculation was performed using the Python package scikit-image [31]. The algorithm requires a global threshold value to determine the desired interface. The gray value histogram of the ELO image showed a bimodal distribution with two very distinct peaks corresponding to molten material and powder bed. Hence, the required threshold value was simply set to be at 50%, i.e. the middle of the two peak maxima. This value is also denoted as 'ISO-50% threshold' [32]. Due to the non-central position of the manufactured part, consideration of deflection error and thermal shrinkage did not only change the dimensions but also the position of the part. To enable quantitative comparison between the three geometry variations, a translation was applied to the coordinates such as the molten area centroid fitted again its original position.

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In case of XCT data, the reconstructed volume of the as-built part was first registered using the software suite VGSTUDIO MAX by Volume Graphics GmbH (Heidelberg, Germany) to compensate for slight rotation of the part during x-ray scanning. Afterwards, slice images in the xy-plane corresponding to the layers of the PBF-EB job were exported from the XCT voxel data set. The required effective layer thickness was calculated by using the as-built height of the validation object. The XCT slice image related to the desired layer was then also analyzed with the marching squares algorithm to determine the contour of the solid object. Again, the image exhibited a bimodal gray value histogram but a similar threshold in the center of the two peaks resulted in a visual overestimation of the solid volume. Thus, the global threshold was slightly adjusted from 50% to 66.67% between background and material peak to obtain a better result ('ISO-66.67% threshold'). Finally, a coordinate translation was applied to shift the centroid of the solid cross-section to the position indicated by the CAD model.

The third variation was the desired geometry as given by the CAD model. After slicing of the model with the chosen layer thickness, the contours of the required layer were exported for comparison. Since the CAD model was used as common reference system, no further translation of the obtained coordinates was required. The obtained polygons were then compared using the Python package Shapely [33] which is based on the GEOS library [34].

The topographical information acquired with the 3D-scanner was used to investigate the dimensional accuracy of the as-built calibration object. Since the beam deflection system consisted of two deflection yokes in a 90^∘ arrangement, the accuracy along the both main axes in x- and y-direction was evaluated. An overview of the scanned calibration object and the two evaluated axes is given in figure 5(a). The measured height profile along x- and y-direction shows distinct peaks which positions correspond to the position of the concentric circular walls of the calibration object (see figure 5(b)). The measured position of each peak was extracted and compared to the respective target position as given by the CAD model. The local deviation, i.e. the difference between actual and target position, is given for both axes in figure 5(c). Both curves show a positive and approximately linear slope which means that the calibration object was slightly larger than expected. For the most outer circular wall with a target diameter of 110 mm, the error in x- and y-direction was around 0.8 and 1.6 mm, respectively.

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The accuracy of the as-built calibration object was then compared to the accuracy obtained by non-calibrated ELO-imaging. As indicated in figure 1, an important factor that must be considered in this comparison is cooling of the PBF-EB part after the layer-wise build-up. The build process was conducted at 740 ^∘C while the 3D-scan of the as-built object was performed at room temperature. Thus, significant thermal shrinkage of the object had to be included in the evaluation. This was performed by acquiring another in-situ ELO image of the build surface after cooling down of the build job. As shown by the authors in another investigation [28], it is possible to quantitatively deduce thermal shrinkage by evaluating ELO-images acquired at different temperatures.

Figure 6 contains the deviation curves created by thermal shrinkage of the calibration object and derived from in-situ ELO-images for both x- and y-axis. A detailed explanation on this measurement is given elsewhere [28]. To facilitate comparison, the deviation curves obtained from 3D-scanning of the final as-built object (see figure 5(c)) are also given in figure 6. In contrast to the as-built curves, the thermal shrinkage curves possess a negative slope since plain thermal contraction during cooling would lead to an object being smaller than defined in the CAD model. Given this data, it was then assumed that the measured as-built deviation curve at room temperature was a superposition of the actual deviation at processing temperature and thermal shrinkage. This is only an approximation but it is reasonable as long as the deviations are much smaller than the dimensions of the object.

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The approximated deviation curves at processing temperature are also given in figure 6 and are denoted as 'deflection error'. The curves are linear and with positive slopes of 0.0138 and 0.0205 for x- and y-axis, respectively. The curves are steeper than the as-built deviation curves which means that, due to thermal shrinkage, the actual inaccuracy produced during PBF-EB manufacturing was even bigger than measured afterwards by 3D-scanning.

As already indicated by name, the reason for the observed inaccuracy was an inadequate parametrization of the the deflection system. First of all, the beam is deflected by a certain angle while the resulting deflection distance in the build plane depends on the working distance of the electron gun. In PBF-EB, this working distance is usually fixed but has to be set with high accuracy because otherwise a systematic error in beam deflection is created. This absolute error is zero in the center position (i.e. no deflection) and increases linear with higher deflection angle as observed in figure 6. Additionally, deflection in x- or y-direction is controlled by two separate deflection yokes. Within usual fabrication tolerances, the physical properties of the magnetic coils may exhibit variations which are leveled by adjusting the coil input signals. In case the chosen parameters are inappropriate, different accuracies in x- and y-direction will occur as observed with the investigated calibration object.

It is a remarkable yet logical finding that this deflection error as observed for the as-built object is not visible in the in-situ ELO-images. As already stated in another investigation [28] and again displayed in figure 7, the positions of the melt tracks in the original in-situ ELO-image match the target positions as defined by the CAD model rather well. The reason why the determined inaccuracy of the as-built object can not be derived from ELO images is that the required deflection performed during ELO imaging is suffering the same deflection error since it uses the same beam deflection system. In other words: the electron beam that melts a track at an inaccurate position also gathers BSEs at an inaccurate position during imaging and hence the error becomes invisible for ELO imaging.

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Through external measurement and the described evaluation of the calibration object, the deflection error was made visible and could be determined quantitatively. Furthermore, it could be assumed to be constant as long as the PBF-EB machines configuration remained unchanged. This enabled a computational calibration step with the goal of including the actual deviation artificially in any ELO-image, even if the image was acquired in another PBF-EB build job. The images were corrected by mapping the acquired pixel values to their actual spatial position and calculating a new ELO-image at the pixel original target positions through linear interpolation between known pixel values. As can be seen in figure 7(b), the resulting calibrated ELO-images were much closer to the actual situation inside the build chamber and thus a better basis for in-situ evaluation of manufacturing accuracy. However, it should already be stated that this approach is only to be considered a workaround for the current scientific investigation while better solutions for industrial application are discussed later.

To validate the capabilities of in-situ ELO-imaging with respect to prediction of as-built dimensional accuracy, the geometry of the validation object was analyzed as described in the experimental section. Figure 8 shows exemplary image data obtained by (a) ELO imaging and (b) XCT scanning. The chosen layer was the central layer of the uppermost step section of the validation object (z = 23 mm). The direct comparison of the two images demonstrates the significantly higher spatial resolution of the XCT data which enables a detailed display of the surface roughness of the object. The rough contour is also visible in the ELO image of the molten area but is much more fuzzy. To evaluate the dimensional accuracy, the target contour as defined by the CAD model is marked as dashed line for both subfigures. For both images, the molten area seems to exceed the target contour of the object in most regions of the layer. The inaccuracy appears to be quite similar for both imaging methods but a quantitative comparison is difficult using these bitmaps.

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To enable the quantitative comparison, the contour of the solid area was extracted for both imaging methods as described above. Figure 9 shows the polygon comparison for the exemplary layer which was already investigated in figure 8. Each subfigure (a, b and c) compares two of the three different geometry variations. Table 2 contains the quantitative measures related to the investigation.

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Figure 9(a) displays the accuracy of the ELO image with respect to the cross-section obtained from the CAD model. It shows that the molten area does not show severe deviations from the general shape of the target cross-section and the reference area (73.4 mm²) is correctly molten to 99.8%. Only in a few locations and a small area (0.2%) the desired material consolidation is missing. Nevertheless, inaccuracies in the border region of the area are clearly visible. The edges are not straight but exhibit roughness in the xy-plane. Furthermore, the molten area seems to be slightly bigger than aimed for, leading to a shell of excess material (10.0% of the reference area) along the contour of the cross-section. The total agreement between both regions is quantified by using the Jaccard similarity index [35]. As given by equation (1), the Jaccard index J is defined as the ratio between the intersection and the union of region Ω and reference region $\Omega_{ref}$. The norm $\Vert \cdot \Vert$ represents the area of the (sub-)region. Thus, the total agreement between ELO image and CAD cross-section is found to be 90.7%:

$$\begin{equation} J (\Omega, \Omega_{ref}) = \frac{\Vert \Omega \cap \Omega_{ref} \Vert}{\Vert \Omega \cup \Omega_{ref} \Vert}. \end{equation} \tag{ 1 }$$

Figure 9(b) compares the data obtained from XCT scanning to the CAD model. The evaluation shows that the XCT slice image exhibits a higher amount of missing material (1.0%) which is mainly located in one edge region of the part. However, the amount of excess material for XCT scanning (5.9%) is significantly lower than seen for ELO imaging. Thus, the total agreement shows a slightly higher value of 93.5%.

Using the CAD model as a reference only gives information about how accurate the layer is molten with respect to the desired geometry. Similar values obtained for ELO and XCT data do not necessarily result from a high similarity between both imaging methods because deviations might be found in different locations of the molten layer. Hence, the third comparison is drawn directly between the ELO and XCT data where the latter acts as reference area. As shown in figure 9(c) the two very different imaging approaches show a remarkable good agreement. The intersection area is similar to the previous comparisons (99.3%) while the amounts of missing (0.7%) and excess material (5.4%) are relatively low. This results in a high total agreement of 94.2%.

A detailed look on figure 9(c) shows that the high agreement is not a random calculation artifact. Despite the erratic course of the contour, many of its characteristic intrusions and extrusions can be found in both imaging approaches. As a result, the local deviation between ELO and XCT data stays rather small everywhere along the contour. To further characterize the agreement between ELO and XCT data, this local deviation may be calculated as a signed distance for every vertex of the contour. Figure 10 shows the deviation profile obtained from this evaluation. It starts in the upper left corner of the molten area (close to x = 5 mm and $y = -5$ mm) and follows the contour in clockwise direction. Again, it shows that the major part of the deviation is caused by excess, i.e. molten areas which are found in ELO imaging but not in XCT scanning. It also shows that, apart from few extreme values for negative ($-130~\unicode{x03BC}$m) and positive (253 μm) deviation, the greater part of the profile is relatively close to zero with an average deviation of 55 μm. The average absolute deviation of 67 μm is only slightly higher.

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The high agreement between ELO and XCT data was not only found for the exemplary layer but for the major part of the validation object. Figure 11 displays the Jaccard similarity indices of the three pairwise comparisons for all layers of the specimen. The Jaccard index between ELO and XCT data is found to be almost everywhere at around 95%. However, it also indicates a lower similarity in the first layers of the part and in regions where the cross-section is abruptly changing due to the staircase structure of the object. The lower similarity in these regions originates from a lower similarity between the as-built part (i.e. XCT) and the CAD geometry which can not be found in the ELO data. It may be noted that both index curves involving the CAD geometry display a step-wise decrease with changing cross-section geometry. The reason is the increasing contour-to-area ratio of the CAD cross-sections. Since deviations are mainly observed along the contour, the similarity with the CAD geometry decreases with increasing contour length. However, the Jaccard index between ELO and XCT data is hardly affected by this effect which underlines the robustness of the observed similarity.

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Thorough post-processing of the ELO images is crucial for the comparison with XCT and CAD data (see figure 4). As shown for the calibration object, the raw ELO images do not necessarily display the actual part geometry inside the build chamber. In case the deflection system is not parametrized precisely, the cross-sections are molten incorrectly. However, the resulting inaccuracy is not depicted by the ELO imaging system due to its own dependence on the deflection system accuracy. This issue was solved in the current investigation by quantifying the deflection error once and then including it into other ELO images by a mathematical correction. This operation returns much more accurate ELO images with respect to the as-built geometry inside the chamber, as long as the parametrization of the deflection systems remains unchanged. However, the inaccuracy of the manufactured part with respect to the target CAD geometry is not solved with this approach. This limitation was not a problem for the current investigation because its focus was only on the assessment of in-situ metrology capabilities of ELO imaging. The applied workaround enabled usage of already acquired data without the necessity of a re-parametrization for the deflection system and a costly repetition of several experiments. Nevertheless, it should be highlighted that for industrial production where manufacturing of high-quality parts is the main objective, the workaround applied in this investigation is not advisable. Instead, a thorough parametrization of the deflection system should be conducted in advance to avoid errors in the first place. That approach inherits the benefit of improving the accuracy of both the manufactured part and the acquired ELO images.

A second important factor to consider is thermal shrinkage of the part during cooling down of the build job. Caltanissetta et al stated that layer-wise imaging could not capture thermal shrinkage and hence in-situ measurement would not be representative of the as-built part [15]. However, as shown in another investigation [28], thermal strain created during cooling down in PBF-EB can be approximated quite well using data obtained from non-AM literature. Thus, thermal shrinkage was included into the current evaluation since that is the only possibility to validate and apply the approach for multiple layers, i.e. real parts. The thermal strain of −0.77% which was corrected in the current investigation appears to be small and actually only has a small influence on the given result. Nevertheless, this assessment is bound to two specific characteristics of the chosen build job and may not be generalized. First, the investigated distances were rather short due to the relatively small size of the validation object (10 × 10 mm²). For larger parts using the full build area (130 × 130 mm²), thermal shrinkage may create inaccuracies of more than 1 mm. Second, the effect strongly depends on the properties of the feedstock material. Many other metal alloy systems exhibit a significantly higher coefficient of linear thermal expansion (up to a factor 3) than the investigated titanium alloy Ti-6Al-4V. Additionally, the PBF-EB processing temperature which must be adjusted for every material may be much higher (up to 1100 ^∘C) which increases thermal shrinkage during cooling down furthermore. Thus, consideration of thermal expansion can be crucial for making accurate predictions with respect to dimensional accuracy and hence must be included into the evaluation.

The third important factor during post-processing of the ELO images is a suitable translation of the determined coordinates to enable a reasonable comparison. Beam deflection for melting and ELO imaging is supposed to follow the same coordinates system as defined in the CAD model. However, deflection error and thermal shrinkage create a displacement of the molten volume. Since a plain displacement of the manufactured part within the build chamber does not affect its dimensional accuracy, the effect should be compensated for prior to comparison. Hence, to obtain a more accurate result, the translation of the molten area's centroid from its original position was calculated and used to back-translate the entire area to its original position. This analytical operation was favored over other possible approaches (e.g. manual or best-fit registration) because it does not rely on an external reference (e.g. the CAD model) and thus preserves the independence and reliability of the acquired ELO image data.

To conduct the comparison, an iso-contour extraction algorithm was applied to the ELO and XCT image data. This approach was favored over applying the threshold values directly to the pixel data and conducting a pixel-wise comparison as proposed by Wong [24]. The reasons was the goal to minimize artifacts related to very different pixel sizes of ELO and XCT and to avoid information loss related to a grid discretization of CAD data. Edge detection and segmentation was performed by applying a global threshold value which was chosen by calculating the very simple ISO-50% value from the gray-level histogram. Due to the high contrast between molten area and powder bed, as well as the absence of disturbing reflections, the approach nonetheless returned excellent results. This highlights a huge advantage of ELO imaging over common light-optical imaging of the build surface where extensive efforts have to be made to develop robust algorithms for image segmentation [12, 13, 15–17]. Nevertheless, in the future, more sophisticated adaptive thresholding algorithms might also be tested on ELO images to further enhance the quality of surface extraction.

Three comparisons were used to identify deviations between the three geometry variations. The deviations were divided into two classes which are missing and excess material. This distinction is not only useful to analyze the origin of the deviations but also has a high practical relevance. Depending on its location, excess material might be removed by post-processing to obtain high accuracy parts while inaccuracies created by missing material can hardly be corrected.

In total, the investigated cross-section of the validation object was molten quite correctly and it did not exhibit any features with severe deviation. The observed inaccuracy was mainly observed as profile roughness along the contour of the molten area. This may be explained with the non-stationary conditions found in these regions due to changing beam velocity and the complex interface between molten material and the particles of the surrounding powder bed. In comparison with the CAD model, both ELO and XCT data showed a large amount of excess material which was found in a shell-like arrangement around the desired cross-section. The reason for this shell is probably the absence of a beam diameter compensation during melting. Due to its finite diameter of approximately 400 μm, the electron beam overshoots the desired area when its center reaches the contour. The observed excess material shell had a thickness of 200–300 μm which is in well agreement with the half diameter of the beam.

The area and area fraction of the deviation regions were measured to obtain quantitative measures for the accuracy of ELO imaging and the as-built part. It should be noted that the size of these quantities strongly depends on the size and especially the surface-to-volume ratio of the target geometry since deviations were mainly observed along the contour of the molten area. Thus, comparing areas and area fractions is only reasonable for similar target cross-sections, e.g. during optimization of scan strategy parameters. The same holds true for the applied Jaccard Index and the comparable Sørensen-Dice index [36, 37] which were also used in other investigations to assess the performance of image segmentation algorithms [15, 17].

As an alternative evaluation approach, the local profile deviation along the contour was calculated which is less dependent on the size and shape of the geometry. Since it gives the signed distance to the reference geometry for every point along the contour, it may be used to extract the average deviation or extreme values either for the whole part or only selected regions. As shown by Pagani et al, this kind of measure is an excellent base for in-process quality control when the CAD model is used as a reference [16]. The obtained graph resembles a profile roughness plot and may actually interpreted in similar way since the deviation between the contour of the as-built part (XCT data) and the CAD model creates roughness within the xy-plane. Together with the roughness that may be measured along the build direction (i.e. z-axis), it defines the total roughness of the as-built PBF-EB surface. Surface roughness often is an important and critical aspect of AM parts. Since ELO imaging shows a good agreement with the as-built geometry, it might be used for in-situ control and optimization of surface roughness. As shown in the comparison with the XCT slice image, the resolution of the contour profile might be further increased by enhancing the resolution of the ELO image, e.g. by using a smaller beam diameter.

The total agreement between ELO and XCT data is remarkably high but yet well below 100%. Beside the different imaging resolutions, there are additional limiting factors to be considered. First, ELO imaging only depicts the surface of the PBF-EB build job for every layer. As shown in figure 12(a), this surface almost always is remolten with the subsequent layer(s). Therefore, most ELO images only display an intermediate state which affects the final as-built geometry, but not exclusively. This inevitably impairs the accuracy of the predictions made via ELO-imaging, not only in terms of dimensional accuracy but also with respect to internal defects which was already shown in another investigation [25]. Further research is necessary to completely evaluate the prediction capabilities of ELO imaging with respect to the different geometrical features of the parts. As an example, first experiments indicated that the presence of upskin and downskin regions may strongly affect the achievable accuracy. This is also observed in figure 11 where the similarity between ELO and XCT data is significantly lower for the bottom layers and the cross-section transition layers of the validation object. The causes of these deviations are probably thermal stress-induced processes which take place during melting of subsequent layers. As already stated by Caltanissetta et al, thermal stress-induced distortions can hardly be captured by layer-wise imaging [15]. However, it should be noted that thermal stresses are significantly smaller in PBF-EB than in PBF-LB due to lower thermal gradients and cooling rates [38].

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Nevertheless, the deficit in agreement between ELO imaging and as-built part may not only be attributed to limitations of ELO imaging. Also the as-built geometry which is used as reference may only be determined with limited accuracy. During the evaluation, the data obtained from XCT scanning was treated as 'ground truth' for the as-built part. Considering its small voxel size of only 10 μm this was a plausible assumption but only as long as the XCT geometry was treated as a whole. However, the layer-wise comparison with ELO and CAD data required the extraction of single XCT slices. Each of these selected XCT slices was supposed to represent a distinct layer of the PBF-EB build job. The selection process entails some uncertainty since a molten layer has a thickness that exceeds the voxel size of the XCT scan. Furthermore, the effective layer thickness of the as-built part, which is required to relate XCT slices and PBF-EB layers, is not equal to the processing layer thickness of 50 μm. Primarily, the effective layer thickness is affected by thermal shrinkage of the part during cooling down. The new value was estimated by measuring the actual height of the sample and dividing the value by the number of layers. This calculation delivered an effective layer thickness of 49.5 μm which equals a thermal strain of −1%. This value is close to the theoretical thermal strain of −0.77% which was used for correction of the ELO images. Nevertheless, it only remains an estimation and a small error per layer accumulates with increasing layer number. Thus, a precise adjustment and data registration becomes even more important for parts with a larger build height. This estimation results in an uncertainty while choosing the optimal z-coordinate for XCT slice extraction. As shown in figure 12(b), the as-built PBF-EB part exhibits a high surface roughness along the build direction. Its maximum roughness depth is approximately 250 μm. Hence, a small variation in the z-coordinate may shift the contour position within the xy-plane by this maximum roughness depth. A comparison with figure 10 shows that this consideration is in excellent agreement with the observed deviation where a maximum excess distance of 253 μm was observed. Also the predominance of excess material in the comparison between ELO and XCT data may be explained with this approach. As depicted in figure 12(a), the surface roughness along the z-direction is partly created by the curvature of the molten layer due to the melt pool temperature profile. ELO imaging always displays the surface of the molten layer which has the largest extension. On the other hand, the XCT slices are extracted in varying position within the layers due to the aforementioned uncertainty in calculating the respective z-coordinate. Therefore, the size of the molten area in the XCT slice has a high probability of being smaller than its ELO equivalent leading to the observed dominance of excess material in the prediction.

The presented results suggest the application of ELO imaging for making in-situ predictions on the dimensional accuracy. This would give several advantages over conventional approaches. First, there is a big economical benefit because a subsequent measurement of the as-built parts requires high-level metrology equipment and trained operators. This leads to high capital and operating expenditure, especially when using XCT systems. This is the reason why the full inspection of as-built AM parts currently is limited to high-cost applications with elevated quality requirements. In comparison, ELO imaging is very economic since the related hardware is inexpensive and the data record is conducted automatically during the PBF-EB process. Furthermore, ELO imaging enables in-situ quality control, i.e. the detection of errors during processing. Compared to post-process quality control, this may spare additional resources by enabling early intervention through adjustment or deactivation of low-quality parts.

XCT scanning is currently seen as the most versatile method to inspect as-built AM parts [5] and may return very accurate measurements. Also the current investigation has shown that the obtainable resolution is much higher for XCT than for ELO imaging. Therefore, for critical parts, an additional XCT scan of the as-built part may still be demanded to identify small-scale defects. However, it must be noted that the resolution of XCT is limited by the attenuation of the x-rays used for scanning. Larger geometries and higher material densities lead to a strong attenuation which must be compensated by increasing the XCT power. This usually leads to an increasing x-ray spot size and thus decreasing spatial resolution. Additionally, due to a limited x-ray detector size, the distance between sample and detector must also be increased for larger geometries which reduces magnification furthermore. In the current investigation, the validation object was relatively small (10 ×10 × 20 mm²) and the density of Ti-6Al-4V is rather low (4.4 g cm⁻³) compared to other alloys used for metal AM. This conditions enabled a low XCT voxel size of 10 μm. However, realistic PBF-EB parts may possess dimensions above 100 mm and common alloys in use show densities above 8 g cm⁻³. Together with the non-linear character of x-ray attenuation, this leads to a drastic decrease of the achievable XCT resolution.

The spatial resolution of ELO imaging mainly depends on the diameter of the electron beam and thus is expected to be much less susceptible to the size of the part. Additionally, the density of the feedstock material does not affect the quality of the ELO images. It may therefore be expected that ELO imaging could outperform XCT scanning for large-scale or high-density parts which are manufactured for technical applications. As alternative to XCT, light-optical 3D scanners might be less susceptible to size and density of the part. However, these devices are not capable of fully inspecting complex parts with undercuts and often suffer problems when measuring reflective metallic surfaces. Due to its layer-wise approach, ELO imaging is capable of measuring undercut regions, independent of geometry and size of the part. Additionally, the ELO images are free of reflections and instead show a high contrast between molten surfaces and powder bed which enables reliable and robust measurements.