Abstract

The finite focal spot is one of the major limitations of the high spatial resolution CT, especially to the high-energy industrial CT system with a macro-focus x-ray source. In this paper, we propose an efficient reconstruction framework through finite focal spot size based projection modeling to improve the spatial resolution of current industrial CT system, and demonstrate the superior performance of this method. First of all, the blurred projection produced by a finite size source is modeled as the integral ideal projection of a given point source over the finite focal spot support. Under the model discretization, the approximate linear equivalence relation between the actual finite focus model and the ideal point source model is established. Then a projection recovery method with this relationship is presented to recover the projection of the finer focal spot from the blurred projection. Finally, a high-spatial resolution image can be reconstructed from the recovered projections using the standard Filtered Back-Projection (FBP) algorithm. Furthermore the noise in the reconstructed image with different model parameters is studied and a difference image based fusion method is presented for the further suppression of the noise caused by the projection analysis processing. Both numerical simulations and real experiments have shown that the proposed reconstruction framework with the outstanding performance and efficiency characteristics can significantly enhance the spatial resolutions of current high-energy industrial CT systems.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
    [Crossref]
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    [Crossref]
  24. P. Kr A Mer and A. Weckenmann, “Multi-energy image stack fusion in computed tomography,” Meas. Sci. Technol. 21, 045105 (2010).
    [Crossref]
  25. C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
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2014 (1)

C. Hofmann, M. Knaup, and M. Kachelriess, “Effects of ray profile modeling on resolution recovery in clinical ct,” Med. Phys. 41, 021907 (2014).
[Crossref] [PubMed]

2013 (3)

A. Weckenmann and P. Kr A Mer, “Computed tomography in quality control: chances and challenges,” P. I. Mech. Eng. B-J. Eng. 227, 634–642 (2013).

Y. Zhu, D. Chen, Y. Zhao, H. Li, and P. Zhang, “An approach to increasing the resolution of industrial ct images based on an aperture collimator,” Opt. Express 21, 27946–63 (2013).
[Crossref]

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

2012 (5)

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

S. Carmignato, “Accuracy of industrial computed tomography measurements: Experimental results from an international comparison,” CIRP Ann.-Manuf. Techn. 61, 491–494 (2012).
[Crossref]

H. Yu and G. Wang, “Finite detector based projection model for high spatial resolution,” J. X-Ray Sci. Technol. 20, 229–238 (2012).

J. Hiller, M. Maisl, and L. M. Reindl, “Physical characterization and performance evaluation of an x-ray microcomputed tomography system for dimensional metrology applications,” Meas. Sci. Technol. 23, 085404 (2012).
[Crossref]

J. Hiller and R. Leonard, “A computer simulation platform for the estimation of measurement uncertainties in dimensional x-ray computed tomography,” Measurement 45, 2166 (2012).
[Crossref]

2011 (1)

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

2010 (3)

P. Kr A Mer and A. Weckenmann, “Multi-energy image stack fusion in computed tomography,” Meas. Sci. Technol. 21, 045105 (2010).
[Crossref]

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

2008 (1)

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

2007 (1)

C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
[Crossref]

2004 (1)

P. J. La Rivi E Re and X. Pan, “Sampling and aliasing consequences of quarter-detector offset use in helical ct,” IEEE T. Med. Imaging 23, 738–749 (2004).
[Crossref]

1982 (1)

Barnes, G.

M. Yester and G. Barnes, “Geometrical limitations of computed tomography (ct) scanner resolution,” in “Proceedings of the Society of Photo-Optical Instrumentation Engr(s), vol. 127. Application of Optical Instrumentation in Medicine. VI,” (1977), pp. 296–303.

Bartscher, M.

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

Bednarek, D. R.

S. K. Gupta, A. Jain, D. R. Bednarek, and S. Rudin, “Overcoming x-ray tube small focal spot output limitations for high-resolution region of interest imaging,” in “Medical Imaging 2012: Physics of Medical Imaging,”.

Beekman, F. J.

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

Bettuzzi, M.

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

Bleys, P.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Brancaccio, R.

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

Brunke, O.

O. Brunke, J. Santillan, and A. Suppes, “Precise 3d dimensional metrology using high-resolution x-ray computed tomography (mu ct),” in “Developements in X-Ray Tomography VII,” vol. 7804 of Proceedings of SPIE (2010), vol. 7804 of Proceedings of SPIE, pp. 78040O–1.
[Crossref]

Carmignato, S.

S. Carmignato, “Accuracy of industrial computed tomography measurements: Experimental results from an international comparison,” CIRP Ann.-Manuf. Techn. 61, 491–494 (2012).
[Crossref]

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

Casali, F.

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

Chen, D.

Choi, K.

L. Fu, K. Choi, and B. De Man, “Enhancement of spatial resolution in model-based iterative ct reconstruction by using sinogram preprocessing filters,” in “Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE,” (IEEE, 2012), pp. 2278–2281.

De Chiffre, L.

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

De Man, B.

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

L. Fu, K. Choi, and B. De Man, “Enhancement of spatial resolution in model-based iterative ct reconstruction by using sinogram preprocessing filters,” in “Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE,” (IEEE, 2012), pp. 2278–2281.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Dewulf, W.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Dong, X.

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

Errico, V. D

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

Fessler, J. A.

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

Flohr, T.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

Fu, L.

L. Fu, K. Choi, and B. De Man, “Enhancement of spatial resolution in model-based iterative ct reconstruction by using sinogram preprocessing filters,” in “Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE,” (IEEE, 2012), pp. 2278–2281.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Grasruck, M.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

Groller, E.

C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
[Crossref]

Gupta, S. K.

S. K. Gupta, A. Jain, D. R. Bednarek, and S. Rudin, “Overcoming x-ray tube small focal spot output limitations for high-resolution region of interest imaging,” in “Medical Imaging 2012: Physics of Medical Imaging,”.

Hanke, R.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Heinzl, C.

C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
[Crossref]

Hiller, J.

J. Hiller and R. Leonard, “A computer simulation platform for the estimation of measurement uncertainties in dimensional x-ray computed tomography,” Measurement 45, 2166 (2012).
[Crossref]

J. Hiller, M. Maisl, and L. M. Reindl, “Physical characterization and performance evaluation of an x-ray microcomputed tomography system for dimensional metrology applications,” Meas. Sci. Technol. 23, 085404 (2012).
[Crossref]

Hofmann, C.

C. Hofmann, M. Knaup, and M. Kachelriess, “Effects of ray profile modeling on resolution recovery in clinical ct,” Med. Phys. 41, 021907 (2014).
[Crossref] [PubMed]

Hsieh, J.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Jain, A.

S. K. Gupta, A. Jain, D. R. Bednarek, and S. Rudin, “Overcoming x-ray tube small focal spot output limitations for high-resolution region of interest imaging,” in “Medical Imaging 2012: Physics of Medical Imaging,”.

Jia, X.

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

Kachelriess, M.

C. Hofmann, M. Knaup, and M. Kachelriess, “Effects of ray profile modeling on resolution recovery in clinical ct,” Med. Phys. 41, 021907 (2014).
[Crossref] [PubMed]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

Kastner, J.

C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
[Crossref]

Kazerooni, E. A.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Khn, U.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

Kiekens, K.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Knaup, M.

C. Hofmann, M. Knaup, and M. Kachelriess, “Effects of ray profile modeling on resolution recovery in clinical ct,” Med. Phys. 41, 021907 (2014).
[Crossref] [PubMed]

Kr A Mer, P.

A. Weckenmann and P. Kr A Mer, “Computed tomography in quality control: chances and challenges,” P. I. Mech. Eng. B-J. Eng. 227, 634–642 (2013).

P. Kr A Mer and A. Weckenmann, “Multi-energy image stack fusion in computed tomography,” Meas. Sci. Technol. 21, 045105 (2010).
[Crossref]

Kr U Ger, P.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Kruth, J. P.

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

Kruth, J.-P.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

La Rivi E Re, P. J.

P. J. La Rivi E Re and X. Pan, “Sampling and aliasing consequences of quarter-detector offset use in helical ct,” IEEE T. Med. Imaging 23, 738–749 (2004).
[Crossref]

Leonard, R.

J. Hiller and R. Leonard, “A computer simulation platform for the estimation of measurement uncertainties in dimensional x-ray computed tomography,” Measurement 45, 2166 (2012).
[Crossref]

Li, H.

Liu, J. M.

Long, Y.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Maisl, M.

J. Hiller, M. Maisl, and L. M. Reindl, “Physical characterization and performance evaluation of an x-ray microcomputed tomography system for dimensional metrology applications,” Meas. Sci. Technol. 23, 085404 (2012).
[Crossref]

Mcolash, S. M.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Mller, S.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

Morigi, M. P.

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

Narayanan, S.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Nilsen, R. A.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Niu, T.

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

Nuyts, J.

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

Pack, J. D.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Pan, X.

P. J. La Rivi E Re and X. Pan, “Sampling and aliasing consequences of quarter-detector offset use in helical ct,” IEEE T. Med. Imaging 23, 738–749 (2004).
[Crossref]

Pierlet, M.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Reindl, L. M.

J. Hiller, M. Maisl, and L. M. Reindl, “Physical characterization and performance evaluation of an x-ray microcomputed tomography system for dimensional metrology applications,” Meas. Sci. Technol. 23, 085404 (2012).
[Crossref]

Rudin, S.

S. K. Gupta, A. Jain, D. R. Bednarek, and S. Rudin, “Overcoming x-ray tube small focal spot output limitations for high-resolution region of interest imaging,” in “Medical Imaging 2012: Physics of Medical Imaging,”.

Rui, X.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Sainath, P.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Salamon, M.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Santillan, J.

O. Brunke, J. Santillan, and A. Suppes, “Precise 3d dimensional metrology using high-resolution x-ray computed tomography (mu ct),” in “Developements in X-Ray Tomography VII,” vol. 7804 of Proceedings of SPIE (2010), vol. 7804 of Proceedings of SPIE, pp. 78040O–1.
[Crossref]

Schmitt, R.

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

Stierstorfer, K.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

Sukowski, F.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Suppes, A.

O. Brunke, J. Santillan, and A. Suppes, “Precise 3d dimensional metrology using high-resolution x-ray computed tomography (mu ct),” in “Developements in X-Ray Tomography VII,” vol. 7804 of Proceedings of SPIE (2010), vol. 7804 of Proceedings of SPIE, pp. 78040O–1.
[Crossref]

Taha, B.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Tang, X.

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Uhlmann, N.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Voet, A. E.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Voland, V.

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Wang, G.

H. Yu and G. Wang, “Finite detector based projection model for high spatial resolution,” J. X-Ray Sci. Technol. 20, 229–238 (2012).

Wang, J.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

Weckenmann, A.

A. Weckenmann and P. Kr A Mer, “Computed tomography in quality control: chances and challenges,” P. I. Mech. Eng. B-J. Eng. 227, 634–642 (2013).

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

P. Kr A Mer and A. Weckenmann, “Multi-energy image stack fusion in computed tomography,” Meas. Sci. Technol. 21, 045105 (2010).
[Crossref]

Welkenhuyzen, F.

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

Yester, M.

M. Yester and G. Barnes, “Geometrical limitations of computed tomography (ct) scanner resolution,” in “Proceedings of the Society of Photo-Optical Instrumentation Engr(s), vol. 127. Application of Optical Instrumentation in Medicine. VI,” (1977), pp. 296–303.

Yu, H.

H. Yu and G. Wang, “Finite detector based projection model for high spatial resolution,” J. X-Ray Sci. Technol. 20, 229–238 (2012).

Zbijewski, W.

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

Zhang, P.

Zhao, Y.

Zhu, L.

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

Zhu, Y.

Appl. Phys. A-Mater. (1)

M. P. Morigi, F. Casali, M. Bettuzzi, R. Brancaccio, and V. D Errico, “Application of x-ray computed tomography to cultural heritage diagnostics,” Appl. Phys. A-Mater. 100, 653–661 (2010).
[Crossref]

CIRP Ann.-Manuf. Techn. (2)

J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. De Chiffre, and A. Weckenmann, “Computed tomography for dimensional metrology,” CIRP Ann.-Manuf. Techn. 60, 821–842 (2011).
[Crossref]

S. Carmignato, “Accuracy of industrial computed tomography measurements: Experimental results from an international comparison,” CIRP Ann.-Manuf. Techn. 61, 491–494 (2012).
[Crossref]

IEEE T. Med. Imaging (1)

P. J. La Rivi E Re and X. Pan, “Sampling and aliasing consequences of quarter-detector offset use in helical ct,” IEEE T. Med. Imaging 23, 738–749 (2004).
[Crossref]

IEEE T. Vis. Comput. Gr. (1)

C. Heinzl, J. Kastner, and E. Groller, “Surface extraction from multi-material components for metrology using dual energy ct,” IEEE T. Vis. Comput. Gr. 13, 1520–1527 (2007).
[Crossref]

J. X-Ray Sci. Technol. (2)

H. Yu and G. Wang, “Finite detector based projection model for high spatial resolution,” J. X-Ray Sci. Technol. 20, 229–238 (2012).

X. Tang, S. Narayanan, J. Hsieh, J. D. Pack, S. M. Mcolash, P. Sainath, R. A. Nilsen, and B. Taha, “Enhancement of in-plane spatial resolution in volumetric computed tomography with focal spot wobbling - overcoming the constraint on number of projection views per gantry rotation,” J. X-Ray Sci. Technol. 18, 251–265 (2010).

Meas. Sci. Technol. (2)

J. Hiller, M. Maisl, and L. M. Reindl, “Physical characterization and performance evaluation of an x-ray microcomputed tomography system for dimensional metrology applications,” Meas. Sci. Technol. 23, 085404 (2012).
[Crossref]

P. Kr A Mer and A. Weckenmann, “Multi-energy image stack fusion in computed tomography,” Meas. Sci. Technol. 21, 045105 (2010).
[Crossref]

Measurement (1)

J. Hiller and R. Leonard, “A computer simulation platform for the estimation of measurement uncertainties in dimensional x-ray computed tomography,” Measurement 45, 2166 (2012).
[Crossref]

Med. Phys. (2)

C. Hofmann, M. Knaup, and M. Kachelriess, “Effects of ray profile modeling on resolution recovery in clinical ct,” Med. Phys. 41, 021907 (2014).
[Crossref] [PubMed]

X. Dong, T. Niu, X. Jia, and L. Zhu, “Relationship between x-ray illumination field size and flat field intensity and its impacts on x-ray imaging,” Med. Phys. 39, 5901–5909 (2012).
[Crossref] [PubMed]

Nucl. Instrum. Meth. A (1)

M. Salamon, R. Hanke, P. Kr U Ger, F. Sukowski, N. Uhlmann, and V. Voland, “Comparison of different methods for determining the size of a focal spot of microfocus x-ray tubes,” Nucl. Instrum. Meth. A 591, 54–58 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

P. I. Mech. Eng. B-J. Eng. (1)

A. Weckenmann and P. Kr A Mer, “Computed tomography in quality control: chances and challenges,” P. I. Mech. Eng. B-J. Eng. 227, 634–642 (2013).

Phys. Med. Biol. (1)

J. Nuyts, B. De Man, J. A. Fessler, W. Zbijewski, and F. J. Beekman, “Modelling the physics in the iterative reconstruction for transmission computed tomography,” Phys. Med. Biol. 58, R63–R96 (2013).
[Crossref] [PubMed]

Other (9)

L. Fu, K. Choi, and B. De Man, “Enhancement of spatial resolution in model-based iterative ct reconstruction by using sinogram preprocessing filters,” in “Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE,” (IEEE, 2012), pp. 2278–2281.

M. Grasruck, U. Khn, S. Mller, K. Stierstorfer, and T. Flohr, “Characterization of focal spots of x-ray tubes in ct systems: method development and examples,” in “Medical Imaging 2010: Physics of Medical Imaging,”, vol. 7622 (2010), vol. 7622, pp. 76224V–76224V–8.
[Crossref]

M. Yester and G. Barnes, “Geometrical limitations of computed tomography (ct) scanner resolution,” in “Proceedings of the Society of Photo-Optical Instrumentation Engr(s), vol. 127. Application of Optical Instrumentation in Medicine. VI,” (1977), pp. 296–303.

J. Wang, Y. Long, L. Fu, X. Rui, E. A. Kazerooni, and B. De Man, “Sinogram rebinning and frequency boosting for high resolution iterative ct reconstruction with focal spot deflection,” in “Medical Imaging 2014: Physics of Medical Imaging,”, vol. 9033 (2014), vol. 9033, pp. 903333.
[Crossref]

S. K. Gupta, A. Jain, D. R. Bednarek, and S. Rudin, “Overcoming x-ray tube small focal spot output limitations for high-resolution region of interest imaging,” in “Medical Imaging 2012: Physics of Medical Imaging,”.

O. Brunke, J. Santillan, and A. Suppes, “Precise 3d dimensional metrology using high-resolution x-ray computed tomography (mu ct),” in “Developements in X-Ray Tomography VII,” vol. 7804 of Proceedings of SPIE (2010), vol. 7804 of Proceedings of SPIE, pp. 78040O–1.
[Crossref]

F. Welkenhuyzen, K. Kiekens, M. Pierlet, W. Dewulf, P. Bleys, J.-P. Kruth, and A. E. Voet, “Industrial computer tomography for dimensional metrology: overview of influence factors and improvement strategies,” in “Proceedings of the 4th International Conference on Optical Measurement Techniques for Structures and Systems: Optimess 2009,” (2009).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

ASTM, “Standard test method for measurement of focal spots of industrial x-ray tubes by pinhole imaging,” (2012).

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Figures (14)

Fig. 1
Fig. 1 Edge blurs caused by the finite focal spot size a and detector unit size d.
Fig. 2
Fig. 2 Illustration of the different influences on the physical resolution BW as a function of focal spot size a (dotted line) and detector bin size d (solid line) respectively..
Fig. 3
Fig. 3 Geometric relationships between the virtual focus projections and the ideal projections.
Fig. 4
Fig. 4 (c) The difference image between the reconstructed images using (a) the measured projections and (b) recovered projections.
Fig. 5
Fig. 5 A complete flowchart of the proposed efficient reconstruction framework.
Fig. 6
Fig. 6 The line-pair phantom and the Gaussian distributed focus spot model.
Fig. 7
Fig. 7 Simulation results of the line-pair phantom based on (a) ideal projection model, (b) 5 virtual focuses projection model and (c) 11 virtual focuses projection model respectively. The gray windows of all images are set to [0.00 0.03].
Fig. 8
Fig. 8 Comparisons of the profiles along the lines in Fig. 7.
Fig. 9
Fig. 9 (a)The low-contrast phantom and the simulation results of the low-contrast phantom based on (b) ideal projection model, (c) 5 virtual focuses projection model and (d) 11 virtual focuses projection model respectively. The gray windows of all images are set to [0.0095 0.0105].
Fig. 10
Fig. 10 Comparisons of the profiles along the lines in Fig. 9.
Fig. 11
Fig. 11 The measurement of the focal spot size by the pinhole imaging method. (a) The image of the focus and (b) the profile of the focus along the horizontal and vertical lines in (a) respectively. The magnification factor of the image was 2.4×.
Fig. 12
Fig. 12 Experimental reconstruction results without image fusions using the measured projections from the 200keV industrial CT. (a) ideal projection model; (b) 3 virtual focus projection model; (c) 5 virtual focuses projection models and (d) 11 virtual focuses projection models. All of the gray windows are set to [0.00 0.07].
Fig. 13
Fig. 13 Comparisons of the profiles along the lines in Fig. 12.
Fig. 14
Fig. 14 Comparisons of reconstructed results with and without the image fusion process. The gray window of the difference image is set to [0, 0.01] and the windows of other images are set to [0, 0.07].

Tables (3)

Tables Icon

Table 1 The explanations of corresponding symbols in Fig. 3.

Tables Icon

Table 2 The geometrical configurations in the experiments.

Tables Icon

Table 3 Results of SNR and CNR using MFFS method with and without image fusion.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

BW = U F 2 + U D 2 = [ ( 1 1 M ) a ] 2 + ( d M ) 2
I ( a , t ) = I 0 ( a , t ) exp ( p ( a , t ) ) where p ( a , t ) = L μ ( l ) d l
I measure ( t ) = Ω I ( a , t ) d a = Ω I 0 ( a , t ) exp ( p ( a , t ) ) d a
I air ( t ) = Ω I 0 ( a , t ) d a
q ( t ) = ln [ I measure ( t ) / I air ( t ) ] = ln { exp ( p ( a 0 , t ) ) [ Ω I 0 ( a , t ) exp ( ( p ( a , t ) p ( a 0 , t ) ) ) d a ] } + ln [ I air ( t ) ] = p ( a 0 , t ) ln ( Ω I 0 ( a , t ) exp ( p ( a , t ) p ( a 0 , t ) ) d a ) + ln [ I air ( t ) ] where a 0 Ω
q ( t ) = p ( a 0 , t ) ln ( Ω I 0 ( a , t ) [ 1 ( p ( a , t ) p ( a 0 , t ) ] d a ) + ln [ I air ( t ) ] = p ( a 0 , t ) ln { 1 Ω I 0 ( a , t ) / I air ( t ) [ ( p ( a , t ) p ( a 0 , t ) ] d a } = Ω I 0 ( a , t ) I air ( t ) p ( a , t ) d a
q ( t ) = Ω w ( a ) p ( a , t ) d a , where w ( a ) = I 0 ( a ) / Ω I 0 ( a ) d a
q ( t ) = i = 1 M w ( a i ) p ( a i , t ) where w ( a i ) = I 0 ( a i ) / i = 1 M I 0 ( a i )
{ p ( a i , t 1 ) = p cir ( β i , t 2 i ) p ( 0 , t 1 ) = p cir ( β 1 , t 1 ) where { θ i = tan 1 ( a i / R ) β i = β 1 + θ i t 2 i = D [ t 1 cos θ i + ( D R ) sin θ i ] [ R + ( D R ) cos θ i t 1 sin θ i ]
q ( β 1 , t 1 ) = i = 1 M w ( a i ) p cir ( β i , t 2 i )
Q = WP
p j ( n + 1 ) = p j ( n ) + q i m = 1 M w im p m ( n ) m = 1 M w im 2 w i j
σ q 2 ( β 1 , t 1 ) = i = 1 M w 2 ( a i ) σ p 2 ( β i , t 2 i )
σ q 2 ( β 1 , t 1 ) = σ 1 2 ( β 1 , t 1 ) i = 1 M w 2 ( a i ) where σ 1 ( β 1 , t 1 ) = σ p ( β i , t 2 i )
I f ( x , y ) = α ( x , y ) I c ( x , y ) + ( 1 α ( x , y ) ) I m ( x , y ) where α ( x , y ) = exp ( | I m ( x , y ) I c ( x , y ) | σ )
SNR = 10 log 10 ( I ROI ¯ σ ROI ) where I ROI ¯ = 1 N i ROI I i σ ROI = [ 1 N i ROI ( I i I ROI ¯ ) 2 ] 1 / 2
CNR = 10 log 10 ( I ROI 1 ¯ I ROI 2 ¯ σ ROI BG ) where I ROI k ¯ = 1 N i ROI k I i σ ROI BG = [ 1 N i ROI BG ( I i I ROI BG ¯ ) 2 ] 1 / 2

Metrics