How beam hardening influences the dimensional geometry in X-ray computed tomography

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1 How beam hardening influences the dimensional geometry in X-ray computed tomography More info about this article: Hannah Corcoran 1, 2, Stephen Brown 2, Stuart Robson 1, Robert Speller 1, Michael McCarthy 1 1 University College London, Gower Street, London, WC1E 6BT, UK, h.corcoran.11@ucl.ac.uk, s.robson@ucl.ac.uk, r.speller@ucl.ac.uk, michael.mccarthy@ucl.ac.uk 2 National Physical Laboratory, Hampton Road, Teddington, TW11 0LW, UK, stephen.brown@npl.co.uk Abstract Dimensional and geometric measurements acquired using X-ray computed tomography can be affected by many variables. This paper focusses on the path length of the X-rays as they travel through an object, which in turn results in varying amounts of beam hardening. The effects of the orientation of the object during imaging is also studied. Four aluminum holeplates, with dimensions of ( ) mm are used, one being complex with a series of 4 mm holes and the others with just a single 4 mm hole in different positions. Results indicate that the amount of distortion to the apparent geometry (in the range of -75 µm to 115 µm) is correlated to the path length and therefore the amount of beam hardening that has occurred as the X-rays are attenuated by the objects. Keywords: Holeplate, dimensional metrology, beam hardening 1 Introduction X-ray computed tomography (XCT) is increasingly being used for dimensional and geometric measurements within manufacturing industries for inspection and quality control. However, there are multiple errors associated with the imaging, reconstruction and analysis processes. Due to the increasing use of this technology, these errors need to be characterized to ensure an increase in the accuracy and precision of the results obtained. This will lead, eventually, to the results being traceable to the SI unit, the metre, which will lead to increased confidence in the results. 1.1 Variables Dimensional and geometric results can be affected by many variables. The VDI/VDE (Association of German Engineers) list these variables in their document 26 Part 1.2 [1]. These variables can be associated with the system itself (e.g. stability of the source [2] and the accuracy of the positioning of the manipulator [3]), the system parameters used to image the object (e.g. voltage and current settings of the X-ray source) and the reconstruction method used. This paper discusses the orientation of the object during imaging and the path lengths of the X-rays as they travel through an object which in turn is related to the effect of beam hardening; this is discussed in Section Beam Hardening One of the errors associated with the acquisition of images using XCT is beam hardening. This is only found with polychromatic X-ray beams that consist of photons of multiple energies. As the X-ray beam travels through an object and is being attenuated, the lower energies are attenuated to a greater extent than the higher energies (see Figure 1). Number of photons 5x10 7 4x10 7 3x10 7 2x10 7 1x10 7 No filter 0.1 mm Copper 0.5 mm Copper Energy (kev) Figure 1: Energy spectrum of X-rays after travelling through varying thicknesses of copper (simulated in SpekCalc, an X-ray spectrum simulation program [4],[5],[6]). 1

2 This results in an increase in the mean energy of the propagating X-rays; this effect is known as beam hardening as the energies appear to become harder. An artefact is created within the images and is known as cupping. In a homogeneous object, where the greyscale values should be uniform, the edges will appear brighter and the centre will appear darker [7]. 1.2 Reference objects To develop a series of tests to simulate those objects and conditions found in industry is complicated therefore a simple object has to be used. A previous study by the authors [8] used a holeplate (see Figure 2), from which simple measurements of the form and geometry were taken. This previous work highlighted that the geometry of the holes within the holeplate varied systematically depending on the orientation of the holeplate when it was imaged. It also showed that the amount of material the X-rays had to pass through before and after reaching the holes affected results. Due to the large number of holes the path length of the X-rays was not a smooth function, it was therefore harder to understand the processes that were occurring. To investigate this further and to verify the cyclic responses, three simple holeplates were also manufactured at the National Physical Laboratory (NPL) (see Figure 3). The simple design allows a more fundamental understanding of how the shape of an object is affected when it is imaged using XCT. The more complex NPL holeplate along with these simple holeplates were used in this study. Although the object shapes are simple the measurements taken from these test objects could be used for more complex objects found in industry, such as cylinder bores found in engine blocks. 2 Method All experiments were carried out on a commercially available metrology XCT system with a maximum voltage of 225 kv and power of 225 W. The manufacturer states the Maximum Permissible Error as (9 + L/50) µm where L is in mm. 2.1 Holeplates The more complex holeplate was manufactured at NPL and is based on a design by Physikalisch-Technische Bundesanstalt (PTB) [9] and the ISO/TC 213/WG 10. It is ( ) mm in size and is made of aluminium, the holes have a nominal radius of 2 mm. Figure 2: NPL holeplate schematic showing position of holes. The simple holeplates have the same dimensions as the NPL holeplate but only have one hole. These correspond to the locations of holes found in the more complex holeplate to allow comparison of the results. A profile has been taken around the midpoint of the holes and the roundness is within ±5 µm. Both the NPL holeplate and the simple holeplate were imaged at 3 different orientations, 0, 45 and 90 to horizontal. The holeplates were supported on a carbon fibre frame and imaged at a magnification of times 1.6, giving a voxel size of 125 µm. Figure 3: holeplates with single holes. Hole number 6, 14 and 17 from left to right. 2

3 The simple holeplates were imaged at 170 kev and µm, this voltage was calculated to obtain a 14 % transmission through the holeplate when it was at 0. This level of transmission allows for the optimum contrast [10]. It was decided to keep the tube voltage at this setting for the other orientations for consistency. The XCT manufacturer s software was used to reconstruct the images into volumes. This voxel data was subsequently imported into VGStudio Max, version 2.2, a commercial visualisation and analysis software for XCT data, developed by Volume Graphics GmbH. To determine the surface of the holeplates, initially the greyscales for the air and the material were defined. This preliminary value was then used as a starting value for an algorithm that searches for the greatest rate of change in the greyscale across the air/material interface; this point is defined as the surface of the holeplate. Once a surface is determined a cylinder is fitted to the holes, this is done using a Chebyshev technique. Data about this cylinder can be obtained, including information on the fit points used to fit the cylinder. This information includes the x, y and z coordinates of the fit points and their deviations from the cylinder edge, as shown in Figure 4. Figure 4: Definitions used for a fitted cylinder. The coordinates of the fit points can be used to define the bearing of the fit point from the top of the holeplate, as shown in Figure 5. An average deviation was taken every 10 and these can then be used to define the shape of the holes. Figure 5: Orientation of bearing of fit point. When the holeplates are imaged at 0, the path lengths of the X-rays through the holeplate were calculated around the cylinders, from one edge of the holeplate to the other, through the centre of the hole, every 10. A schematic of this can be seen in Figure 6. Figure 6: Schematic of some path lengths through the holeplate, in this example for Cylinder 14. 3

4 3 Results The shape and geometry of the holes can be determined by studying the fit point deviations used to fit the cylinders. The fit points plotted against the average deviation taken every 10 can be seen below in Figure 7, Figure 8, Figure 9 and Figure Comparison of complex and simple holeplates at 0 orientation When imaging the complex NPL holeplate, Cylinder 17 as identified in Figure 2 as the central hole, shows the most distinctive trend with a trough at 45, 135, 225 and 315 bearing, the deviation being approximately - µm (see Figure 7). There are also peaks of equal magnitude at an offset of 45 to the troughs. The trends are very similar to when the simple holeplate was imaged with the peaks and troughs at similar bearings around the holes. For Cylinder 6 (identified in Figure 2), which is a corner hole, there are less defined peaks and troughs for the complex holeplates, the main trough being at 225 with a deviation of approximately - µm. The main peak is at 315 with a deviation of 10 µm. For the simple holeplate, the two peaks and troughs are much more pronounced, they also differ in amplitude. The deviations range from -75 µm to 115 µm. Cylinder 6 Cylinder Total path length (mm) Cylinder Path length (mm) Cylinder Cylinder Bearing (degrees) Cylinder Bearing (degrees) Figure 7: Fit point deviations around cylinder and total path length for the complex holeplate and the simple holeplates imaged at 0. It should be noted that the individual holes in the different holeplates are not identical. Path length (mm)

5 Both Cylinder 6 and 17 show a cyclic trend for both the complex and simple holeplates, this however is not the case for Cylinder 14. For the complex holeplate the deviations range from -25 µm to 18 µm. For the simple holeplate, the range is between -29 µm and 28 µm. When comparing the two trends for the two holeplates there does not appear to be a correlation. For Cylinder 6 there is a positive correlation between the deviations and the path lengths, i.e. as the path lengths increase the deviations become more positive. However, for Cylinders 14 and 17 the correlation is negative, as the path lengths increase the deviations become more negative. The path lengths for Cylinder 17 in the simple holeplate have a very symmetrical trend with troughs at the sides and peaks at the corners (as shown in Figure 7). However, this is not reflected in the deviation plots which are not even, this will be discussed further in section 4.1. Cylinder 6 Cylinder 14 Cylinder 17 0 degrees Deviation (mm) Figure 8: Comparison of all three holes at 0 orientation. When the holeplate is at 0 there is no correlation between fit point deviations and the bearing around the cylinders (as shown in Figure 8). Cylinder 6 has the biggest deviation range from -75 µm to 115 µm. Cylinder 14 shows the least variation with the fit points ranging from - 27 µm to 27 µm. 3.2 Comparison of orientations for simple holeplates during imaging Figure 7 illustrates how the apparent shape of the hole changes depending on the orientation of the holeplate. Each hole shows similar trends for orientations of 45 and 90, if in varying amounts. When the simple holeplates are imaged at 45, the maximum deviations can be found at a bearing of 0 /3 and 180. The central cylinder, cylinder 17, shows the greatest deviations, with a maximum of -70 µm at the top of the cylinder. Cylinder 14 shows the least deviation with a range of between -25 µm and 20 µm. When the simple holeplates are in a vertical position, 90, all holes show a cyclical trend, with troughs at a bearing of 45, 135, 215 and 315. The peaks for all three holes are less pronounced than the troughs and are not of similar amplitude. The peaks at 0 /3 and 180 are larger than those at 90 and 270 for all three holes. 45 degrees Cylinder 6 Cylinder 14 Cylinder degrees Deviation (mm) - Deviation (mm) Figure 9: Fit point deviations for the simple holeplates imaged at 0, 45 and 90 to the horizontal. 5

6 4 Discussion The results indicate that this series of tests is useful to characterize systematic errors during the imaging and measurement process when using XCT. All of the results indicate that the fit points vary around the cylinder and that they follow a trend depending on their bearing around the centre of the hole. When comparing the results from the previous study [8], it shows that the simple holeplates can exacerbate the problems associated with the cylindricity, especially if the hole is off centre of the holeplate, which is the case for Cylinders 6 and X-ray path lengths The graphs in Figure 7 show that there appears to be a correlation between the path length of the X-rays as they travel through the holeplate and the shape of the hole. However, as described in section 3.1 the correlation is not always positive and this makes it difficult to characterize as it can then not be presumed that the shape of an object should be corrected in a particular way just because the path length along that particular line is a given length. There appears to be an optimum length along which deformation does not occur. A study by Dewulf et al. [11] states that due to beam hardening, the number of photons hitting the detector, after attenuation by the material, is not strictly linearly related to the material thickness. The greyscale value of the pixel is related to the attenuation coefficient of the material which is dependent on the energy. As the effective energy is dependent on the path length (i.e. it increases as the X-ray beam becomes harder) the estimate of the pixel value is dependent on the path length. As mentioned earlier in Section 1.1.1, beam hardening changes the mean energy spectrum of the X-rays as it travels through an object. Figure 10 illustrates how the spectrum changes for the minimum and maximum path lengths found within the holeplates. This indicates how much the beam hardens as it travels through the holeplate and how this could change the apparent attenuation coefficients for a given part of the object resulting incorrect greyscale values being assigned to the pixels which results in apparent distortion in the geometry of the object. Number of photons 6x10 7 5x10 7 4x10 7 3x10 7 2x10 7 1x10 7 Simulated spectrum No material 13mm Aluminium 64mm Aluminium 3x10 5 2x10 5 1x Energy (kev) Figure 10: Simulated spectrum for minimum and maximum path lengths through simple holeplates (simulated in SpekCalc [4],[5],[6]). In Figure 7 the deviations of the fit points for Cylinder 17 are not exactly symmetrical indicating an uneven deformation despite the path lengths being even at different points around the holeplate; this would indicate that another error is affecting the results. This could include the source, holeplate and detector not being in exact alignment with each other. 4.2 Orientation of holeplate during imaging The simple holeplates more greatly illustrate the effects caused by the orientation of the holeplate during imaging. The results show that the shape of the hole is optimized and more accurate when the object is at 45 with all the holes having a systematic shape, the holes are however still being pushed in at the two poles. The errors are systematic when the holeplate is at 90 and show the same trends for all of the holes. The variation in deviation could again be caused partly by beam hardening, the amount of which will varying depending on the orientation as the path lengths will also change depending on the orientation. 4.3 Shape of cylinders and lines of symmetry When comparing the position of the hole within the overall holeplate and the surrounding material it can be seen that the deformation around a given hole is related to the symmetry of the holeplate itself, as seen in Figure 11. This is most obvious for Cylinder 6 where the shape of the hole is elliptical with the major axis running down the line of symmetry. It can be noted that 6

7 although the peaks run along this line the peak sizes are not even and this could be related to the fact that on the bearing of 315 there is a greater amount of material for the X-rays to travel through than at 135. Cylinder 17 in Figure 11 highlights the fact that the deviations are greatest when the path lengths are at their shortest. These errors are most likely associated with beam hardening. Villarreal et al. [12] state that the effective attenuation coefficient will change depending on the thickness of the material and this can lead to distortions in the reconstructed volume Cylinder Figure 11: Radial plots of the fit point deviations around the cylinders along with lines of symmetry (orange line). The fit points have been offset by 0.2 mm for ease of viewing Cylinder Cylinder Conclusions This series of experiments has shown that there is a correlation between the reconstructed geometry of a cylinder within a holeplate and the amount of material that X-rays have to pass through in order to create the images necessary for reconstruction. In the ( ) mm aluminum holeplate, clear systematic discrepancies of between -75 µm and 115 µm are apparent in the reconstruction for each 4 mm cylindrical hole, however, these errors are as yet not fully understood. For example, a longer X- ray path length through the plate does not necessarily mean a larger deformation so this needs to be investigated further. The use of a range of holeplates, each bearing just a single hole, but in different positions, provided a simple test object that is easily manufactured but shows efficiently the effects of differing X-ray path lengths through the material. Future work will include imaging the holeplates at a repeatable location to ensure alignment between the source, object and detector. The correct settings based on ISO [7] will also be used for the different orientations. The path lengths around the holes when the holeplates are at 45 and 90 will also be calculated. Acknowledgements This research is based on a collaborative project funded by the EPSRC (Engineering and Physical Sciences Research Council) and the National Physical Laboratory through the VEIV (Virtual Environments Interaction and Visualisation) Engineering Doctorate Centre at University College London. References [1] VDI/VDE-Richtlinien, VDI Computed tomography in dimensional measurements, Dusseldorf, [2] N. Flay, W. Sun, S. B. Brown, R. K. Leach, and T. Blumensath, Investigation of the Focal Spot Drift in Industrial Conebeam X-ray Computed Tomography, in Digital Industrial Radiology and Computed Tomography (DIR 2015) 22-25, 2015, no. June, pp [3] M. Ferrucci, R. K. Leach, C. L. Giusca, W. Dewulf, and S. Carmignato, Towards geometrical calibration of X-ray computed tomography systems - A review, Meas. Sci. Technol., vol. 26, p., [4] G. Poludniowski, G. Landry, F. DeBlois, P. M. Evans, and F. Verhaegen, SpekCalc: a program to calculate photon spectra from tungsten anode x-ray tubes., Phys. Med. Biol., vol. 54, no. 19, pp. N433 N438, [5] G. Poludniowski and P. M. Evans, Calculation of x-ray spectra emerging from an x-ray tube. Part I: Electron penetration characteristics in x-ray targets, Med. Phys., vol. 34, no. 6, pp , [6] G. G. Poludniowskia, Calculation of x-ray spectra emerging from an x-ray tube. Part II. X-ray production and filtration in x-ray targets, Med. Phys., vol. 34, no. 6, pp , [7] J. F. Barrett and N. Keat, Artifacts in CT: recognition and avoidance., Radiographics, vol. 24, no. 6, pp , Jan [8] H. C. Corcoran, S. B. Brown, S. Robson, R. D. Speller, and M. B. McCarthy, Observations on the performance of X- Ray computed tomography for dimensional metrology, in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives, 2016, vol. 41, no. July, pp [9] M. Bartscher, O. Sato, F. Härtig, and U. Neuschaefer-Rube, Current state of standardization in the field of dimensional 7

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