Article Article
X-ray Computed Tomography for Dimensional Measurements

Industrial X-ray computed tomography (CT) systems have the ability to map internal and external structures simultaneously in a non-destructive way with high imaging resolution. Recently, there has been an increase of surveys in the field of dimensional metrology referring to CT as a tool for nondestructive dimensional quality control (i.e., traceable measurement and geometrical tolerance verification of industrial components). This increase in surveys runs parallel to the growth of commercial markets for industrial X-ray CT technologies and research institutes as well as metrology-governing bodies’ growing interest in creating standarization. Currently, there is a lack of international standards that provide comprehensive procedures and guidelines for dealing with the verification of CT systems’ dimensional metrology performance and developing task-specific measurement uncertainty budgets in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM). To overcome this, some CT manufactures have opted to design their own calibration methods so that they can provide an estimate of maximum permissible error (MPE) for the measurements obtained with systems dedicated to metrology tasks. Essentially, the traceability of the instrument to the meter is provided with an expanded uncertainty upper-bounded by the MPE. In an effort to clarify some of these concepts, this paper gives a brief review of the use of X-ray CT for dimensional metrology with an update on the international attempt to create standards for metrological testing and uncertainty assessment with this technique. An example of in-house calibration is presented, which found deviations in the range -4.4 μm to 3.5 μm between CT measurements and calibrated references obtained at the National Institute of Standards and Technology (NIST), and this is contrasted to the MPE limits pre-established for CT measurement. A particular emphasis is made in the understanding of the terms “trueness,” “precision,” “accuracy,” and “uncertainty,” so the main metrology-related terminology is revisited with reference to international standards and other guidelines. It is concluded that while in-house calibrations might suffice, international standards are still needed, not only to reach homogeneity in the commercial market but also to avoid misinterpretations. In addition, users and manufacturers from the industry of measuring equipment need to better understand the terms “accuracy” and “uncertainty,” which are often misused and interchanged.

  • [1] L. De Chiffre, S. Carmignato, J. P. Kruth, R. Schmitt and A. Weckenmann, "Industrial applications of computed tomography," CIRP Annals - Manufacturing Technology, vol. 63, pp. 655-677, 2014.
  • [2] H. Villarraga-Gómez, "Seeing is believing: X-ray computed tomography for quality control," Quality Magazine, vol. 55, no. 6, pp. 20-23, June, 2016.
  • [3] F. Léonard, S. B. Brown, P. J. Withers, P. M. Mummery and M. B. McCarthy, "A new method of performance verification for x-ray computed tomography measurements," Measurement Science and Technology, vol. 25, no. 6, pp. 1-10, 2014.
  • [4] H. Villarraga-Gómez, E. P. Morse, R. J. Hocken and S. T. Smith, "Dimensional metrology of internal features with X-ray computed tomography," in 29th ASPE Annual meeting, Boston, MA, 684-689, 2014.
  • [5] H. Villarraga-Gómez, D. O. Clark and S. T. Smith, "Strategies for coordinate metrology on flexible parts: CMMs vs CT," in ASPE Mets & Props, 60, J. Phys.: Conf. Ser., Charlotte, NC, 1-7, 2015.
  • [6] H. Villarraga-Gómez, C. Lee, S. P. Charney, J. A. Tarbutton and S. T. Smith, "Dimensional metrology of complex inner geometries built by additive manufacturing," in ASPE Spring Topical Meeting, Raleigh, NC, 164-169, 2015.
  • [7] A. M. Cormack, "Reconstruction of densities from their projections, with applications in radiological physics," Phys. Med. Biol., vol. 18, no. 2, pp. 195-207, 1973.
  • [8] A. M. Cormack, "Representation of a function by its line integrals, with some radiological applications," J. Appl. Phys., vol. 34, no. 9, pp. 2722-2727, 1963.
  • [9] A. M. Cormack, "Representation of a function by its line integrals, with some radiological applications II," J. Appl. Phys., vol. 35, no. 10, pp. 2908-1913, 1964.
  • [10] J. Radon, "Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten (“On the determination of functions by their integral values along certain manifolds”)," Ber. König Säch. Aka. Wiss. (Leipzig), Math. Phys., vol. 69, pp. 262-267, 1917.
  • [11] G. N. Hounsfield, "Computerized transverse axial scanning (tomography)—part 1 Description of the system," Br. J. Radiol., vol. 46, pp. 1016-1022, 1973.
  • [12] J. Ambrose, "Computerized transverse axical scanning (tomography)—part 2. Clinical applications," Br. J. Radiol., vol. 46, pp. 1023-1047, 1973.
  • [13] B. J. Perry and C. Bridges, "Computerized transverse axial scanning (tomography)—Part 3. Radiation dose considerations," Br. J. Radiol., vol. 46, pp. 1048-1051, 1973.
  • [14] J. W. Kress and L. A. Feldkamp, "X-Ray tomography applied to NDE of ceramics," in ASME 1983 International Gas Turbine Conference and Exhibit, Phoenix, AZ, 1-5, 1983.
  • [15] W. B. Gilboy, "X- and γ-ray tomography in NDE applications," Nuclear Instruments and Methods in Physics Research, vol. 221, no. 1, pp. 193-200, 1984.
  • [16] P. Reimers, W. B. Gilboy and J. Goebbels, "Recent developments in the industrial application of computerized tomography with ionizing radiation," NDT International, vol. 17, no. 4, pp. 197-207, 1984.
  • [17] L. A. Feldkamp, L. C. Davis and J. W. Kress, "Practical cone-beam algorithm," J. Opt. Soc. Am. A, vol. 1, no. 6, pp. 612-619, 1984.
  • [18] L. A. Feldkamp and G. Jesion, "3D X-ray computed tomography," in Review of Progress in Quantitative Nondestructive Evaluation, New York, USA, Springer Science, 555-566, 1986.
  • [19] J. Hsieh, B. Nett, Z. Yu, K. Sauer, J.-B. Thibault and C. A. Bouman, "Recent advances in CT image reconstruction," Current Radiology Reports, vol. 1, no. 1, pp. 39-51, 2013.
  • [20] T. M. Buzug, Computed Tomography: From Photon Statistics to Modern Cone-Beam CT, Leipzig, Germany: Springer-Verlag Berlin Heidelberg, 2010.
  • [21] A. Katsevich, "Exact filtered back projection (FBP) algorithm for spiral computer tomography". US Patent 6,574,299, 2003.
  • [22] A. Katsevich, "Theoretically exact filtered backprojection-type inversion algorithm for spiral cone-beam," SIAM J. Appl. Math., vol. 62, no. 6, p. 2012–2026, 2002.
  • [23] A. Katsevich, "An improved exact filtered backprojection algorithm for spiral computed tomography," Adv. Appl. Math., vol. 32, no. 4, p. 681–697, 2004.
  • [24] J. Muders, J. Hesser, A. Lachner and C. Reinhart, "Accuracy Evaluation and Exploration of Measurement Uncertainty for Exact Helical Cone Beam Reconstruction Using Katsevich Filtered Backprojection in Comparison to Circular Feldkamp Reconstruction with Respect to Industrial CT Metrology," in International Symposium on Digital Industrial Radiology and Computed Tomography, Berlin, Germany, 2011.
  • [25] V. Aloisi, S. Carmignato, J. Schlecht and E. Ferley, "Investigation on metrological performances in CT helical scanning for dimensional quality control," in 6th Conference on Industrial Computed Tomography, Wels, Austria, 2016.
  • [26] R. H. Bossi, J. L. Cline and G. E. Georgeson, "X-ray computed tomographic inspection of castings," Review of Progress in Quantitative Nondestructive Evaluation, vol. 10B, pp. 1883-1790, 1991.
  • [27] R. Bossi, A. Crews, G. Georgeson, J. Nelson and J. Shrader, "X-ray computed tomography for geometry acquisition," Review of Progress in Quantitative Nondestructive Evaluation, vol. 12, pp. 343-349, 1993.
  • [28] G. Georgeson and R. Bossi, "X-ray CT for quantitative casting material evaluation," Review of Progress in Quantitative Nondestructive Evaluation, vol. 12, pp. 1681-1688, 1993.
  • [29] S. T. Neel, D. S. Eliasen and R. N. Yancey, "Dimenasional measurement of internal features in complex castings," Review of Progress in Quantitative Nondestructive Evaluation, vol. 14, pp. 689-694, 1995.
  • [30] S. T. Neel and R. N. Yancey, "X-ray computed tomography application in research," Review of Progress in Quantitative Nondestructive Evaluation, vol. 15, pp. 497-502, 1996.
  • [31] S. T. Neel, R. Gibson and C. R. Daniels, "Dimensional accuracy in X-ray computed tomographic imaging," Review of Progress in Quantitative Nondestructive Evaluation, vol. 17, pp. 411-418, 1998.
  • [32] H. C. Saewert, D. Fiedler, M. Bartscher and M. Wäldele, "Obtaining dimensional information by industrial CT scanning – present and prospective process chain," in International Symposium on Computed Tomography and Image Processing for Industrial Radiology, Berlin, Germany, 163-172, 2003.
  • [33] M. Bartscher, U. Neuschaefer-Rube and F. Wäldele, "Computed Tomography - a highly potential tool for Industrial quality control and production near measurement," in 8th International Symposium on Measurement and Quality Control in Production, Erlangen, Germany, 3-8, 2004.
  • [34] C. Reinhart, C. Poliwoda, T. Guenther, W. Roemer, S. Maas and C. Gosch, "Modern voxel based data and geometry analysis software tools for industrial CT," in 16th World Conference on NDT, Montreal, Canada, 1-8, 2004.
  • [35] S. Carmignato, E. Savio and L. De Chiffre, "CT techniques for reconstructing 3D geometrical models of complex parts: an approach for traceability establishment and uncertainty evaluation," in IMEKO Int. Symp. and Mediterraneanterranean Conference on Measurement, Genova, Italy, 387-390, 2004.
  • [36] R. Hennessy, "Dimensional measurement enters new era," Quality Magazine, vol. 44, no. 7, pp. 20-21, 2005.
  • [37] C. Ralf and H. Joachim-Neumann, X-ray Tomography in Industrial Metrology, Munich, Germany: Süddeutscher verlag onpact GmbH, 2012.
  • [38] W. Sun, S. B. Brown and R. K. Leach, "An overview of industrial X-ray computed tomography," National Physical Laboratory, Teddington, UK, 42-47, 2012.
  • [39] J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre and A. Weckenmann, "Computed tomography for dimensional metrology," CIRP Annals - Manufacturing Technology, vol. 60, pp. 821-842, 2011. 
  • [40] S. R. Deans, The Radon transform and some of its applications, Mineola, New York, USA: Dover Publications, Inc., 2007.
  • [41] A. C. Kak and M. Slaney, Principles of computerized tomographic imaging, New York, USA: IEEE Press, 1988.
  • [42] H. Villarraga-Gómez, C. Lee, T. Corbett, J. A. Tarbutton and S. T. Smith, "Assesing additive manufacturing processes with X-ray CT metrology," in ASPE Spring Topical Meeting, Raleigh, NC, Vol 60, pp 116-120, 2015.
  • [43] H. Villarraga-Gómez, A. Ramsey, M. Seifi, J. Lewandowski and Y. Uchiyama, "Assessing the Structural Integrity of Additive Manufactured Metal Parts with X-Ray CT," in ASPE Summer Topical Meeting, Raleigh, NC, 2016.
  • [44] MarketsandMarkets, "Non Destructive Testing (NDT) Market by Method (UT, RT, LPT, MPT, ECT, VI), End-User (Aerospace & Defense, Power Generation, Infrastructure, Oil & Gas, Automotive), Technique, Application & Region (G7, BRICS, RoW) – Global Forecast to 2020," January 2016. [Online]. Available: [Accessed 11 June 2016].
  • [45] Global Industry Analysts, Inc, "Industrial X-Ray Inspection Systems: A Global Strategic Business Report," November 2014. [Online]. Available: [Accessed 11 June 2016].
  • [46] Frost & Sullivan, "Strategic Analysis of Computed Tomography Technology in the Dimensional Metrology Market," 11 September 2015. [Online]. Available: [Accessed 11 June 2016].
  • [47] Frost & Sullivan, "Adapting to the Future of Industrial Measurement using Computed Tomography," 21 October 2015. [Online]. Available: [Accessed 11 June 2016].
  • [48] ISO/IEC Guide 98-3, Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM:1995), ISO copyright office, 2008.
  • [49] S. Kasperl, R. Schielen, F. Sukowski, P. Hornberger and A. Gruber, "CT simulation study to demonstrate material impact using hole plates," in 11th European Conference on Non-Destructive Testing, Prague, Czech Republic, 2014.
  • [50] M. Bartscher, O. Sato, F. Härtig and U. Neuschaefer-Rube, "Current state of standardization in the field of dimensional computed tomography," Meas. Sci. Technol., vol. 25, p. 14pp, 2014.
  • [51] F. Borges de Oliveira, M. Bartscher and U. Neuschaefer-Rube, "Analysis of combined probing measurement error and length measurement error test for acceptance testing in dimensional computed tomography," in Digital Industrial Radiology and Computed Tomography, Belgium, Ghent, 2015.
  • [52] M. Bartscher, J. Illemann and U. Neuschaefer-Rube, "ISO test survey on material influence in dimensional computed tomography," Case Studies in Nondestructive Testing and Evaluation, Vols. --, p. 14pp, to be published by Elsevier, 2016.
  • [53] ASME, "B89 Division 4 - Coordinate Measuring Technology," [Online]. Available: [Accessed 11 June 2016].
  • [54] VDI/VDE 2630-1.3, Computed Tomography in Dimensional Measurement - Guideline for the application of DIN EN ISO 10360 for coordinate measuring machines with CT sensors, Berlin: Beuth Verlag GmbH, 2011.
  • [55] ISO 10360-2, Geometrical Product Specifications (GPS) - Acceptance and reverification tests for coordinate measuring machines (CMM) - Part 2: CMMs used for measuring linear dimensions, Geneva: ISO copyright office, 2009.
  • [56] VDI/VDE 2630-2.1, Computed tomography in dimensional measurement - Determination of the uncertainty of measurement and the test process suitability of coordinate measurement systems with CT sensors, Berlin: Beuth Verlag GmbH, 2015.
  • [57] A. Menditto, M. Patriarca and B. Magnusson, "Understanding the meaning of accuracy, trueness and precision," Accred. qual. Assur., vol. 12, no. 1, pp. 45-47, 2006.
  • [58] E. Prenesti and F. Gosmaro, "Trueness, precision and accuracy: a critical overview of the concepts as well as proposals for revision," Accred. Qual. Assur., vol. 20, pp. 33-40, 2015.
  • [59] Royal Society of Chemistry, "Terminology - the key to understanding analytical science. Part 1: Accuracy, precision and uncertainty," AMC Technical Brief, no. 13, pp. 1-2, 2003.
  • [60] EUROLAB, "EUROLAB Technical Report 1/2006: Guide to the Evaluation of Measurement Uncertainty for Quantitative Test Results," EUROLAB Technical Secretariat, Paris, France, 2006.
  • [61] USA Food and Drug Administration, "Appendix J – STWG Part 3: Uncertainty Associated with Microbiological Analysis," 2006. [Online]. Available:
  • fdagov-foods-gen/documents/document/ucm088762.pdf. [Accessed 26 June 2016].
  • [62] J. Weitzel, "Accuracy, trueness, error, bias, precision, and uncertainty: what do these terms mean?," 2015. [Online]. Available: [Accessed 26 June 2016].
  • [63] D. G. Theodorou, Measurement data analysis in quality management systems - Application to fuel test methods, PhD Thesis, School οf Chemical Engineering: National Technical University of Athens, 2015.
  • [64] BIPM/JCGM, "International Vocabulary of Metrology – Basic and general concepts and associated terms," 2012. [Online]. Available:
  • [65] B. N. Taylor and C. E. Kuyatt, "NIST Technical Note 1297 - Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results," National Institute of Standards and Technology, Gaithersburg, MD, 1994.
  • [66] ISO 5725-1, "Accuracy (trueness and precision) of measurement methods and results — Part 1: Introduction and basic principles," Geneva, ISO copyright office, 2011.
  • [67] Nikon Metrology, "MCT225, Absolute Accuracy for Inside Geometry," [Online]. Available:
  • Metrology-CT-Absolute-accuracy-for-inside-geometry. [Accessed 11 June 2016].
  • [68] S. G. Rabinovich, Evaluating Measurement Accuracy, A practical Approach, 2nd Ed, New York, NY: Springer, 2013.
  • [69] J. J. Lifton, A. A. Malcolm and J. W. McBride, "On the uncertainty of surface determination in x-ray computed tomography for dimensional metrology," Measurement Science and Technology, vol. 26, no. 3, pp. 1-8, 2015.
  • [70] M. Fleßner, A. Müller, D. Götz, E. Helmecke and T. Hausotte, "Assessment of the single point uncertainty of dimensional CT measurements," in 6th Conference on Industrial Computed Tomography, Wels, Austria, 2016.
  • [71] C. Affenzeller, C. Gusenbauer, M. Reiter and J. Kastner, "Measurement uncertainty evaluation of an X-ray computed tomography system," in Digital Industrial Radiology and Computed Tomography, Belgium, Ghent, 2015.
  • [72] P. J. de Groot, "Progress in the specification of optical instruments for the measurement of surface form and texture," in SPIE Vol. 9110 “Dimensional Optical Metrology and Inspection for Practical Applications III”, Baltimore, MD, 2014.
  • [73] R. K. Leach, "Is one step height enough?," in 30th ASPE Annual Meeting, Austin, TX, pp 110-113, 2015.
  • [74] S. Carmignato, A. Pierobon and E. Savio, "Interlaboratory Comparison of Computed Tomography Systems for Dimensional Metrology: CT Audit," Final Report, University of Padova - Lab. MGI, Italy, 2012.
  • [75] J. J. Lifton, A. A. Malcolm, M. J. W and K. J. Cross, "The application of voxel size correction in X-ray computed tomography for dimensional metrology," in Singapore International NDT conference, Marina Bay Sands, Singapore, 2013.
  • [76] P. Müller, "Use of reference objects for correction of measuring errors in X-ray computed tomography," DTU Mechanical Engineering, Technical University of Denmark, 2010.
  • [77] W. Sun, S. B. Brown and R. K. Leach, "An overview of industrial X-ray computed tomography, NPL Report ENG 32," National Physical Laboratory, Teddington, UK, 2012.
Usage Shares
Total Views
707 Page Views
Total Shares
0 Tweets
0 PDF Downloads
0 Facebook Shares
Total Usage