Investigation of the Independence of the Best Assembly Orientations With Respect to X-ray Source Parameters in Industrial Computed Tomography

Industrial computed tomography (CT) is a proper tool for extracting both internal and external geometry in one measuring procedure without destroying or rebuilding an assembly. The diversity of assemblies and unique measurement requirements demand an expert user to be able to determine appropriate CT setup parameters. Recent publications have concentrated on the automatic choice of the CT setup parameters or on the determination of features to qualify the chosen setup parameters. Setup parameters consist of X-ray source parameters (i.e., voltage, current, and exposure time), a number of projections, a source-to-object distance (SOD), and an assembly orientation. For multi-material assemblies, it is advantageous to combine two different energies from one or two X-ray sources. Beneﬁts of this combination are a reduction of artifacts, caused by a high absorbing material, and a increased resolution of the CT acquisition (i.e., the combination of high-voltage and low voltage-micro targets). On the basis of previous works, the assembly orientation depends on other CT parameters and requires a correction between measurements with different energies. However, to avoid additional uncertainties due to the fusion of CT volumes, the assembly orientation in the CT system should remain constant for both of the measurements. This study considers the independence of the best assembly orientation tendency and X-ray source parameters. To test the concept, the authors produced CT acquisitions of a multi-material assembly (a polyoxymethylene (POM) cube with two aluminum cylinders) in four different assembly orientations. The choice of assembly orientations was based on the sorted list of minimal required energy. The two sets of X-ray setup parameters that were chosen for the experiment were maximally distant from each other. The concept was validated by statistical analysis of the standard deviations on 48 features of the assembly. The results demonstrated that the group with the best assembly orientations is independent of the X-ray source parameter sets.


Introduction
Modern assemblies have tight tolerance and combine various materials [1,2].To reduce the CT artifacts and introduce the dimensional measurements to all of the involved materials, special measurement techniques are required.Researchers have simulated the CT system with the aim to define the best X-ray source parameters.Some works have concentrated on the contrastto-noise (CNR) ratio of reconstructed volume with respect to a single point on the assembly surface, while others have used neuronal networks to predict the favorable CT measurement parameters [3,4].These studies did not analyze the assembly orientation along x-and y-axis as a part of the set of CT parameters (see Figure 1).10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020idea behind their studies was to simulate the CT system with respect to a penetration length and assembly faces perpendicular to the rotation axis (i.e., bad faces).An average and a maximum penetration lengths through all projections were calculated for each of considered assembly orientations.The assembly orientations with the smallest combination of the average and the maximum value and without bad faces, were defined as the best possible ones.The investigated concept did not suitable for multi-material geometries, because the penetration length requires a weighting factor with respect to attenuation coefficients, which depend not only on the material itself but also on the measuring energy (see chapter "Orientation Search").Ametova et al. considered the cone-beam artifacts to identify the most suitable assembly orientation for the known assembly model [8].The method seemed to be effective in defining the bad faces and is GPU-compatible.However, it did not assume the multi-material assemblies and beam hardening.One of the up-to-date techniques, authored by Herl et al., recommended that the multi-material assembly should be measured in two different assembly orientations [9].In this case, beam-hardening artifacts influenced different assembly areas by different assembly orientations.Data fusion was performed by sinogram merging.This approach required additional time in the case of manual assembly orientation changing, and a special marker for the correct fusion of measurement volumes.However, their work did not consider artifact reduction due to other X-ray setup parameters or due to other set of measured assembly orientations.One of the possible solutions for multi-material assemblies is a multi-spectral CT measurement.The assembly orientation of the assembly and the source-to-object distance (SOD) remains stable for both low-and high-energy measurements to ensure the correct fusion of the reconstructed volumes without any additional markers (see Figure 1).The energies for this approach must be maximally different but sufficient to radiograph the assembly.Therefore, the best possible assembly orientation cannot be determined based on the minimization of the measurement energy, as has been done in previous studies [10][11][12].In addition, simple minimization of the penetration length is unsuitable for multi-material assemblies.The aim of the current work is to test whether the best assembly orientations remain constant by changing the X-ray setup parameters.The following chapter demonstrates how the tested assembly orientations and X-ray setup parameters were determined and how the authors propose to weight the penetration length of different materials for further research.The last chapter validates the independency of the best assembly orientations' tendencies and investigates whether the assembly orientations' tendencies vary when the X-ray source parameters are changed.

Orientation Search
The determination of the measured assembly orientations is based on a ray-tracing simulation of the CT system.In accordance with the Lambert-Beer law (Equation 1), the attenuation of the beam intensity (I) depends on the projection integral (Pro j(E)) and differs depending on the X-ray photon energies (E) .
where I(E) and I 0 (E) are the X-ray beam intensity after and before the interaction with the assembly.2).
Because of the dependency of the projection integrals on the mass attenuation coefficient, this factor needs to be considered by weighting the different materials for multi-material assembly.For the photon energies essential for the study (under 225 keV because of the limitations of the available CT system, and under 450 keV for future works), linear attenuation of the material is dominated by photoelectric absorption and Compton scattering (see Equation 3).
where k i is a shell constant, Z i is an atomic number and A i is an atomic weight of the i-th material, hν is an energy of an X-ray photon, N A is the Avogadro constant, n el is a density of a weakly valence electron in outer shell and σ Compton is a total cross-section for Compton scattering [13].McAlister demonstrated, that for photon energies under 450 keV and for low atomic weight materials (e.g., iron, aluminum, and steel), the atomic number and material density of the element play a key role in the calculation of the attenuation coefficient [14].Therefore, the best assembly orientations can be calculated due to combination of penetration lengths with material properties and considered to remain constant for different photon energies.The aim of the previous studies was to maximize a contrast-to-noise ration CNR by projection images with the minimization of the required photon energy [12].Furthermore, the assembly orientations were ordered due to their smallest required photon energies (see Equation 4).
10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020In order to validate the indenepdency concept two assembly orientations, which are related to the used low-and to high-energy, are applied to measure the test assembly.Moreover, to reduce the energy influence two more assembly orientations, for which both of the energies are not the optimal ones, are investigated in the validation step.(see Figure 2).
To determine the optimal assembly orientation for both of X-ray parameter sets, the authors replaced the CNR of a projection image with the CNR of a sinogram.Sinograms form the basis of the CT reconstruction process and demonstrate the separation of the materials in one slice of the reconstructed volume by the rotation of the assembly (see Figure 3).The simulation calculates the sinograms for each detector row.Furthermore, the CNR of a sinogram of an assembly orientation 105 • x165 • is a maximum between four investigated assembly orientations.Figure 3.

Experiment
In order to achieve the desired goal of the work, namely, to prove the independence of the tendency of the best assembly orientations in the CT system from the adjustment of X-ray tube setup parameters, statistical analysis was conducted.Moreover, CT acquisitions were performed with two groups of X-ray setup parameters, stable SOD, and a stable number of projections on each assembly orientation.In addition, stochastic deviations were the focus of the statistical analysis, as varied X-ray tube parameters have more influence on systematic errors than varied assembly orientations.Therefore, the analysis was based on the analysis of standard deviations and required at least 20 measurements in each assembly orientation.Four chosen assembly orientations were adjusted using polystyrene clampings.All of the 80 measurements (20 for each assembly orientation) were performed with a Werth Tomoscope HV Compact (Werth Messtechnik GmbH, Germany).The system has a transmission micro-target X-ray tube with a maximum tube voltage of 225 kV and a maximum tube power of 50 W.Hence, with these limitations, the combination of aluminum with polyoxymethylene (POM) was the most efficient way to perform the multi-material assembly.This assembly consisted of a POM cube with four openings (boreholes) and two aluminum cylinders (see Figure 4).The four openings ensured that the POM-Al-cube had a variable geometry.Two cylinders could be unscrewed and installed in two of the four cube openings.Moreover, all three components could be calibrated in a deconstructed state with a CMM.The cube had sides of 100 mm and the cylinders were 60 mm in length with a 10 mm radius.The multi-material assembly was measured in each of the orientations (see Figure 2) in a repetitive loop without being removed from the CT system.Table 1 demonstrates two groups of X-ray setup parameters.The first group had the minimum required energy to perform the CT acquisition for all of the assembly orientations and rotation steps.It was advantageous for the POM part of the assembly.The second group of X-ray setup parameters overexposed the POM cube but was suitable for the aluminum cylinders.SOD was a minimum requirement to acquire the whole assembly in the four chosen assembly orientations for each of the rotation steps.To reduce the measuring time, the experiment was performed with 700 projections and detector binning (1000 to 1000 pixels).The WinWerth software application (Werth Messtechnik GmbH, Germany) executed dimensional measurements of 48 features on the basis of stereolithography (STL) models and automated macro files.Used STL models are created with the volume section algorithm for each of the two materials.The volume section algorithm enables the choice of an area for the stable calculation of a threshold value for multi-material assemblies.Half of the measured features specified high-attenuating aluminum, while the other half specified low-attenuating POM areas.A target variable of the experiment was a standard deviation (std) of the measurement process, with the assembly orientation as an input.An analysis of variance (ANOVA) was conducted to determine whether the difference between the standard deviations was significant or not.Significantly different assembly orientations have less than 5% of the probability (p-value) of the hypothesis that the assembly orientations are equal.Therefore, more than one assembly orientation can be significantly good for one nominal feature.To score assembly orientations inside the group of the significantly good ones, their confidence intervals (CI = [CI low ,CI up ]) were analyzed (see Equation 5).The overlapping area between the confidence interval of the assembly orientation with the minimum of the standard deviation for the feature(CI min ) and each other assembly orientation was measured between zero and one.If the assembly orientation is significant different to the assembly orientation with minimum standard deviation, their confidence intervals were not overlapping and the score for this assembly orientation was zero.If the assembly orientation had a minimum standard deviation, the score was one.
The mean value of the scores was calculated for all of the measured dimensional features.In this case, the assembly orientation could have a global score equal to one only if it had the minimum of the standard deviations for all of the measured features.Figure 5 represents the results of the analysis for both groups of X-ray setup parameters.The results demonstrated that the assembly orientations 30 • x45 • and 105 • x165 • were significantly better than both other ones independent of the X-ray setup parameters.Moreover, the second X-ray parameter set decreased the difference between assembly orientations because of the artifacts in the POM features.In terms of mean score for POM and aluminum features separately the assembly orientation 105 • x165 • was the best one in three of four cases (except of overexposed POM features by the second X-ray parameter set, see Figure 6).Therefore, the choice of the best assembly orientation predominantly depends on the region or material of interest, but not on the X-ray setup parameters.

Conclusion and further research
The paper investigated the independence between the best assembly orientations and the chosen X-ray source parameters.The assembly orientations and X-ray setup parameters for validation were based on previous authors' works and were validated for the new concept of multi-spectral measurements.The results of the statistical analysis confirm the paper's hypothesis.
10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020 Therefore, the statistical analysis demonstrated that a maximal sinogram-CNR identifies the best assembly orientation.In the future works authors plan to calculate the best possible assembly orientations by using the combination of penetration lengths with the energy independence parameters of the attenuation coefficient.Moreover, due to the combination of more than one material instead of the maximization of the contrast-to-noise ratio in the projection picture, the CNR of the sinogram will be maximized.The available results demonstrate the validity of this approach.

Figure 1 :
Figure 1: The assembly orientation and SOD in CT system However, Villarraga-Gomez et al. experimentally demonstrated the existence of the optimal assembly orientations based on the smallest deviation between CT and coordinate measuring machine (CMM) measurements [5].Heinzl et al. and Amirkhanov et al. investigated the aspect of the best possible assembly orientation on the basis of simple mono-material geometries [6, 7].The Projection integral Pro j o,r,b (E) calculates with respect to the penetration length d o,r,b,m for each of the assembly orientations o, materials m, rotation steps r and X-ray beams b.Projection integrals Pro j o,r,b (E) depend on the density ρ m and mass attenuation coefficient µ mass m (E) = µ total m (E)/ρ m of the material (Equation

Figure 5 :
Figure 5: Statistical estimation of the assembly orientations a) first group of X-ray tube parameters, b) second group of X-ray tube parameters

Figure 6 :
Figure 6: Statistical estimation of the assembly orientations a) first group of X-ray tube parameters and POM features, b) first group of X-ray tube parameters and Al features, c) second group of X-ray tube parameters and POM features, d) second group of X-ray tube parameters and Al features

Table 1 :
Two groups of X-ray tube setup parameters