1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Industrial Computer Tomography for Dimensional Metrology: Overview of Influence Factors and Improvement Strategies F. a, K. Kiekens b, M. Pierlet b, W. Dewulf b, P. Bleys a, J.-P. Kruth a and A. Voet c Abstract While Computer Tomography (CT) has since long been used for medical applications and material inspection, its application field has recently been broadened to include dimensional metrology in industry. In particular, it provides a unique means of measuring assemblies, complex structures as well as the inner geometry of parts made by rapid manufacturing in a non-destructive way. However, the accuracy of CT-based measurements remains yet largely uncertain, due to a number of influencing factors related to the workpiece, the CT equipment as well as the measurement setup. This paper first classifies the factors influencing the CT performance on the basis of the basic components of the CT system. Next, the obtained knowledge is used to suggest improvement strategies to ameliorate the accuracy of CT measurements. Contact information a frank.welkenhuyzen@mech.kuleuven.be philip.bleys@mech.kuleuven.be jean-pierre.kruth@mech.kuleuven.be Department of Mechanical Engineering, K.U.Leuven Celestijnenlaan 300B, B-3001 Leuven, Belgium b kim.kiekens@groept.be mieke.pierlet@groept.be wim.dewulf@groept.be Groep T - International University College Leuven, K.U.Leuven Association A. Vesaliusstraat 13, B-3000 Leuven, Belgium c andre.voet@denayer.wenk.be De Nayer Instituut J. De Nayerlaan 5, B-2860 Sint Katelijne Waver, Belgium 1
41 42 43 44 45 46 47 48 49 1. Introduction Computer Tomography (CT) is a well known technique in the medical world and in the field of material inspection. Its application field has recently been broadened to include dimensional metrology. CT enables measuring the objects outside as well as the inside (e.g. invisible holes) in a non-destructive way. The ability to measure the inside of a part makes industrial Computer Tomography attractive and unique in the world of dimensional metrology. Assemblies, complex structures as well as the inner geometry of parts made by rapid manufacturing can be measured in a non-destructive way. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 Figure 1: Principle of industrial Computer Tomography (illustrated in case of a flat panel detector) [1]. Figure 1 illustrates the principle of Computer Tomography. A source produces X-rays by projecting electrons on a target. As the X-rays penetrate the workpiece (sample), the X-rays are attenuated (made weaker), due to absorption or scattering. The amount of attenuation is determined by the amount of material penetrated, but also by the material composition, After penetrating the workpiece, the attenuated X-rays will incident on the detector, resulting in a 2D gray image. 2D images are taken for many rotation steps of the workpiece. Reconstruction based on these projected images leads to a 3D voxel model (a voxel is the 3D analogue of a pixel), where the gray value of the voxels are a measure for the density of the material. This paper describes the different factors influencing CT performance (Section 2) and considers improvement strategies to ameliorate the accuracy of CT measurements (Section 3). 2. Factors influencing CT performance In order to quantify the accuracy of measurements using Computer Tomography, one has to identify the error sources. Figure 2 classifies the most important factors influencing CT performance using the basic components of the CT system as a starting point. X-ray Source The factors related to the X-ray source are partly determined by the machine, but also partly to be chosen by the operator. The X-ray tube voltage can be chosen by the operator within a machine specific range. The higher the voltage, the more penetrating the X-ray beam becomes. The applied current is a user-defined input as well, which affects the intensity of the beam (i.e. the quantity of radiation energy) [2]. 2
77 78 79 80 81 82 83 84 85 86 87 Figure 2: Classification of factors influencing the CT performance. Another important quantity is the focal spot size. Figure 3 illustrates the effect induced by the spot size. The smaller the spot size, the sharper the edges will be. In case of large spot sizes unsharpness will occur, known as the penumbra effect. A disadvantage of a smaller spot size is the concentrated heat produced at the spot on the target (transmissive, rotating, ) inside the X- ray tube, requiring cooled targets and limiting the maximum applicable voltage. 88 89 90 91 92 93 94 95 96 97 98 99 Figure 3: Small spot size (left) compared to large spot size (right). Other influencing factors are the target material and type (reflective or transmission target), the X-ray spectrum, The polychromatic character of conventional X-ray sources causes the well known effect of beam hardening: while the X-ray beam penetrates material, the low-energy X-rays (soft X-rays) are more easily attenuated than the higher-energy X-rays. As a consequence the image on the detector differs from the expected image, resulting in observable errors in the reconstructed volume. The amount of beam hardening depends on the initial X-ray spectrum as well as on the composition, density and the amount of material traversed. One way to reduce beam hardening is to place a thin sheet filter in front of the workpiece in order to absorb the low 3
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 energy radiation from the spectrum, hence approximating a more monochromatic energy distribution. Disadvantages are the loss of intensity with corresponding reduction of the signal-to-noise ratio due to a limited dynamic range of the detector [3] and inadequate results in case of multi-material objects [4]. Rotation Table and Workpiece Since CT implies a reconstruction of X-ray images taken at different orientations, the workpiece is mounted on a rotation table. Influencing factors of this rotation table are the geometrical errors of the mechanical axes and the number of rotation steps chosen by the operator. Also workpiece characteristics including e.g. material composition and dimensions influence the accuracy of the CT results. Detector Two types of detectors can be distinguished: 2D flat panel detectors and 1D line detectors. When using a flat panel detector, a single rotation of the object normally suffices, provided the detector is sufficiently large (in combination with restricted magnification). For line detectors, the rotation of the object should be complemented with an additional vertical displacement for every slice to be measured (e.g. 10,000 shifts of 10 µm for a 100 mm workpiece with 10 µm resolution). Consequently, the use of a line detector is more time consuming. Line detectors may however accommodate higher beam power (i.e. thicker objects) and better accuracy. A recent possibility (yet, since long applied in the medical world) is the use of a helix CT [5], where the workpiece makes a helical movement. Other important detector characteristics include pixel size, number of pixels, exposure time and signal-to-noise ratio. Data Processing Processing the detector output consists of two steps: reconstruction of the 2D images into a 3D voxel model, followed by the actual measurements (including determination of the edges, thresholding). While discussing the drawbacks of the polychromatic character of the X-ray source above, the problem of beam hardening was already mentioned: without appropriate corrections, beam hardening results in observable errors in the reconstructed volume. Another problem related to the reconstruction is X-ray scattering: as the X-ray beam passes through material some of the original energy in the beam can be deflected onto a new path. The effect changes with each projection resulting in artifacts in the reconstructed image [6]. Positional Relationship The distances between the detector, X-ray source and workpiece have a great influence on the accuracy of the CT measurements. A geometrical magnification is achieved by positioning the object close to the source. As a result more pixels of the detector are used, theoretically improving the resolution. However, at the same time the image becomes more blurred annihilating part of the benefit: A smaller distance between the source and the workpiece results in less parallel X-ray beams and a larger penumbra effect (i.e. less sharp edges). 4
142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 3. Improvement strategies Section 2 provided a short overview of the factors influencing CT performance. Hilpert et al. [7] provided a list of strategies improving this performance; an extended list is provided and discussed in this section. Improvement of dedicated CT components This improvement strategy is more devoted to CT equipment manufacturers; for users it is primarily a concern at the time of purchase. Particularly the X-ray source and the detector are concerned in this improvement strategy, e.g. a detector with smaller pixel size and better signal-to-noise ratio, or an X-ray source with a smaller spot size. Improvement of the hardware stability Using CT as a measuring device raises the question whether the machine construction techniques used for Coordinate Measuring Machines (CMMs) should be adopted: granite tables, air bearings, Referring to Figure 2, this concerns the geometrical errors of the mechanical axes, precision of and minimal rotation steps of the rotational table, and the positional relationship between rotation table, source and detector. Wenig et al. [8] investigate the dependency of the measurement error and the measurement quality on the adjustment accuracy of the mechanical positioning system by simulation of various alignment accuracies. 0,4 0,35 0,3 162 163 164 165 166 167 168 169 170 171 172 173 174 175 Error (mm) 0,25 0,2 positive Z-direction: measurement 1 0,15 positive Z-direction measurement 2 0,1 negative Z-direction measurement 1 0,05 negative Z-direction measurement 2 0 0-0,05 100 200 300 400 500 600 700 800 Position (mm) Figure 4: Positioning errors of the Z-axis (Magnification axis). To illustrate the occurrence of geometrical errors of the mechanical axes, Figure 4 represents the positioning errors (error between inputted and actual position) of the Z-axis (magnification axis, axis between source and detector) of a CT machine available to KULeuven. The errors on the position are measured over a range of 700 mm. The values are represented both when moving in positive Z-direction and when moving in negative Z-direction. All errors are measured twice, using a laser interferometer, similar to the international standard ISO 230, Part 2: Determination of accuracy and repeatability of positioning numerically controlled axes [9]. The results show a high difference in repeatability of the both directions. Furthermore there is a large direction dependency. It can be concluded that positioning of the object at the same Z-position can lead to high differences in the actual position. For instance if a reference standard 5
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 is used, the Z-axis by preference shouldn t be moved when interchanging the object and the reference standard. If movement of the Z-position is nevertheless necessary the final movement direction to obtain the required position should be the same (for this machine the positive Z-direction is preferred because of the higher repeatability). Optimization of user defined settings Different settings are to be chosen by the operator: voltage and current of the X-ray source, detector exposure time, threshold value, use of appropriate filters (material and thickness) to avoid beam hardening,. There is no simple textbook describing the optimal settings. Instead the user has to determine the values based on his own knowledge and experience, or by prior testing or computer simulation [8,10]. Furthermore the operator is responsible for an optimal orientation of the workpiece. This is illustrated by an experiment, measuring a stepped workpiece with several length dimensions in two directions. Figure 5 demonstrates 2 possible orientations to measure the workpiece. The lengths in Y direction and in Z-direction were measured in both orientations. The results demonstrated that the length measurements in the rotational plane (XZ plane) were much more accurate than those in the Y-direction. Figure 6 also shows that there is much more noise on the planes parallel to the XZ plane (lower accuracy in Y). 195 196 197 198 Figure 5: Two possible orientations for the workpiece of Figure 6. 199 200 201 202 Figure 6: Effects of orientation (left: set-up 1, right: set-up 2) on the workpiece measurements: noise on planes parallel to XZ-plane. 6
203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 Improvement of data processing The captured images obtained by the detector have to be processed. Two steps can be distinguished: Tomographic data reconstruction Reconstructed voxel data post-processing Tomographic data reconstruction combines the 2D projection images to a 3D voxel model. Section 2 (X-ray Source and Data Processing) described two unwanted effects occurring when performing CT: beam hardening and scattering. One way to reduce beam hardening is to use a filter (Section 2, X-ray Source). Another way to decrease these unwanted effect is by algorithmic adaptations, as described by several authors (e.g. [3,4,8,11]). Krumm et al. [4] provide a short overview of common methods to correct beam hardening: pre-filtering (described before), linearization, the dual energy approach and the post-reconstruction method. In addition, Krumm et al. [4] propose a new method to perform beam hardening correction on CT images of multi-material objects. The method combines the advantages of the linearization technique and the post-reconstruction method. Another model to correct beam hardening is presented by Graham et al. [3]. A 3D voxel model is obtained after reconstruction. The next step before being able to measure dimensions is the detection of the edges. The voxel model doesn t simply consist of voxels of 2 (or more in case of multi-material) possible gray values: one representing material and the other one representing air (background). Instead there is a wide range of gray values. A gradual transition, not a simple sharp edge, can be observed at the borders of the workpiece. It is the operator s (or software s) responsibility to determine the edges (Figure 7). Different strategies are possible: one threshold value can be calculated for the complete voxel model (all voxels having a gray value less than the threshold value represent air and the voxels having a higher gray value represent material). More sophisticated methods can be used that evaluate the local gray values near the edge, for instance by taking the average of the local gray values as threshold value or by evaluating the gradients. 231 232 233 234 235 236 237 238 239 240 241 242 243 Figure 7: Edge detection [12]. Reduction of systematic measurement errors via calibrated reference standards Reference standards can be used to reduce measurement errors and to ensure traceability of the measurements to the unit of length (the meter). Reference standards can for instance be used for the correction of scale errors or for the determination of threshold values [13], but also for acceptance and accuracy verification of the CT system. PTB (Physikalisch-Technische Bundesanstalt) developed reference standards for applications in the field of CT metrology. Figure 8 provides some examples [13]: Aluminum hollow cylinders for determining the CT threshold; An Aluminum step-cylinder for CT system analysis and parameterization for cast parts; 7
244 245 246 A Ball-bar made from ceramic balls on a carbon fibre rod for assessment of scale errors and traceability. 247 248 249 250 Figure 8: Reference standards for CT, developed by PTB [13]. 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 Figure 9: Sphere calotte plate made from Zerodur [7]. In [7] and [13] a sphere calotte plate (figure 9), manufactured by PTB is used as reference standard. The results in these publications proof the accuracy improvement. Additional measurement of the workpiece Making use of the data retrieved by an additional (more accurate) measurement of the workpiece by a conventional Coordinate Measuring Machine or by an optical measurement system (e.g. laser line scanner or fringe projection system) improves the CT-data. The extra information can for instance be used to rescale the CT-data. The major advantage of industrial Computer Tomography is the possibility to measure the inside (e.g. holes) of a workpiece. Rescaling the CT data by measurement data obtained from external features of the workpiece by a more accurate machine (which is not capable of measuring the inside) improves the accuracy of the overall CT measurement results (including the inside measurements). Experiments using a flat panel detector illustrate that the use of one scale factor is not sufficient, and at least two distinct scale factors have to be used. The experiment consisted of measuring the lengths in X, Y and Z direction of the workpiece in Figure 5 and Figure 6. It was clear that one scale factor was needed for the Y direction, and another scale factor was necessary for the X and Z direction. Some manufacturers combine the CT principle and additional measurement systems in one machine. Another possibility is accomplishing the additional measurement with a stand-alone machine. Neumayer et al. [14] use an additional optical measurement system to enhance the overall accuracy of CT-data by merging the dataset obtained by CT measurement and a dataset obtained by optical measurement. Franz and Kasperl [11] explain a method that makes use of an additional optical sensor for beam hardening correction, which results in a quality and speed improvement for the industrial CT. This way, beam hardening correction can be achieved during the data collection, whereas this is normally performed afterwards in a very time-consuming step. 8
281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 4. Conclusion Computer Tomography is an interesting technique, well-known in the medical world and in the field of material inspection. The possibility to examine the outside as well as the (invisible) inside of objects makes the technique very attractive for dimensional metrology applications. Nevertheless, significant research efforts remain necessary to enhance the quality of the CT measurements. This paper first classified the factors influencing CT performance. This allows spotting the weaknesses and detecting ways to improve the CT measurements. Next, a list of improvement strategies was listed and discussed. Improvements regarding hardware, software, input parameters as well as the possibility to do an additional measurement of the workpiece or of a reference standard were considered. 5. Acknowledgement The authors acknowledge the support of the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT-Vlaanderen) in the framework of the TETRA programme (project IWT080137). References [1] Phoenix X-ray, http://www.phoenix-xray.com. [2] BALL, J., MOORE, A. D., Essential Physics for Radiographers. Oxford: Blackwell Science, 2006. [3] GRAHAM, D., NITIN, J., JAMES, E., A modelling approach to beam hardening correction. In: Proceedings of the SPIE, September 2008, San Diego. S.R. STOCK, ed., 2008, 707801. [4] KRUMM, M., KASPERL, S., FRANZ, M., Reducing non-linear artifacts of multi-material objects in industrial 3D computed tomography. NDT and E International, 41 (4), 242-251, 2008. [5] Helix-CT, Fraunhofer-Institut für Integrierte Schaltungen ISS, Produktbeschreibung, 2009. [6] KAK, A., SLANEY, M., Principles of Computerized Tomographic Imaging, Philadelphia: SIAM,2001 [7] HILPERT, U., BARTSCHER, M., NEUGEBAUER, M., GOEBBELS, J., WEIDEMANN, G., BELLON, C., Simulation-aided computed tomography (CT) for dimensional measurements, International Symposium on Digital industrial Radiology and Computed Tomography, June 25-27 2007, Lyon, France. [8] WENIG, P., KASPERL, S., Examination of the Measurement Uncertainty on Dimensional Measurements by X-ray Computed Tomography. In: ECNDT Proceedings, September 2006, Berlin. [9] ISO 230-2:2006, Test Code for Machine Tools, Part 2: Determination of Accuracy and Repeatability of Positioning Numerically Controlled Axes. [10] KERKHOFS, G., MOESEN, M., VAN BAEL, S., ELICEGUI, L., MAES, F., LOECKX, D., SCHROOTEN, J., WEVERS, M., Mechanical characterization of porous structures by combining micro- CT imaging and 3D image analysis with in-situ loading, FEA and local strain mapping, submitted to Advanced engineering materials. [11] FRANZ, M., KASPERL, S., Quality and Speed Improvements in Industrial CT by the Use of an additional Optical Sensor, In: ECNDT Proceedings, September 2006, Berlin. [12] Metris, http://www.metris.com. [13] BARTSCHER, M., HILPERT, U., GOEBBELS, J., WEIDEMANN, G., Enhancement and Proof of Accuracy of Industrial Computed Tomography (CT) Measurements, Annals of the CIRP, 56 (1), 495-498, 2007. [14] NEUMAYER, D., MODRICH, K., MAISL, M., KASPERL, S., Computed Tomography as a tool for industrial measurement. In: ECNDT Proceedings, September 2006, Berlin. 9