An initial experimental study on the influence of beam hardening in X-ray CT for dimensional metrology

An initial experimental study on the influence of beam hardening in X-ray CT for dimensional metrology Joseph J. Lifton 1,2, Andrew A. Malcolm 2, John W. McBride 3 1 The University of Southampton, United Kingdom; e-mail: J.J.Lifton@soton.ac.uk. 2 Singapore Institute of Manufacturing Technology, Singapore; e-mail: Andy@SIMTech.a-star.edu.sg. 3 The University of Southampton Malaysia Campus (USMC), Malaysia; e-mail: J.W.Mcbride@soton.ac.uk. Abstract X-ray computed tomography (CT) enables the visualisation and dimensional evaluation of both the internal and external geometry of a workpiece, it is therefore well suited for measuring geometric features that are otherwise inaccessible to tactile and optical instruments. Beam hardening is a wellknown physical process that can degrade the quality of CT images and influence edge detection algorithms that define surface points used for dimensional evaluation. The influence of beam hardening on dimensional measurements has yet to be fully characterised; in this work a comparison is made between measurements evaluated with and without beam hardening correction. The results show beam hardening reduces internal dimensions and increases external dimensions; this effect is shown for two different surface determination methods in the absence of scattered radiation Keywords: Computed tomography, beam hardening, scatter, linearisation, beam stop array, surface determination. 1 Introduction X-ray computed tomography (CT) is a radiographic scanning technique for imaging the cross-sectional material distribution of an object and thus reveals both the internal and external structure of the object. X-ray CT is a powerful tool for non-destructive visualisation and its use is widespread in the medical, automotive, aerospace and semiconductor industries. Recently, advanced manufacturing technologies have enabled the fabrication of components with increasing dimensional complexity, thus for the purpose of quality assurance, new measurement technologies capable of evaluating the dimensions of both internal and external features are required. X-ray CT is an instrument able to resolve such features, however, its measurement accuracy, precision and traceability are still subject to on-going research and standardisation [1, 2]. Beam hardening is the name given to the change in photon energy distribution that occurs as a beam of polychromatic X-rays propagates through an object. Lower energy photons are preferentially absorbed causing the mean energy of the beam to increase; the beam becomes more penetrating and is said to become harder. As a result of beam hardening, the X-ray spectrum that falls incident on a particular volume element becomes dependent on the X-ray path length, thus the attenuation caused by a volume element may differ from one projection to the next. The inverse Radon transform, on which most reconstruction algorithms are based, considers the attenuation caused by any volume element to be independent of X-ray path length and projection angle; this discrepancy leads to artefacts in reconstructed data-sets. Such artefacts include streaks between highly attenuating structures and false density gradients in homogenous materials [3], thus beam hardening degrades the quality of CT datasets. Pre-filters, placed between the source and the workpiece, are used to pre-harden the X-ray spectrum thus reducing the degree of beam hardening, furthermore, beam hardening can be addressed ict Conference 2014 www.3dct.at 197

via algorithmic correction; both pre-filtration and algorithmic correction typically improve image quality statistics of CT images [4, 5, 6]. Since beam hardening influences CT image quality, it follows that it will influence edge detection algorithms that define surface points used for dimensional evaluation; based on this premise, beam hardening will influence dimensional measurements. The effect beam hardening has on dimensional measurements is not yet fully understood; Dewulf et al. [7, 8, 9] have assessed how changing the parameters of a beam hardening correction influences the accuracy and repeatability of dimensional measurements, however, additional research is required to understand the mechanism through which beam hardening influences dimensional measurements and to be able to quantify this influence for the purpose of evaluating measurement uncertainty. To evaluate the influence of beam hardening experimentally, additional influencing factors must also be considered, such as scattered radiation. Scattered radiation causes artefacts similar to those induced by beam hardening; this is most likely due to the fact that both scattered radiation and beam hardening can lower attenuation values in projections. Scattered radiation is considered in this work based on the following consideration: polychromatic attenuation is written as per equation (1), where I 0 is the intensity of X-rays incident on a homogenous object with linear attenuation coefficients µ(e) and thickness t, I is the intensity of X-rays emerging from the object having not undergone an interaction. The term W(E) describes the contribution of each photon energy to the total polychromatic attenuation and is dependent on both the incident X-ray spectrum and the energy characteristics of the detector. Equation (1) concerns a pencil beam of X-rays and a collimated detector; whereas for industrial CT, cone-beam X-ray sources are used in combination with a flat panel detector, thus scattered radiation contributes to the detector output. Scatter raises the detected signal I and thus reduces attenuation values; with this in mind, scattered radiation should be supressed or removed from projections prior to applying a beam hardening correction, else attenuation values may be over-corrected. -ln( I I 0 ) =-ln W(E)e -μ E t de (1) 2 Methodology Starting from the same initial conditions, an aluminium cylinder is CT scanned three times; the cylinder is shown in figure 1. With the aid of a beam stop array, an estimate of scattered radiation is derived and subtracted from each projection; following scatter correction, a linearisation beam hardening correction is applied. Finally, the inner and outer diameters of the cylinder are evaluated using both the ISO50 and local surface determination algorithms; the measurement results are then compared with and without beam hardening correction. Figure 1: The aluminium cylinder used for assessing the influence of beam hardening on both internal and external dimensions. The nominal inner and outer diameters of the cylinder are 30 mm and 40 mm respectively. 198

2.1 Projection acquisition and reconstruction The cylinder is CT scanned with an YXLON FeinFocus Y.Fox (YXLON Int. GmbH), which features a 160 kev tungsten transmission X-ray source, and a Varian PaxScan indirect detector (Varian Medical Systems, Inc.) with 1480 by 1848 pixels, and a pixel size of 0.127 mm. The X-ray source voltage is set as 140 kev, with a current of 6 µa, 720 projections are acquired, with an exposure time of 2 seconds. Projection values from the central detector row are reconstructed into a 1480 2 CT image using a ramp filter and backprojection algorithm as implemented by VG Studio (Volume Graphics GmbH). Only the central slice is reconstructed to simplify the problem from 3D to 2D; this further mitigates the possible influence of Feldkamp artefacts [10]. For each data-set the voxel size is defined by evaluating the accurately known dimensional features of a reference workpiece scanned immediately after the cylinder; details of the reference workpiece and evaluation strategy are given in ref. [11]. 2.2 Scatter correction Scatter is estimated using a beam stop array: this is an array of lead cylinders placed between the X-ray source and the object. It is assumed that all radiation incident on a beam stop is absorbed, thus signals in the beam stop shadows arise from scattered radiation. The beam stop array is comprised of a line of 9 lead cylinders with an interspacing of 5 mm; the lead cylinders are 1 mm in diameter and 6 mm long. Due to the rotational symmetry of the aluminium cylinder, the scatter signal is assumed not to vary with respect to the projection angle; thus the scatter distribution is evaluated for a single projection. Scatter signals are interpolated between beam stop shadows using cubic spline interpolation, the resulting scatter estimate is subtracted from projections acquired without the beam stop array. Figure 2 shows projection values for an uncorrected projection, a projection with scatter correction and the scatter signal itself; the scatter signal shows features observed by Schorner et al. [12], and Peterzol et al. [13], in that the scatter signal closely follows the primary signal. 4 3 Intensity x 10000 2 1 Uncorrected Scatter corrected Scatter signal 0 0 370 740 1110 1480 Pixel number Figure 2: Line profiles showing projection values for the aluminium cylinder with and without scatter correction, the scatter signal is derived from scatter measurements using a beam stop array. ict Conference 2014 www.3dct.at 199

2.3 Beam hardening correction Beam hardening is corrected using a simulation-based linearisation method [5]: the method relies on simulating both polychromatic and monochromatic attenuation, the beam hardening correction function is derived by plotting polychromatic attenuation against monochromatic attenuation and the function approximated with a sixth order polynomial. Polychromatic attenuation is calculated by evaluating equation (1): values of µ(e) are obtained from the NIST XCOM database [14], the maximum X-ray path length is estimated via a ray-tracing algorithm and the term W(E) is estimated from X-ray transmission measurements of an object of known dimensions and composition using the method proposed by Sidky et al. [15]. Monochromatic attenuation is calculated by evaluating the Beer- Lambert law: -ln( I I 0 ) =μt (2) where µ is chosen to be 1.21 cm -1. For the present experimental conditions, this value of µ represents the linear attenuation coefficient of aluminium in the absence of beam hardening; i.e. the attenuation that would result if the incident X-ray spectrum remained unchanged as it propagated through the attenuator [16]. Following scatter correction, projections values are converted to attenuation values and the beam hardening correction function is applied. Figure 3 shows the effect the correction has: attenuation values are raised, and a larger correction is seen for larger X-ray path lengths. 3 Attenuation 2 1 Beam hardening corrected Uncorrected 0 0 370 740 1110 1480 Pixel number Figure 3: Attenuation profiles for the aluminium cylinder with and without beam hardening correction. 2.4 Surface determination and geometry fitting To evaluate dimensional information from a CT data-set discrete surface coordinates are required that describe both the internal and external surfaces of a workpiece; the process of identifying surfaces from CT data is termed surface determination. Surface determination is performed using two different methods: the first is the ISO50 method, which relies on a single grey value to identify surface coordinates. This single grey value is termed the ISO50 value and is derived from a grey value histogram of the CT data-set. The second surface determination method evaluates the turning point of 200

second order polynomials fitted to the grey value gradient normal to the ISO50 edge, and is termed the local method. Both the ISO50 and local method yield sub-pixel surface coordinates; with these surface coordinates circles are fitted by the non-linear least-squares algorithm and the diameter evaluated. 3 Results Figure 4 shows CT images that have been reconstructed from projections with: A) no correction, B) scatter correction, and C) both scatter and beam hardening correction; figure 4D shows line profiles across the inner and outer rightmost edge for each CT image. The line profiles in figure 4D visualise how each correction influences the inner and outer edge profile: for the inner edge, scatter correction reduces blurring, whilst beam hardening correction increases the edge contrast. For the outer edge, scatter correction reduces the background grey values, whilst beam hardening correction raises them slightly. Comparing the line profiles before and after beam hardening correction, the grey value variation in the material region has notably reduced, furthermore, the inner edge contrast has increased and the outer edge contrast has decreased. A B C D 6 Intensity x 10000 4 2 Uncorr. Scatter corr. Scatter & BH corr. 0 1000 1150 1300 Pixel number Figure 4: CT images reconstructed from projections with A) no correction, B) scatter correction, and C) scatter correction and beam hardening correction. D) Line profiles across the rightmost edge of each CT image. A ict Conference 2014 www.3dct.at 201

The measurement results for both the inner and outer diameters evaluated by both the ISO50 and local surface determination methods are shown in figure 5A and B; the labels mono and poly correspond to data reconstructed with and without beam hardening correction respectively and the error bars represent the standard deviation of the three repeated measurement results. The negative slope of the lines in figure 5A indicate that beam hardening reduces the size of the internal diameter, conversely, figure 5B shows that beam hardening increases the size of the external diameter; these observations hold for both surface determination methods. A further comparison of figure 5A and B suggests the influence of beam hardening is greater for external dimensions than internal dimensions. This result is explained based on the following consideration: the outer surface of a workpiece absorbs the majority of the low energy photons that contribute to beam hardening, thus the degree of beam hardening is greater for external surfaces; this is shown in figure 4D by the raised grey values at the outer edge. Based on this reasoning, material surrounding internal surfaces essentially acts a pre-filter, thus the degree of beam hardening is reduced for internal surfaces, i.e. a more monochromatic beam irradiates internal features and thus a reduced effect is seen. Table 1 and 2 summarise the effects and standard deviations of the results plotted in figure 5. Effects are calculated as the mean polychromatic measurement result minus the mean monochromatic measurement result; the standard deviation for each surface determination method is calculated by propagating the standard deviations of all the repeated measurements. Looking to table 1, the voxel size of the data evaluated is 41 µm and the largest effect is 34.4 µm, this being the effect of beam hardening on the outer diameter evaluated via the ISO50 method; based on this result, beam hardening appears to influence dimensional measurements on a sub-voxel level. For the local surface determination method, both the effects and standard deviation are lower than those of the ISO50 method; this result suggests the local method is more robust to the influence of beam hardening and can reduce the variation between repeated measurements; this holds for both inner and outer diameters. The latter result is in agreement with the work of Yagüe-Fabra et al. [17], who showed a particular surface determination algorithm, based on the Canny edge detector, to give a more robust edge definition and therefore lower measurement uncertainty. The agreement of these results is attributed to both methods identifying surface points by evaluating local grey value statistics, rather than a single, global, grey value, as per the ISO50 method 30,06 40,06 Inner cylinder diameter (mm) 30,04 30,02 30,00 ISO50 Local 29,98 Mono Poly Mono Poly. A) B) 40,04 40,02 40,00 39,98 Figure 5: The influence of beam hardening on measuring the inner A) and outer B) diameters of the aluminium cylinder, evaluated using both the ISO50 and local surface determination methods. The error bars are the standard deviation of three repeated measurements. Outer cylinder diameter (mm) ISO50 Local Mono Poly Mono Poly 202

Voxel size = 41 Surface determination method µm Effect ISO50 Local Inner diameter (µm) -22.1-9.3 Outer diameter (µm) 34.4 18.3 Table 1: The effect of beam hardening on the inner and outer diameters of the aluminium cylinder. Standard (µm) deviation Surface determination method ISO50 Local 7.8 7.0 Table 2: Standard deviations of measurement results evaluated with both surface determination methods. 4 Discussion The influence of beam hardening on dimensional measurements is not yet fully understood, however, based on the results of this initial experimental study, beam hardening has been shown to reduce internal dimensions and to increase external dimensions. To further support these observations, reference is made to the work of Dewulf et al. [7], who showed correcting beam hardening to reduce the diameter of a sphere when compared to the uncorrected case; this is to be expected based on our observations, thus the results are in agreement. Beam hardening does not influence dimensional measurements directly, but rather it influences CT image quality [5, 6, 16]. Based on the observation that beam hardening influences internal and external dimensions in opposition, it is hypothesised that beam hardening reduces the contrast of internal edges and increases the contrast of external edges. This change in contrast influences the position of surface coordinates from which dimensional measurements are evaluated, thus beam hardening is considered to have an indirect influence on dimensional measurements. In the presence of beam hardening, internal and external edge profiles differ, it follows that internal and external dimensions require separate treatment when it comes to surface determination; thus the ISO50 method should not be used to evaluate internal and external surfaces simultaneously, unless beam hardening artefacts are corrected. The local surface determination method relies on evaluating local grey value properties and has been shown to be more robust to the influence of beam hardening than the ISO50 method. In future work, the influence of edge contrast on the accuracy of surface determination should be evaluated, this will aid the design of new surface determination algorithms that are robust to artefacts that degrade the quality of CT data-sets. For cone beam CT, scattered radiation should be considered when evaluating the influence of beam hardening experimentally. In this work scatter was assumed constant for all projection angles, furthermore, veiling glare was neglected: this being the spread of a detector signal from the site of primary interaction and has been shown to influence scatter signals estimated via the beam stop method [18]. Motivated by the number of potential sources of error in the experimental set-up, the influence of beam hardening will be further assessed via simulation, with the intention to evaluate the measurement uncertainty due to beam hardening. It is envisioned that by repeatedly evaluating a ict Conference 2014 www.3dct.at 203

geometric feature for spectra of varying polychromaticity and for a given noise distribution, the influence of beam hardening on both measurement accuracy and uncertainty can be evaluated in a Monte Carlo simulation. 5 Conclusions An investigation has been presented on how beam hardening influences dimensional measurements for both internal and external dimensions, using both the ISO50 and local surface determination methods. The influence of beam hardening was assessed in the absence of scattered radiation, thus mitigating the influence scattered radiation may have on dimensional measurements and isolating the influence of beam hardening. The experimental results show beam hardening to reduce internal dimensions and to increase external dimensions, with a greater influence seen for external dimensions. Finally, a comparison of the ISO50 and local surface determination methods showed the local method to be more robust to beam hardening and to reduce measurement variation. References [1] W. Sun, S. B. Brown, R. K. Leach, An overview of industrial X-ray computed tomography, NPL Report ENG 32, 2012. [2] J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, A. Weckenmann, Computed tomography for dimensional metrology, CIRP Annals Manufacturing Technology, 60, 821-842, 2011. [3] BS EN 16016-1, Non destructive testing - radiation methods - computed tomography, 2011. [4] M. Krumm, S. Kasperl, M. Franz, Reducing non-linear artifacts of multi-material objects in industrial 3D computed tomography, NDT&E International, 41, 242-251, 2008. [5] J. J. Lifton, A. A. Malcolm, J. W. McBride, The application of beam hardening correction for industrial X-ray computed tomography, 5 th International Symposium on NDT in Aerospace, Singapore, 2013. [6] E. Van de Casteele, D. Van Dyck, J. Sijbers, E. Raman, An energy-based beam hardening model in tomography, Phys. Med. Biol., 47, 4181-4190, 2002. [7] W. Dewulf, Y. Tan, K. Kiekens, Sense and non-sense of beam hardening correction in CT metrology, CIRP Annals - Manufacturing Technology, 61(1), 495-498, 2012. [8] Y. Tan, K. Kiekens, F. Welkenhuyzen, J. P. Kruth, W. Dewulf, Beam hardening correction and its influence on the measurement accuracy and repeatability for CT dimensional metrology applications, ict Conference Proceedings, Wels, Austria, 2012. [9] Y. Tan, K. Kiekens, F. Welkenhuyzen, J. Angel, L. De Chiffre, J. P. Kruth, W. Dewulf, Simulation-aided investigation of beam hardening induced errors in CT dimensional metrology, ISMTII Conference Proceedings, Aachen and Braunschweig, Germany, 2013. [10] P. Muller, J. Hiller, A. Cantatore, M. Bartscher, L. De Chiffre, Investigation on the influence of image quality in X-ray CT metrology, ict Conference, Austria, 2012. [11] J. J. Lifton, K. J. Cross, A. A. Malcolm, J. W. McBride, A reference workpiece for voxel size correction in X-ray computed tomography, Proc. SPIE, International Conference on Optics in Precision Engineering and Nanotechnology (icopen2013), 87690E, 2013. [12] K. Schorner, M. Goldammer, J. Stephan, Comparison between beam-stop and beam-hole array scatter correction techniques for industrial X-ray cone-beam CT, Nuclear Instruments and Methods in Physics Research B, 269, 292-299, 2011. [13] A. Peterzol, J. M. Letang, D. Babot, A beam stop based correction procedure for high spatial frequency scatter in industrial cone-beam X-ray CT, Nuclear Instruments and Methods in Physics Research B, 266, 4042-4054, 2008. [14] NIST XCOM: Photon cross sections database, http://www.nist.gov/pml/data/xcom. 204

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