Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements

Among the influence factors affecting CT measurement chain, the study and analysis of CT system geometrical errors is of primary importance. In fact, the system geometry provides the necessary information to fully describe the geometry of data acquisition and performing the tomographic reconstruction on which all the dimensional analyses are based. In this work, different sets of CT experimental investigations, performed with a calibrated ball plate, were specifically designed to investigate the effects of CT system detector angular misalignments on CT measurement results. After characterizing the effects produced by each detector angular misalignment on CT measurement results, the paper shows results from NSI proprietary automatic method that effectively corrects for detector misalignments providing a significant enhancement of CT measurement accuracy.


Introduction
Fundamental requirements for using CT systems as coordinate measuring systems (CMSs) for traceable coordinate metrology are the study of measurement accuracy and the establishment of traceability to the unit of length, the meter. Due to their complex nature, CT scanning technology and thus CT measurements are affected by multiple error sources that complexly interact in the measurement chain. The German guideline VDI/VDE 2630-part 1.2 [1] provides a detailed description of the factors influencing CT dimensional measurements. Examples of these influence factors are CT scanning parameters, workpiece properties (e.g. material, size, surface roughness), geometrical errors, software and data processing etc. Because of the multitude of these influencing quantities and the complexity and non-linearity of their interaction, CT measurements traceability is a major challenge for metrological applications. In particular, the assessment of measurement uncertainty, which is essential for traceability establishment, is one of the most critical tasks. Among the influence factors affecting CT measurement chain, the study and analysis of CT system geometrical errors is of primary importance [2,3]. As for most precision measuring instruments, the design of a CT system involves the assembly of several components, the most important of which are the X-ray source, the rotary table and the detector. In the majority of the systems, moreover, at least one of these components, i.e. the rotary stage, is moved e.g. on linear guideways to reach the desired configuration or set-up to perform the CT scan. The physical structure of a CT system is therefore itself a source of measurement uncertainty. The determination of the CT system geometry is a crucial step. In fact, the system geometry provides the necessary information to fully describe the geometry of data acquisition and performing the tomographic reconstruction on which all the dimensional analyses are based. An error in the determination of the CT system geometry (i.e. geometric set-up) or the presence of geometrical errors not accounted for during the reconstruction could affect all the subsequent steps in the measurement chain and could lead to artifacts, distortions and measurement errors in the reconstructed volume [2]. It is evident therefore that it is extremely important to investigate and quantify the influence of CT system geometrical errors on CT measurements.
2 Cone-beam CT system geometry X-ray computed tomography is a non-destructive technique based on the attenuation of the X-rays when they pass through a matter and the subsequent tomographic reconstruction of the X-ray projections recorded by the detector. It is therefore an imaging technique. However, the machine frame of a CT system is typically composed of three ideally orthogonal linear axes which generate the geometry of a Cartesian coordinate system and allow for motion in X, Y and Z directions. Moreover, a rotary axis enables for sample rotation and the recording of the projections at the different angular steps. Figure 1a) describes a typical industrial cone-beam CT system geometry. Also other designs exist, however for the purpose of the work the design reported in Figure 1 is considered. In Figure 1 b) the line passing through the X-ray cone vertex (i.e. the X-ray focal spot, which ideally is a point) and the center of the detector is defined as the z axis, also the magnification axis. The axis which is parallel to the rotation axis of the object is called y axis, finally the x axis is perpendicular to both the y and z axis. The x, y, and z axis form therefore a Cartesian coordinate system. Figure 1:a) Typical cone-beam system geometry. b) Ideal alignment of a cone-beam CT system. The origin of the coordinate system is placed on the detector center. The three rotations θ, γ, η describe the detector angular misalignments.
The distance between the X-ray source and the center of the detector is defined as the source-to-detector-distance SDD, whereas the distance between the X-ray source and the intersection between the rotation axis and the magnification axis is referred to as source-to-object distance SOD (or also SRD: source-to-rotation axis distance). The ratio between the SDD and the SOD distances gives the magnification factor M which describes the geometrical magnification and thus the voxel size used for the CT scan.

Alignment of a CT system
In a perfectly aligned CT system (see Figure 1 b)), the X-ray focal spot center (the vertex of X-ray cone), the center of rotation and the detector center are positioned on a straight line. This line is perpendicular to the detector surface on its center and coincides with the central ray (i.e. the X-ray path on the central plane of the cone which goes perpendicularly from the vertex of the cone to the center of the detector). Moreover, the rotation axis is perpendicular to the line containing the center of rotation, the X-ray focal spot and the detector center, while its projection is parallel to the detector columns [2]. In real practice, however, some residual errors between the three components could be present in the system geometry [2]. To describe the geometry of a CT system the right-handed Cartesian coordinate system with origin on the detector surface and depicted in Figure 1 b) is used. The positive z direction points towards the X-ray source, the positive y axis direction is in the opposite direction of gravity and the x direction is defined by the right-hand rule. A rotation of the detector about the x axis is described by the angle θ, whereas detector rotations about the y and z axis are described respectively by the angles γ and η. Positive rotations are also defined by the right-hand rule. The origin O of the reference system is located at the intersection between the central column and the central row of the detector. This paper focuses on detector angular misalignments which are described in the following.

Detector angular misalignments
Considering the detector as a rigid body, it can be affected by three angular misalignments and three positional misalignments. Vertical and longitudinal positional misalignments i.e. ∆y and ∆z will not be addressed since vertical misalignments can be relevant in case of movements along the y direction (e.g. fan-beam systems or different scanning trajectories) which do not occur during traditional cone-beam circular scans, whereas ∆z shifts along the magnification axis lead to errors in SDD and therefore in the magnification factor M. These errors have already been studied in literature and their effects are analyzed for example in [4,5].

Detector pitch
Detector pitch (θ) is an out-of-plane rotation of the detector which occurs about the detector horizontal axis. Figure 2 a) represents a detector pitch about the x axis, which is the horizontal axis passing through the detector center. In this case, the condition of perpendicularity of the straight line (containing the X-ray source focal spot center, the center of rotation and the detector center) to the detector surface on its center is not respected. Due to this kind of misalignment, the upper and lower regions of the detector are respectively closer and further away from the center of the X-ray source. In the presence of a detector pitch about the x axis of Figure 2 a), from the X-ray source perspective the height of the detector becomes smaller.

Detector yaw
A detector yaw (γ) occurs when the detector is tilted around its vertical axis. Detector yaw, as detector pitch, also describes an out-of-plane rotation. Figure 2 b) describes a detector yaw about its central vertical axis, y. Also in this case due to the detector misalignment some regions of the detector are closer of further from the X-ray source. In Figure 2 b) the right-hand side of the detector is closer to the X-ray source whereas the left-hand side is further away from the X-ray source. Also here the condition of perpendicularity between the straight line and the detector surface on its center is not respected. In the presence of a detector yaw about the y axis of Figure 2 b), from the X-ray source perspective the width of the detector becomes smaller.

Detector roll
Detector roll (η) describes an in-plane rotation of the detector. Figure 2 c) represents a detector in presence of a detector roll about the z axis. When in presence of a detector roll the condition requiring the projection of the rotation axis to be parallel to the detector columns is not respected. Due to a detector roll about the z axis, the effective width and height of the detector viewed from the X-ray source are altered.
Detector misalignments can occur also about axes different than the detector central axes represented in Figure 2. For example, detector angular misalignments can occur about any row and column of the detector. Moreover, the misalignments described in Figure 2 can be combined together and happen simultaneously. These types of misalignments can be decomposed and expressed as functions of the parameters which describe the detector misalignments about its central axes [6,7].

Actual CT system geometry
In CT process chain, the accurate knowledge of the actual system geometry is a fundamental information. In fact, the CT system geometry describes the geometry of the data acquisition which is essential to perform the tomographic reconstruction. Any discrepancy between the actual system geometry and the geometry used in the reconstruction phase (i.e. the use of an incorrect CT system geometry for reconstruction) could lead to the presence of artifacts, distortion and measurement errors. The CT system geometry input to the reconstruction algorithm may be incorrect for two reasons which can be described with two different scenarios [2]. In the first case the actual CT system geometry is affected by the presence of hardware physical misalignments. In this scenario, if the misalignments present in the actual geometry are not properly accounted for during reconstruction, the reconstructed volume will be affected by errors, distortions and artifacts.
In the second scenario, the geometry of the CT system is estimated directly from images for example as in references [8][9][10]. In this case, the presence of a physical misalignment is not necessarily a problem. In [11] Kumar et al. investigated the influence of specific geometrical errors on simulated ball bars showing that they can have significant impact on CT data. In [12] different simulated detector angular misalignments of 1°, 2°, 5° and 10° are studied showing that, depending on the kind of misalignments, significant distortions might be present in the CT volume. Thus, it is of fundamental importance to study the effects of geometrical misalignments on CT measurements and to determine the sensitivity of measurements to the different misalignments. Knowing which effects are produced by each misalignment, and which is the sensitivity of CT measurements to the particular misalignment enables also to identify which are the most critical geometrical errors and to enhance CT measurement accuracy.
The following sections focus on the investigation of the effects of detector angular misalignments on the measurement results obtained using CT cone-beam circular scanning trajectories. Other studies are present in literature, which investigate the influence of other geometrical errors for example magnification errors as discussed in [13,14]. In this work, different sets of experimental investigations were performed to investigate the effects of CT system detector misalignments on the measurement results and to determine the sensitivity of measurements to the particular type of misalignment. Specifically, the influence of the measurement direction and object positioning in the CT volume was also determined.

Experimental investigation
In order to investigate the influence of measurement direction and object positioning on the measurement errors caused by a misaligned detector a ball plate containing 25 equally spaced ruby spheres with nominal sphere diameter of 5 mm, glued on a carbon-fiber reinforced polymer plate was used for the experimental investigation (Figure 3 a)) [15]. Calibrated measurements of sphere diameters, sphere center-to-center distances (including the distances between non-adjacent pairs of spheres) and form errors were acquired with a tactile CMM [15]. The ball plate of Figure 3 allows for multiple measurements between spheres centers in different directions and different locations on the CT volume. More specifically the array of 5x5 spheres enables the measurements of 50 center-to-center distances along the horizontal direction (i.e. x axis), and 50 center-to-center distances along the vertical direction (i.e. y axis). Moreover, the horizontal and vertical measurements are homogeneously distributed in 5 equally spaced rows and 5 equally spaced columns which therefore homogeneously cover the surface a 2D flat-panel detector. This enables to fully investigate, with the use of one reference object, the influence of measurement direction and feature location on the errors caused by a misaligned detector. CT scans of the ball plate were performed with a NSI metrology CT system featuring a 225kV micro-focus directional X-ray source, a 2D flat panel detector with a 127 µm pixel size, and an air-cooled cabinet according to the scanning parameters of Table 1. The ball plate was manually positioned in the CT system measurement volume so that it was oriented in the vertical direction (i.e. line through sphere 1 to 21 nominally parallel to the y axis) and with row number 3 (sphere 11 to 15) nominally positioned in the central plane of the detector. In this way, two rows of the ball plate, namely row 4 and row 5 are positioned in the upper part of the detector and respectively at increasing distance from the central plane of the detector. Whereas two rows, namely row 1 and row 2 are positioned in the lower part of the detector at nominally symmetric position with respect to row 5 and 4. In the same way two columns of the ball plate, namely column 1 and column 2 are positioned in the left side of the detector and respectively at increasing distance from the detector vertical axis passing through its center. Columns 4 and column 5 are positioned at nominally symmetric position with respect to column 2 and 1 but on the right side of the detector. In this way the flat-panel detector is homogeneously covered by the ball plate. This enables to reveal the sensitivity of measurement errors caused by detector pitch, yaw and roll on measurements performed in the horizontal, vertical and tilted directions and for different positioning of the spheres.
After performing the CT scans with the system properly aligned, physical misalignments were purposefully induced on the flatpanel detector by physically acting on the detector hardware. With reference to the coordinate system defined in Figure 1 b), the investigated misalignments are: three angular misalignments in the positive θ rotation, three misalignments in the positive γ rotation and three misalignments in the negative η rotation (see Figure 1 b)). Each misalignment was induced separately in order to analyze the effects of the single type misalignment individually (no superimposition of detector pitch, yaw and roll). Of course in real practice misalignments of the detector can occur simultaneously however the purpose of this study is to investigate the effects of the misalignments separately in order to quantify the effects that each misalignment produces on the measurement results. For each set of misalignments three angular misalignments of nominally 0.5°, 1° and 1.5° were induced to study the sensitivity of the errors caused by the misalignments to the varying angles, for a total of 9 different misaligned configurations. Three repeated CT scans were performed in each of the 9 misaligned configurations with the sample oriented in the same way as for the scans performed with the aligned system for a total of 27 CT scans. After each set of misalignments, the system was re-aligned by re-performing NSI's alignment procedures in order to guarantee the system was in the aligned configuration before starting the next set of misalignments, and to avoid therefore the superimposition of the effects of different misalignments. After each re-alignment a CT scan of the ball plate was also performed 9th Conference on Industrial Computed Tomography, Padova, Italy (iCT 2019) in order to check the consistency of the measurement results. A schematic describing the workflow of the experimental campaign is reported in Figure 4. Minimum misalignments of 0.5° were chosen in order to be able to isolate the effects of detector angular misalignments on the measurement results and guarantee that detector misalignments are the preponderant influence quantity. On the other hand, the presence of misalignments bigger than 1.5° instead is unlikely for industrial systems in which an alignment procedure has been carried out and with a certain degree of accuracy in the mechanical assembly.
For each scan a procedure to determine the geometry of the system was applied as per NSI's guidelines. Sections 4.1.1 to 4.1.3 report the measurement results obtained when out of plane rotations and in plane rotations of the detector were disabled from the geometry determination. Therefore, the detector misalignments intentionally physically induced about the x, y and z axis were purposefully not accounted for during reconstruction. Section 4.2 reports some examples of the measurements results obtained on the same datasets (acquired in presence of the intentionally induced physical misalignments) after applying NSI's proprietary automatic method that effectively corrects for detector misalignments physically present on the CT system hardware. NSI's proprietary reconstruction software efX CT, featuring an in house developed algorithm capable of correcting for detector misalignments, was used for the reconstruction of CT scans and it is demonstrated how a significant enhancement of CT measurement accuracy is obtained.

Data analysis
All CT data were reconstructed by means of NSI's reconstruction software efX-CT. After reconstruction the CT volumes were imported and analyzed using VGStudio MAX 3.0. The local adaptive surface determination algorithm was used for surface determination. For each sphere of the plate a region of interest, consisting of the top hemisphere, was taken into account in order to remove the part of the spheres glued to the carbon-fiber reinforced plate, which could lead to inaccuracies in measurements. Sphere diameters, sphere center-to-center distances and spheres form errors were then calculated for each of the CT scans in the aligned and misaligned configurations using Gaussian least squares fitting. The measurement results of the CT scans performed with the system in the aligned configuration were compared to the calibrated CMM data in order to study the residual measurement errors which are present when scanning the ball plate. For the three repeated CT scans of the ball plate performed with the system properly aligned, the measurement errors calculated as (CT measurements ̶ CMM measurements) showed sphere center-to-center errors smaller than 3.5 µm and standard deviations smaller than 0.5 µm. These measurement errors obtained from the comparison to the calibrated CMM data provide a quantification of the residual errors, which cannot be primarily attributed to CT system geometrical misalignments, but that are likely to be the result of the superimposition of influence quantities that typically interact in CT measurement chain. In all the following sections CT measurement results in the misaligned configurations are compared to the CT measurements obtained with the system in the aligned configuration. This was done in order to have consistent comparison between CT measurements performed under the same scanning conditions and to investigate the errors which can be primarily attributed to geometrical misalignments.

Detector pitch
In order to study the effects produced by detector pitch on measurements performed along the vertical and horizontal direction, the sphere center-to-center distance errors obtained for vertical and horizontal measurements of the ball plate are represented respectively in Figure 5 a)  Detector pitch strongly affects sphere center-to-center measurements. In this case, for a detector pitch of 1.5° sphere distance errors reach maximum values of 56 µm. Maximum errors of 36 µm and 18 µm are present respectively for 1° and 0.5° detector pitch. It is therefore confirmed, that the amplitude of the misalignments significantly affects the measurement results and for increasing misalignments also the measurement error increases. Figure 5 a) reports the measurement results obtained for the 50 vertical measurements performed on the ball plate, namely measurements between spheres belonging to the same column of the ball plate (10 measurements for each of the 5 columns). Vertical measurements show a symmetric behavior about the x axis. For example, the error between sphere 1 and 6 is similar to the error between sphere 16 and 21 (that belong to the same column of sphere 1 and 6) but with the opposite sign. Distances between spheres positioned below the central plane of the detector present positive errors, whereas distances between spheres positioned above the central plane present negative errors. The angle introduced in fact affects the SDD symmetrically about the detector center. With respect to the aligned configuration, for the induced misalignments, SDD is affected in opposite directions and it decreases for spheres above the central plane of the detector and it increases for spheres below. As a consequence, for spheres positioned below the central plane of the detector the actual SDD, and therefore the actual magnification, are bigger. In the regions of the detector above the central plane instead, the actual SDD, and as a consequence the actual magnification, are smaller. These magnification errors increase for spheres far away from the center of the detector. For example, the distance between spheres 10 and 15 is smaller than the distance between spheres 5-15. Moreover, the lengths which comprise points symmetric about the x axis are characterized by a smaller error because they have opposite errors that cancel out; for example, this happens for sphere center-to-center distances 5-25 and 10-20. The obtained results show how the vertical measurements performed on the ball plate are not affected by the column horizontal position. In fact, the measurement results obtained for column 1,2,3,4 and 5 present the same behavior and really close measurement results. It can be concluded that for the detector pitch experimentally investigated and up to 1.5° vertical measurements are strongly affected and do not significantly depend on the horizontal position of the columns of the ball plate. Figure 5 b) reports the measurement results obtained for the 50 horizontal measurements of the ball plate, namely measurements between spheres that belong to the same row (10 measurements for each of the 5 rows). Row 3 which nominally is positioned in the middle plane of the detector (see Figure 3), presents small measurement errors which are close to zero for all the three amplitudes of detector pitch investigated. For rows at increasing vertical distance from the middle plane of the detector instead the sphere distance errors are affected by scaling errors. This is visible in the graph from the measurement errors that almost linearly increase with increasing sphere center-to-center distances between the spheres of the ball plate. For example, in the case of 1.5° detector pitch, row 5 which is positioned close to the upper edge of the detector is characterized by the biggest scaling error with a maximum error of 56 µm for a 40 mm center-to-center nominal distance. Row 4 which is positioned at a vertical position on the detector in between row 3 and row 5 is characterized by a maximum error of 28 µm for the 40 mm center-tocenter nominal distance. Row 1 (at nominally opposite position of row 5 on the detector vertically) presents a similar behavior to row 5 but with errors characterized by opposite sign, and in the same way row 2 shows a similar behavior to row 4 but again with errors characterized by opposite sign. This behavior holds true for all the three investigated amplitudes of detector pitch, and the bigger is the amplitude the stronger is the presence of this behavior. The explanation for this particular behavior of horizontal measurements of the ball plate is presented in the following. With respect to the aligned configuration, due to the angles introduced up to 1.5°, the magnification is affected symmetrically about the detector center and magnification errors are present which increase for spheres far away from the center of the detector vertically. As a consequence of the magnification errors, the actual voxel size differs from the voxel size of the reconstructed volume. Errors in the dimension of the voxel size produce scaling errors when measuring increasing lengths because more voxels are comprised in the measurements.  Form errors were also investigated and in presence of detector pitch up to 1.5° no significant differences between the aligned and misaligned configurations were found.        It is visible also here how all the balls of the plate except sphere 13 do not have anymore a spherical shape. In particular, the deviation from the spherical shape increases with increasing vertical and horizontal distance from the center of the detector. Moreover, spheres which are at symmetrically opposite positions are characterized by extremely similar deviations from the spherical shape. For example, spheres 3 and 23. This is valid for all spheres at radially opposite position from the detector center. Figure 12 reports the sphere center-to-center errors for the vertical and horizontal measurements of the ball plate. Figure 12: Sphere center-to-center errors for the 100 measurements of the ball plate for the three investigated detector roll values.

Detector roll
The sphere center-to-center measurements are not significantly affected by detector roll of 0.5° and 1° even if visible deformations of the spheres are present. With a detector roll of 1.5° instead, also center-to-center measurements are affected by the misalignment and maximum errors of 40 µm are present. In Figure 13 the measurement errors obtained for the sphere diameters are shown. Sphere diameters are affected by significant measurement errors, and they are always smaller than the diameters calculated from CT scans performed with the system in the aligned configuration. 23 that also show similar diameter errors but bigger than the spheres mentioned above. For all the three amplitudes investigated the bigger diameter errors are obtained for spheres 1,5,21, 25 that are positioned at maximum distance from the center of the detector. Figure 14 reports the form errors for all the three amplitudes of misalignment investigated. The same behavior found for the diameter measurements is present also for form measurements. In this case as well, form errors increase with the radial distance from the center of the detector, and with the amplitude of the misalignment. For the 1.5° configuration maximum errors of 647 µm are present.

Accuracy enhancement of CT measurements
In this section results from NSI's proprietary automatic method that effectively corrects for detector misalignments are presented. NSI's proprietary reconstruction software efX CT, featuring an in house developed algorithm capable of correcting for detector misalignments was used for the reconstruction of the same CT scans presented in the sections above (and acquired in presence of purposefully induced detector misalignments) and it is demonstrated how a significant enhancement of CT measurement accuracy is obtained.
As an example, the results of the CT scans acquired when a 0.5° detector tilt about the x axis and a 0.5 ° detector roll about the z axis were purposefully induced on the detector are shown before and after the use of the NSI's automatic method. Figure 15 a) reports the sphere center-to-center measurement errors for the horizontal and vertical measurements of the ball plate when a 0.5° detector tilt about the x was induced on the detector. As it is visible, when applying the NSI's automatic method ("after correction" in the charts), the measurement errors are strongly reduced and are smaller than 3µ m providing a significant enhancement of measurement accuracy even when detector misalignments were purposefully physically induced on the CT system hardware. The significant enhancement of measurement accuracy is shown also in Figure 15 b) where it is demonstrated how the diameter errors of the spheres of the ball plate are smaller than 1µm after applying NSI's procedure (blue triangles) and the trend caused by detector tilt described in Figure 6 is not present anymore. Figure 15 c) reports the form errors when a 0.5° detector roll about the z axis was purposefully induced on the detector. Detector roll was chosen as example as it was demonstrated that it causes significant distortions on the CT volume and strongly affects form measurements. Also in this case, it is shown how after applying NSI's proprietary method the form errors calculated from the same dataset acquired when a 0.5° detector roll was physically present on the CT system hardware are comparable to the ones obtained with the system properly aligned.

Conclusions
The influence of measurement direction and object positioning on the errors caused by a misaligned detector was investigated by using a tactile CMM calibrated ball plate consisting of an array of 5x5 equally spaced ruby spheres. The ball plate was positioned vertically in the CT volume so that it homogenously covered the detector surface with the central column and central row of the ball plate nominally positioned on the detector center. Two rows occupied the upper part of the detector and the other two rows occupied the nominally symmetrical position on the lower part of the detector. In the same way, two columns were positioned in the left-hand side of the detector, and the remaining two columns were positioned at nominally symmetrical positions on the right side of the detector. The experimental campaign was designed to investigate the influence of detector pitch about the x axis, detector yaw about the y axis and detector roll about the z axis. For this purpose, the flat-panel detector was purposefully mechanically misaligned and three different amplitudes, i.e. 0.5°, 1° and 1.5°, for each of the misalignments described above were physically induced. The use of three different amplitudes of misalignments enabled to investigate the sensitivity of the errors with the amplitude of the induced misalignments. The resulting experimental set-up therefore led to the investigation of three detector pitch about the horizontal central axis of the detector and in the positive rotation direction, three detector yaw about the vertical central axis of the detector and in the positive rotation direction, and three detector roll about the longitudinal central axis of the detector and in the negative rotation direction. Each CT scan was repeated three times, leading to a total of 27 CT scans in the misaligned configurations (9 misalignments x 3CT scans for each misalignment). Detector pitch, yaw and roll were investigated separately in order to isolate the effects caused by each angular misalignment. For this purpose, a realignment of the CT system was performed in between each set of misalignments in order to avoid the superimposition of other unwanted geometrical misalignments.
The obtained results showed that detector pitch strongly affects the measurements of sphere center-to-center distances in the experimentally tested conditions. For detector pitch up to 1.5°, the sphere center-to-center distance errors present a symmetric behavior about the x axis of the detector. The investigated misalignments, with respect to the aligned configuration, affect the source-to-detector distance symmetrically about the detector center. As a consequence, magnification errors are present which increase for spheres far away from the center of the detector. The experimental results enabled also to prove that, in the tested conditions, the 50 vertical measurements performed on the ball plate (i.e. measurements between spheres belonging to the same column) cause the symmetric behavior about the x axis, and this behavior does not vary with the detector columns, i.e. the horizontal position of the column does not affect the measurement errors. In this case maximum errors of 30 µm were found for the 1.5° detector pitch. The 50 horizontal measurements, i.e. measurements between spheres belonging to the same row, are affected by scaling errors which increase with increasing vertical distance of the rows from the central plane of the detector (and with increasing amplitude of the misalignment). These scaling errors are caused by the magnification errors that are present by vertically moving away from the central plane of the detector. In this case for a 1.5° pitch, maximum errors of 56 µm were found. Diameter errors were also showed a symmetrical behavior about the x axis. Spheres which occupy similar regions on the detector but at opposite sides vertically showed diameter errors with opposite sign. Moreover, it was observed that spheres belonging to the same row present similar diameter errors and that with increasing vertical distance of the rows from the central plane of the detector diameter errors increase. Form errors do not show significant differences between the aligned and misaligned configurations for detector pitch up to 1.5°. In the case of the investigated detector yaw, the experimental results show how this kind of misalignment also affects image quality. The edges of the spheres of the ball plate appear as doubled, and the presence of these artifacts increases with increasing distance from the central horizontal and vertical planes of the detector. Especially form errors are mostly affected by detector yaw. Specifically, bigger form errors were observed for increasing distance horizontally from the center of the detector. Maximum errors of 32 µm were found for a 1.5° yaw. The presence of a detector roll causes strong artifacts on the reconstructed volumes. Already with a 0.5° misalignment the balls do not present anymore a spherical shape. Mostly diameter errors and form errors are affected by this kind of misalignment which is the one among the investigated ones (i.e. pitch, yaw and roll) that produces the biggest and most visible artifacts and errors. In particular, both diameter errors and form errors exhibit a trend with errors increasing with increasing radial distance from the center of the detector. The spheres located at the edges of the ball plate present the biggest diameter and form errors which in the case of a 1.5° misalignment reach respectively absolute values of 1.026 mm and 647 µm. The experimentally obtained results enable to study the influence of the measurement direction and the object positioning on the measurement volume with regards to the measurement errors obtained in presence of a misaligned detector. Measurement direction and object positioning strongly affect the measurement results and cause the presence of particular behavior and trends. The detailed comprehension and quantification of the effects caused by CT system geometrical misalignment is of extreme importance and it is an essential step to enhance CT measurements accuracy. In this paper it was also demonstrated how when applying NSI's proprietary automatic method that effectively corrects for detector misalignments a significant enhancement of CT measurements accuracy is obtained. Specifically, an in house developed algorithm capable of correcting for detector misalignments was used for the reconstruction of the same CT scans acquired in presence of intentionally physically induced misalignments on the detector hardware and experimental results are presented showing how a significant enhancement of CT measurement accuracy is obtained.