Abstract

X-ray computed laminography is widely used in nondestructive testing of relatively flat objects using an oblique scanning configuration for data acquisition. In this work, a new scanning scheme is proposed in conjunction with the compressive-sensing-based image reconstruction for reducing imaging radiation dose and scanning time. We performed a numerical study comparing image qualities acquired by various scanning configurations that are practically implementable: single-arc, double-arc, oblique, and spherical-sinusoidal trajectories. A compressive-sensing-inspired total-variation (TV) minimization algorithm was used to reconstruct the images from the data acquired at only 40 projection views in those trajectories. It was successfully demonstrated that the proposed scanning scheme outperforms the others in terms of image contrast and spatial resolution, although the oblique scanning scheme showed a comparable resolution property. We believe that the proposed scanning method may provide a solution to fast and low-dose nondestructive testing of radiation-sensitive and highly integrated devices such as multilayer microelectronic circuit boards.

© 2014 Optical Society of America

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    [CrossRef]
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2013

L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
[CrossRef]

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

S. Abbas, J. Min, and S. Cho, “Super-sparsely view-sampled cone-beam CT by incorporating prior data,” J. XRay Sci. Technol. 21(1), 71–83 (2013).
[PubMed]

2012

2009

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
[CrossRef]

2008

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[CrossRef] [PubMed]

E. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

2007

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

2006

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Tech. (Paris) 14, 119–139 (2006).

2004

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[CrossRef] [PubMed]

2003

J. T. Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65–R106 (2003).
[CrossRef] [PubMed]

1999

D. N. Nguyen, S. M. Guertin, G. M. Swift, and A. H. Johnston, “Radiation effects on advanced flash memories,” IEEE Trans. Nucl. Sci. 46(6), 1744–1750 (1999).
[CrossRef]

1984

Abbas, S.

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

S. Abbas, J. Min, and S. Cho, “Super-sparsely view-sampled cone-beam CT by incorporating prior data,” J. XRay Sci. Technol. 21(1), 71–83 (2013).
[PubMed]

Adrien, J.

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
[CrossRef]

Allcock, D. T. C.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Altapova, V.

Ballance, C. J.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Baumbach, T.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
[CrossRef]

V. Altapova, L. Helfen, A. Myagotin, D. Hänschke, J. Moosmann, J. Gunneweg, and T. Baumbach, “Phase contrast laminography based on Talbot interferometry,” Opt. Express 20(6), 6496–6508 (2012).
[CrossRef] [PubMed]

F. Xu, L. Helfen, T. Baumbach, and H. Suhonen, “Comparison of image quality in computed laminography and tomography,” Opt. Express 20(2), 794–806 (2012).
[CrossRef] [PubMed]

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[CrossRef] [PubMed]

Brooks, K.

Candes, E.

E. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Cecilia, A.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Chen, Z.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
[CrossRef]

Cheng, J.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
[CrossRef]

Cheng, Y.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Cho, M. K.

M. K. Cho, H. Youn, S. Y. Jang, and H. K. Kim, “Cone-beam digital tomosynthesis for thin slab objects,” NDT Int. 47, 171–176 (2012).
[CrossRef]

Cho, S.

S. Abbas, J. Min, and S. Cho, “Super-sparsely view-sampled cone-beam CT by incorporating prior data,” J. XRay Sci. Technol. 21(1), 71–83 (2013).
[PubMed]

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

Cloetens, P.

L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
[CrossRef]

Davis, L. C.

Defrietas, K.

Di Michiel, M.

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Dobbins, J. T.

J. T. Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65–R106 (2003).
[CrossRef] [PubMed]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

Duan, X.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
[CrossRef]

Fauler, A.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Feldkamp, L. A.

Fiederle, M.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Godfrey, D. J.

J. T. Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65–R106 (2003).
[CrossRef] [PubMed]

Guertin, S. M.

D. N. Nguyen, S. M. Guertin, G. M. Swift, and A. H. Johnston, “Radiation effects on advanced flash memories,” IEEE Trans. Nucl. Sci. 46(6), 1744–1750 (1999).
[CrossRef]

Gunneweg, J.

Hamann, E.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Hänschke, D.

Harty, T. P.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Helfen, L.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
[CrossRef]

V. Altapova, L. Helfen, A. Myagotin, D. Hänschke, J. Moosmann, J. Gunneweg, and T. Baumbach, “Phase contrast laminography based on Talbot interferometry,” Opt. Express 20(6), 6496–6508 (2012).
[CrossRef] [PubMed]

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
[CrossRef]

F. Xu, L. Helfen, T. Baumbach, and H. Suhonen, “Comparison of image quality in computed laminography and tomography,” Opt. Express 20(2), 794–806 (2012).
[CrossRef] [PubMed]

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Jang, S. Y.

M. K. Cho, H. Youn, S. Y. Jang, and H. K. Kim, “Cone-beam digital tomosynthesis for thin slab objects,” NDT Int. 47, 171–176 (2012).
[CrossRef]

Johnston, A. H.

D. N. Nguyen, S. M. Guertin, G. M. Swift, and A. H. Johnston, “Radiation effects on advanced flash memories,” IEEE Trans. Nucl. Sci. 46(6), 1744–1750 (1999).
[CrossRef]

Kao, C.-M.

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Tech. (Paris) 14, 119–139 (2006).

Keitch, B. C.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Kim, H. K.

M. K. Cho, H. Youn, S. Y. Jang, and H. K. Kim, “Cone-beam digital tomosynthesis for thin slab objects,” NDT Int. 47, 171–176 (2012).
[CrossRef]

Koenig, T.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Kress, J. W.

Krishnaswamy, V.

Landron, C.

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
[CrossRef]

Lee, R.

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

Lee, T.

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

Linke, N. M.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Lucas, D. M.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
[CrossRef]

Maire, E.

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
[CrossRef]

Michaelsen, K. E.

Mikulík, P.

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Min, J.

S. Abbas, J. Min, and S. Cho, “Super-sparsely view-sampled cone-beam CT by incorporating prior data,” J. XRay Sci. Technol. 21(1), 71–83 (2013).
[PubMed]

Moosmann, J.

Morgeneyer, T.

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
[CrossRef]

Myagotin, A.

V. Altapova, L. Helfen, A. Myagotin, D. Hänschke, J. Moosmann, J. Gunneweg, and T. Baumbach, “Phase contrast laminography based on Talbot interferometry,” Opt. Express 20(6), 6496–6508 (2012).
[CrossRef] [PubMed]

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Nguyen, D. N.

D. N. Nguyen, S. M. Guertin, G. M. Swift, and A. H. Johnston, “Radiation effects on advanced flash memories,” IEEE Trans. Nucl. Sci. 46(6), 1744–1750 (1999).
[CrossRef]

Pan, X.

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[CrossRef] [PubMed]

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Tech. (Paris) 14, 119–139 (2006).

Paulsen, K. D.

Pernot, P.

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Pogue, B. W.

Poplack, S. P.

Rack, A.

L. Helfen, A. Myagotin, A. Rack, P. Pernot, P. Mikulík, M. Di Michiel, and T. Baumbach, “Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices,” Phys. Status Solidi 204(8), 2760–2765 (2007).
[CrossRef]

Ruat, M.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Scheel, M.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Shaw, I.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[CrossRef] [PubMed]

Shin, S.

S. Abbas, T. Lee, S. Shin, R. Lee, and S. Cho, “Effects of sparse sampling schemes on image quality in low-dose CT,” Med. Phys. 40(11), 111915 (2013).
[CrossRef] [PubMed]

Sidky, E. Y.

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E. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
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Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
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L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
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X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
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Zuber, M.

A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
[CrossRef]

Appl. Phys. Lett.

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, and D. M. Lucas, “A microfabricated ion trap with integrated microwave circuitry,” Appl. Phys. Lett. 102(4), 044103 (2013).
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C. R. Phys.

E. Maire, T. Morgeneyer, C. Landron, J. Adrien, and L. Helfen, “Bulk evaluation of ductile damage development using high resolution tomography and laminography,” C. R. Phys. 13(3), 328–336 (2012).
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E. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
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Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
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X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-View Projection Reconstruction With an Iterative Reconstruction-Reprojection Algorithm and TV Constraint,” IEEE Trans. Nucl. Sci. 56(3), 1377–1382 (2009).
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A. Cecilia, E. Hamann, T. Koenig, F. Xu, Y. Cheng, L. Helfen, M. Ruat, M. Scheel, M. Zuber, T. Baumbach, A. Fauler, and M. Fiederle, “High resolution 3D imaging of bump-bonds by means of synchrotron radiation computed laminography,” J. Instrum. 8(12), C12029 (2013).
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L. Helfen, F. Xu, H. Suhonen, L. Urbanelli, P. Cloetens, and T. Baumbach, “Nano-laminography for three-dimensional high-resolution imaging of flat specimens,” J. Instrum. 8(05), C05006 (2013).
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Figures (7)

Fig. 1
Fig. 1

Geometric illustration of CL configurations in 3D Cartesian coordinate: (a) Single-arc, (b) Double-arc, (c) Oblique, and (d) Spherical sinusoidal.

Fig. 2
Fig. 2

Numerical resolution-test phantom in: (a) increasing and (b) decreasing aspect ratio. The arrow represents the x-axis directed toward the source.

Fig. 3
Fig. 3

Reconstructed images and midline profiles of resolution-test phantom aligned along x-axis in different orientation: i.e. (a) increasing and (b) decreasing aspect ratio. The left top corner corresponds to the single-arc and the left bottom to the double-arc scans. The right top corresponds to the oblique and the right bottom to the spherical sinusoidal scans.

Fig. 4
Fig. 4

Reconstructed images and midline profiles of the resolution-test phantom acquired by all the scanning schemes in different phantom orientations: i.e. aligned along (a) y-axis and (b) z-axis. In each first row, images arranged in an order starting from left to right with ground truth image, reconstructed images from 40 views in single-arc and double-arc scanning schemes. Similarly, in second row reconstructed images are arranged in an order starting from 360 view in oblique, and from 40 views in oblique and spherical sinusoidal scanning schemes.

Fig. 5
Fig. 5

Reconstructed images of the resolution-test phantom aligned along the x-axis in decreasing aspect ratio from noisy data by all the scanning schemes: (a) single-arc, (b) double-arc, (c) oblique, and (d) spherical sinusoidal scan.

Fig. 6
Fig. 6

Reconstructed images and MTF profiles acquired at different positions starting from surface to its depth in the box phantom by different scanning schemes. Reconstructed images are arranged in an order starting from top with (a) single-arc, (b) double-arc, (c) oblique, and (d) spherical sinusoidal.

Fig. 7
Fig. 7

Schematic illustration of data correlation in the sampled data.

Tables (1)

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Table 1 SSIM values of the reconstructed images of a resolution-test phantom.

Equations (1)

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z ^ =argmin z TV s.t. M z p <δ

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