Investigation of the kinematic system of a 450 kv CT scanner and its influence on dimensional CT metrology applications

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1 Investigation of the kinematic system of a 450 kv CT scanner and its influence on dimensional CT metrology applications Frank Welkenhuyzen 1, Bart Boeckmans 1, Ye Tan 1,2, Kim Kiekens 1,2, Wim Dewulf 1,2, Jean-Pierre Kruth 1 1 KU Leuven, Mechanical Engineering Department, Celestijnenlaan 300B, 3001 Heverlee, Belgium, Frank.Welkenhuyzen@mech.kuleuven.be 2 KU Leuven, Campus Group T, Andreas Vesaliusstraat 13, 3000 Leuven, Belgium Abstract The accuracy of CT-based dimensional measurements remains yet largely uncertain, due to the high number of influencing factors related to the workpiece as well as the CT equipment, the measurement setup and subsequent data processing steps. [1] gives an overview of these unwanted effects which disturb the dimensional CT measurements. This paper focuses on the kinematic system of the CT scanner and the subsequent errors introduced by the imperfect positioning of this kinematic system. First, a kinematic model for a 450 kv CT scanner is presented. Next the geometrical error components (specified in ISO 230-1) and alignment errors between X-ray source, rotation table and detector have been determined. Finally a calibrated reference object and simulations have been used to show the influence of the geometrical errors and alignment errors on the dimensional measurements conducted using CT. Keywords: Computed Tomography, Dimensional Metrology, Simulation 1 Introduction 1.1 Problem description The accuracy of CT-based dimensional measurements is largely uncertain, due to the high number of influencing factors related to the workpiece as well as the CT equipment, the measurement setup and subsequent data processing steps. The many influencing factors, together with various additional often unknown influences (e.g. drift of the source, temperature), make it difficult to correlate separate influencing factors to observed variations in dimensional measurements when performing experimental investigations or measurements, and hence it is inconvenient to draw correct conclusions from these experimental measurements. [1] gives an overview of unwanted effects that disturb dimensional CT measurements. There is quite some literature that describes, investigates and/or provides corrections for beam hardening effects, scatter artifacts, ring artifacts, etc. Furthermore different suggested calibration objects for voxel size calibration (rescaling), beam hardening correction, etc. can be found in literature. This paper focuses on the kinematic system of the CT scanner and the subsequent errors introduced by the imperfect positioning of this kinematic system. When discussing the influencing factors on dimensional CT measurements, the main discussion topics are often related to beam hardening and edge detection. The kinematic system is another important aspect influencing the dimensional CT measurements. First of all it has a direct influence on the voxel size. Regularly a calibration object is used to rescale the voxel sizes but this is often insufficient. As a second point the kinematic system is linked to alignment errors between the rotation axis, the X-ray source and the detector: the rotation axis is supposed to be aligned parallel, resp. perpendicular to the detector and its pixel rows or columns [1]). This link will not only influence each individual measurement, but will also affect the initial machine calibration (alignment), executed by the manufacturer, to align the X-ray source, rotation ict Conference

2 table and detector. Furthermore the negative influences of the kinematic system and subsequent alignment errors play a role in two other critical steps of dimensional CT metrology: during the volume reconstruction step and during the segmentation or edge detection (determining the respective transitions between solid materials and surrounding air or between different solid materials). In addition a better knowledge of the kinematic system and subsequent alignment errors allows to perform better measurement uncertainty calculations, as the uncertainty parameters related to the kinematic system are often (incorrectly) defined by means of guessing while these errors are often repeatable. Therefore the errors of the kinematic system should be known in advance to make an accurate estimation of the measurement uncertainty. 1.2 Hardware and software The investigated CT scanner is a Nikon Metrology XT H450. With a voltage ranging up to 450 kv, the scanner is well equipped for penetrating thicker structures and materials with a high attenuation coefficient compared to standard CT scanners for dimensional metrology. The CT scanner makes use of two detectors: a flat panel detector (FPD) and a curved linear detector array (CLDA). After data acquisition, the 2D images are reconstructed using CTPro (reconstruction software of Nikon Metrology). Ensuing volume reconstruction, the volume can be loaded in VGStudio Max 2.2 for further data processing and geometrical analysis. A critical step is edge detection or segmentation: determining the respective transitions between solid materials and surrounding air or between different solid materials. The edge detection has been performed as follows in this paper: first a global threshold is determined by defining one threshold gray value. This results in a rough part contour. After this the advanced surface determination of VGStudio MAX 2.2 is used: starting from the previously defined contour, a more accurate surface determination is obtained. Further measurements have taken place in VGStudio. 2 Definition of the kinematic model 2.1 Problem description Figure 1: Kinematic system of the investigated CT scanner. The kinematic system of the investigated CT scanner is illustrated in figure 1. It consists of a turntable for stepwise or continuous rotation, two axes for horizontal translation (x and z) and a vertical translation axis (y). Furthermore the FPD can shift along a vertical axis, to be able to work with the CLDA which is positioned behind the FPD (figure 1, right). Errors of the kinematic system will unambiguously introduce errors on the dimensional measurements: The rotation axis is supposed to be aligned parallel, resp. perpendicular, to the detector and its pixel rows or columns [1]. 218

3 Error from wrong identification of rotation center: at the beginning of the 3D reconstruction the software of the CT device will try to identify the location of the axis around which the part was rotated during CT image capturing. Failure in precise identification of the rotation center/axis will introduce reconstruction errors [1]. Positioning errors and repeatability problems of the Z-axis directly influence the measured dimensions through a change in magnification factor. Errors of the kinematic system will hinder the initial machine calibration (to align the rotation axis parallel, resp. perpendicular, to the detector and its pixel rows or columns, and to determine the source/object and source/detector distances) performed by the manufacturer. 2.2 Kinematic model The kinematic system of the CT scanner has been modelled as a kinematic chain of 4 rigid bodies connected by 3 prismatic joints. The frames have been assigned as follows: Frame {0} connected to fixed structure. Frame {1} connected to z-carriage. Frame {2} connected to y-carriage. Frame {3} connected to x-carriage. Frame {rt} which is positioned at the center of the turntable. Frame {rt} is a translation of frame {3} to the center of the turntable, as the object will be described in function of this frame. The pose of each frame with respect to the previous frame can be described with the help of homogeneous transformation matrices. Taking into account the different error motions (conventions according to [2] are used) these transformation matrices look like: ict Conference

4 With the parameters defined as follows: z enc the value read from the z-scale. ( 0 x0z, 0 y0z, 0 z0z) corresponding to the beginning (home position) of the z-scale expressed in frame {0}. exz and eyz the straightness error motions of the z-axis in x and y direction ezz the positioning error of the z-axis. eaz, ebz and ecz the angular error motions of the z-axis around x, y and z. Similar notations are used for the x and y axes. Squareness errors have not been added as a separate value but have been taken into account in the previously described errors. The coordinates of a point with respect to frame {rt} can now be calculated in frame {0} as: Determination of the error components Figure 2: Measurement of the error components with the laser interferometer (a), electronic level (b) and verification with the dial gauge and a granite square with a precise angle of 90 degrees (c). The above described errors for each axis (one positional error, two straightness errors and three angular errors) in function of the axis position, and the squareness errors between the axes, have been determined using a laser interferometer and an electronic level (figure 2). Furthermore a granite square with a precise angle of 90 degrees and dial gauge have been used to verify the measured errors (figure 2c). Figure 3 shows some of the results. Figure 3a shows the error on the magnification position (error in z of the z-axis) on a certain height (the table can move from z=-285, which is near the source, up to z=280, which is near the detector). It is clear that these errors will have a negative influence on the determination of the magnification, and therefore also on the voxelsizes and dimensional measurements. Figure 3b shows the straightness error (ezy) along the y-axis (squareness error not yet included); this already points out that scanning a calibration object for rescaling should be done at the same table height. Figure 3c shows the pitch error measurement (eaz) along the z-axis. 220

5 Figure 3: Measured error components. 2.4 Measurement of relative errors between source, turntable and detector The above explained method calculates errors/positions with respect to frame {0}, which is connected to the fixed structure. Now the errors should be determined relative to the source and detector position and orientation. The following rule has been used to estimate these values: a point object in the center(line) of the detector should stay on the centerline of the detector when moving in the plane determined by this center line and the source. Figures 4a and 4b give the example for an angular error of the rotation axis around x. In the ideal situation the point (intersection of x) should stay in the center of the detector when rotating (figure 4a). Figure 4b, illustrates the real situation where we see a shift downwards on the detector due to an inclination of the rotation axis. With this rule the position of the turntable relative to the X-ray source and detector has been estimated. Two touching spheres have been used (figure 4c), where the touch point served as the before mentioned point. The composed object has been turned 90 degrees for errors in the horizontal direction. The previously calculated errors of the kinematic system have been taken into account when estimating the relative errors. Figure 4: The influence of the inclination of the rotation axis (a and b) and an X-ray image of the object used to determine the relative errors (c). 3 Simulation program A simulation program has been developed and was presented in earlier work [3]. The simulation program generates 2D TIFF images that can be reconstructed into a 3D model as if they are real projections from a CT scan. Multiple inputs are needed and are taken into account in the simulation program. The object can be constructed out of geometrical features like (truncated) cylinders, (truncated) cones, (truncated) spheres, bars and al kind of combinations. A short overview of the input parameters: Source: spot size, position, drift in time, current, voltage, etc. Object: definition of the object, object position, material composition, etc. Turntable: source object distance, number of rotation steps, etc. Detector: number of pixels, pixelsize, distance source detector, detector attenuation processes (type and thickness of the scintillator), etc. ict Conference

6 The simulation program has been extended by taking into account the errors described in section 2. This will result in more realistic simulations. Furthermore for each input parameter there is the possibility to define an uncertainty range with respect to this input parameter. This allows to perform uncertainty calculations, which is necessary as the real input parameters are never known perfectly and can deviate from measurement to measurement. 4 Case study 4.1 Reference object A reference object is developed and produced by fixing CMM probing styli on a socket (figure 5, left), which has screw holes on distances 22.5, 37.5 and 52.5 mm to the center. The use of such styli has already been described in some literature [4]. The styli are made of ruby spheres on carbon fiber rods, with diameters 4, 6 and 8 mm. The application of the reference object is twofold. Firstly, it is possible to measure distances between sphere centers. Using sphere centers cancels out existing beam hardening and threshold errors. The sphere centers are independent of the sphere diameter. Secondly, sphere diameters can be measured to quantify beam hardening and/or threshold errors. Distance sphere diameters 1 Dist mm 2 Dist mm 3 Dist mm 4 Dist mm 5 Dist mm 6 Dist mm 7 Dist mm 8 Dist mm Figure 5: Styli calibration object (left) with schematic representation (middle) and measured distances (right). 4.2 Calibration As a reference, the sphere distances (listed in figure 5, right) between several spheres are measured with a conventional tactile CMM Mitutoyo FN 905 with specified accuracy: u1 = L/1000 µm (with L in mm, for each axis). Each investigated distance has been measured 13 times, spread over 3 days. Afterwards the standard deviation on each distance has been calculated, resulting in a maximum standard deviation value of 1 µm. Figure 6 shows the CMM measurement results for the distance between spheres 2 and 3. The specified nominal values have been used as reference values for the diameters, as the sphere diameters have sub micrometer accuracy. Figure 6: Measured CMM distance (distance 2-3) in function of measurement number. 222

7 4.3 Results CT measurements are repeated for different magnifications (figure 7, left). After performing a CT scan and reconstructing the volume, this volume is loaded in VGStudio. Because of the inaccuracy of the magnification axis, it is necessary to rescale the volume. The volume can be rescaled by adjusting the voxelsize in VGStudio. Determining the correct voxelsize is done by compensating the CT measured distance between spheres 2 and 3 to the calibration value (CMM measurement of distance between spheres 2 and 3) Distances The investigated distances are listed and schematically represented in figure 7. Figure 7, right, gives the deviations between the measured CT values and the calibrated CMM values (blue rhombus) in function of the measured distance (see figure 5) for measurement 1 (magnification 2.66). The red squares give the results of the simulated measurement with the same input parameters. However these input parameters are never exactly known. Therefore 30 additional simulations have been done where each simulation input parameter (errors of the kinematic system, source spotsize, source drift, object position, ) was chosen out of a small uncertainty interval related to that parameter: this way a 95% uncertainty interval has been determined (green triangle and the purple x representing the upper and lower limit of the 95% interval). Distance number 1 (distance between spheres 2 and 3) has zero deviation as this distance is used for rescaling. It is clear that the result obtained from real CT measurement is similar to the simulated measurement, although there is still a small difference, but it is contained in the 95% uncertainty interval. Further research will be performed to determine the relative errors between source, turntable and detector more accurately. Figure 7: The magnification and the resulting voxel size of each CT measurement (left) and deviations (in mm) to the nominal distances for measurement 1 (right) Diameters When evaluating the diameters of the 4 mm spheres, there was a trend visible for all magnifications (figure 8a): the diameter of the center sphere (sphere 12, located near the rotation axis of the CT scanner while scanning) is always largest, the sphere furthest away from the center (sphere 1) always has the smallest diameter and the other spheres seem to have comparable diameters. As a test, a new CT scan has been executed with sphere 6 closest to the rotation axis. The results are shown in figure 8b: a similar trend is present. Again the measured sphere diameters depend of the distance to the axis of rotation. Figure 8c shows the deviations of a large number of points on a CT measured sphere (real or simulated CT measurement) with respect to its least square fitted sphere. This least square fit is assumed to represent the real physical sphere since this sphere is highly accurate with very small unroundness. Those deviation plots allow to evaluate the sphere form errors introduced by the (real or ict Conference

8 simulated) CT measurement: the real sphere being assumed to have no or minimal form errors. Figure 8c compares the sphere near the axis of rotation (left) and another sphere (right). It is clear that the latter sphere (top right) suffers from a form deviation introduced by the CT measurement. The results of real CT measurements (two top spheres) have been compared to the results of simulated CT measurements: Figure 8c, bottom spheres, shows the deviations of the sphere closest to the axis of rotation and another sphere when no alignment errors are implemented in the simulation and when there are alignment errors implemented. It is clear that the deviations are similar to these of the real measurements (top right) in case of the simulation with errors (middle right). In case of the simulation without alignment errors (bottom), all spheres have similar small deviations that fail to represent the effect of kinematic errors of the CT equipment. Figure 8d shows the calculated diameters for the 4 mm sphere diameters in case of the simulation with errors (sphere 12 on the rotation axis and magnification 2.66). A similar trend can be seen as for the real CT measurements (figure 8a). In case of the simulation without errors, this trend was not present. Figure 8: Figures a and b give the measured sphere diameters in case of sphere 12 near the axis of rotation (a) and in case of sphere 6 near the axis of rotation (b, only measurements 2 to 5 have been executed). Figure c gives the fitpoint deviations to the fitted least square spheres for the real measurement and the simulation with and without errors for the sphere near the axis of rotation and another sphere. Figure d gives the measured sphere diameters in case of sphere 12 near the axis of rotation for a simulated measurement with errors. 5 Conclusions This paper presented a kinematic model for a 450 kv CT scanner. The error components (specified in ISO 230-1) have been determined using a laser interferometer and an electronic level. Furthermore the alignment between the X-ray source, rotation table and detector has been investigated with a calibration object. Results of dimensional CT measurements are shown to validate the results and prove the importance. Real-life CT measurements as well as simulated results are presented. References [1] J.P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, A. Weckenmann, 2011, Computed Tomography for Dimensional Metrology, CIRP Annals - Manufacturing Technology, 60/2:

9 [2] ISO 230-1:1996. Test code for machine tools Part 1: Geometric accuracy of machines operating under no-load or finishing conditions. ISO, [3] F. Welkenhuyzen, B. Boeckmans, J.P. Kruth, W. Dewulf, A. Voet, Simulation of X-ray projection images for dimensional CT metrology, 2012, Proc. 5th Intern. Conf. on optical measurement techniques for structures and systems pages: [4] H. Lettenbauer, B. Georgi, and D. Weiß. Means to verify the accuracy of ct systems for metrology applications (in the absence of established international standards). DIR - International symposium on digital industrial radiology and computed tomography, 4, ict Conference