Abstract

In computed tomography (CT), projection images of the sample are acquired over an angular range between 180 to 360 degrees around a rotation axis. A special case of CT is that of limited-angle CT, where some of the rotation angles are inaccessible, leading to artefacts in the reconstrucion because of missing information. The case of flat samples is considered, where the projection angles that are close to the sample surface are either i) completely unavailable or ii) very noisy due to the limited transmission at these angles. Computed laminography (CL) is an imaging technique especially suited for flat samples. CL is a generalization of CT that uses a rotation axis tilted by less than 90 degrees with respect to the incident beam. Thus CL avoids using projections from angles closest to the sample surface. We make a quantitative comparison of the imaging artefacts between CL and limited-angle CT for the case of a parallel-beam geometry. Both experimental and simulated images are used to characterize the effect of the artefacts on the resolution and visible image features. The results indicate that CL has an advantage over CT in cases when the missing angular range is a significant portion of the total angular range. In the case when the quality of the projections is limited by noise, CT allows a better tradeoff between the noise level and the missing angular range.

© 2012 OSA

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  5. F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
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  9. V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).
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    [CrossRef]
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  12. T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
    [CrossRef] [PubMed]
  17. S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
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  18. P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.
  19. R. Gordon, R. Bender, and G. Herman, “Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
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  21. S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
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    [CrossRef]
  23. P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
    [CrossRef]
  24. P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
    [CrossRef] [PubMed]
  25. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
    [CrossRef]
  26. A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
    [CrossRef]
  27. W. Baumeister, R. Grimm, and J. Walz, “Electron tomography of molecules and cells,” Trends Cell Biol. 9, 81–85 (1999).
    [CrossRef] [PubMed]

2011 (4)

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

2010 (2)

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

2009 (1)

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

2008 (1)

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

2007 (2)

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

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 A 204, 2760–2765 (2007).
[CrossRef]

2006 (2)

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

2005 (2)

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

2004 (1)

G. Wang and M. Jiang, “Ordered-subset simultaneous algebraic reconstruction techniques (OS-SART),” J. X-ray Sci. Technol. 12, 169–177 (2004).

2003 (1)

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

2002 (4)

A. Kalukin and V. Sankaran, “Three-dimensional visualization of multilayered assemblies using X-ray laminography,” IEEE T. Compon. Pack. A 20, 361–366 (2002).
[CrossRef]

T. Moore, D. Vanderstraeten, and P. Forssell, “Three-dimensional x-ray laminography as a tool for detection and characterization of BGA package defects,” IEEE Compon. Pack. T 25, 224–229 (2002).
[CrossRef]

S. Rooks, B. Benhabib, and K. Smith, “Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE. Compon. Pack. A 18, 851–861 (2002).

V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).

1999 (3)

G. Lauritsch and W. H. Härer, “A theoretical framework for filtered backprojection in tomosynthesis,” in “Proceedings SPIE; Medical Imaging: Image Processing,”  3338, 1127–1137 (1999).
[PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

W. Baumeister, R. Grimm, and J. Walz, “Electron tomography of molecules and cells,” Trends Cell Biol. 9, 81–85 (1999).
[CrossRef] [PubMed]

1970 (1)

R. Gordon, R. Bender, and G. Herman, “Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

1917 (1)

J. Radon, “Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math.-Nat. Kl 69, 262–277 (1917).

Baruchel, J.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Baumbach, T.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

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 A 204, 2760–2765 (2007).
[CrossRef]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Baumeister, W.

W. Baumeister, R. Grimm, and J. Walz, “Electron tomography of molecules and cells,” Trends Cell Biol. 9, 81–85 (1999).
[CrossRef] [PubMed]

Bayat, S.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Bellon, P.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Bender, R.

R. Gordon, R. Bender, and G. Herman, “Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Benhabib, B.

S. Rooks, B. Benhabib, and K. Smith, “Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE. Compon. Pack. A 18, 851–861 (2002).

Berthold, A.

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

Bleuet, P.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Buffière, J.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Calzada, E.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

Cantele, F.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Chabli, A.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

Cheng, Y.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

Chevalier, N.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

Choi, D.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

Cloetens, P.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Di Michiel, M.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

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 A 204, 2760–2765 (2007).
[CrossRef]

DiMichiel, M.

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

Elgrabli, D.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Elyyan, M.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

Eyberger, C.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Ferroir, T.

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Feser, M.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Forssell, P.

T. Moore, D. Vanderstraeten, and P. Forssell, “Three-dimensional x-ray laminography as a tool for detection and characterization of BGA package defects,” IEEE Compon. Pack. T 25, 224–229 (2002).
[CrossRef]

Gelb, J.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Gergaud, P.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

Gordon, R.

R. Gordon, R. Bender, and G. Herman, “Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Grimm, R.

W. Baumeister, R. Grimm, and J. Walz, “Electron tomography of molecules and cells,” Trends Cell Biol. 9, 81–85 (1999).
[CrossRef] [PubMed]

Guigay, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Härer, W. H.

G. Lauritsch and W. H. Härer, “A theoretical framework for filtered backprojection in tomosynthesis,” in “Proceedings SPIE; Medical Imaging: Image Processing,”  3338, 1127–1137 (1999).
[PubMed]

Helfen, L.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

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 A 204, 2760–2765 (2007).
[CrossRef]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Herman, G.

R. Gordon, R. Bender, and G. Herman, “Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Hsieh, J.

J. Hsieh, Computed tomography: Principles, design, artifacts, and recent advances (SPIE Press, 2003).

Järvenpää, S.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Jiang, M.

G. Wang and M. Jiang, “Ordered-subset simultaneous algebraic reconstruction techniques (OS-SART),” J. X-ray Sci. Technol. 12, 169–177 (2004).

Johnson, G.

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

Kaipio, J.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Kalukin, A.

A. Kalukin and V. Sankaran, “Three-dimensional visualization of multilayered assemblies using X-ray laminography,” IEEE T. Compon. Pack. A 20, 361–366 (2002).
[CrossRef]

V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).

Kiel, D.

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

Koistinen, P.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Kolehmainen, V.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Kraft, R.

V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).

Kreman, M.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Krüger, P.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Kyu Han, J.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

Lai, B.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Lanzavecchia, S.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Lassas, M.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Lauritsch, G.

G. Lauritsch and W. H. Härer, “A theoretical framework for filtered backprojection in tomosynthesis,” in “Proceedings SPIE; Medical Imaging: Image Processing,”  3338, 1127–1137 (1999).
[PubMed]

Lemelle, L.

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Ludwig, W.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Maire, E.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Mariolle, D.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

McNulty, I.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Mikulík, P.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[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 A 204, 2760–2765 (2007).
[CrossRef]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

Moffat, A.

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

Mokso, R.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Moore, T.

T. Moore, D. Vanderstraeten, and P. Forssell, “Three-dimensional x-ray laminography as a tool for detection and characterization of BGA package defects,” IEEE Compon. Pack. T 25, 224–229 (2002).
[CrossRef]

Myagotin, A.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[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 A 204, 2760–2765 (2007).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

Niese, S.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Pernot, P.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[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 A 204, 2760–2765 (2007).
[CrossRef]

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

Pirttilä, J.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

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 A 204, 2760–2765 (2007).
[CrossRef]

Radon, J.

J. Radon, “Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math.-Nat. Kl 69, 262–277 (1917).

Reischig, P.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Rooks, S.

S. Rooks, B. Benhabib, and K. Smith, “Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE. Compon. Pack. A 18, 851–861 (2002).

Sankaran, V.

V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).

A. Kalukin and V. Sankaran, “Three-dimensional visualization of multilayered assemblies using X-ray laminography,” IEEE T. Compon. Pack. A 20, 361–366 (2002).
[CrossRef]

Schillinger, B.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Siltanen, S.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Simionovici, A.

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Sinclair, I.

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

Smith, K.

S. Rooks, B. Benhabib, and K. Smith, “Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE. Compon. Pack. A 18, 851–861 (2002).

Somersalo, E.

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Spearing, S.

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

Suhonen, H.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Susini, J.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Tian, T.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

Tu, K. N.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

Tucoulou, R.

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Vanderstraeten, D.

T. Moore, D. Vanderstraeten, and P. Forssell, “Three-dimensional x-ray laminography as a tool for detection and characterization of BGA package defects,” IEEE Compon. Pack. T 25, 224–229 (2002).
[CrossRef]

Voropaev, A.

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

Walz, J.

W. Baumeister, R. Grimm, and J. Walz, “Electron tomography of molecules and cells,” Trends Cell Biol. 9, 81–85 (1999).
[CrossRef] [PubMed]

Wang, G.

G. Wang and M. Jiang, “Ordered-subset simultaneous algebraic reconstruction techniques (OS-SART),” J. X-ray Sci. Technol. 12, 169–177 (2004).

Weitkamp, T.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

Wright, E.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Wright, P.

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

Xu, F.

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

Zampighi, G.

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
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S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

Zanette, I.

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

Zschech, E.

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

Appl. Phys. Lett. (5)

L. Helfen, T. Baumbach, P. Mikulík, D. Kiel, P. Pernot, P. Cloetens, and J. Baruchel, “High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography,” Appl. Phys. Lett. 86, 071915 (2005).
[CrossRef]

T. Tian, F. Xu, J. Kyu Han, D. Choi, Y. Cheng, L. Helfen, M. Di Michiel, T. Baumbach, and K. N. Tu, “Rapid diagnosis of electromigration induced failure time of pb-free flip chip solder joints by high resolution synchrotron radiation laminography,” Appl. Phys. Lett. 99, 082114 (2011).
[CrossRef]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

P. Bleuet, A. Simionovici, L. Lemelle, T. Ferroir, P. Cloetens, R. Tucoulou, and J. Susini, “Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples,” Appl. Phys. Lett. 92, 213111 (2008).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
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J. Radon, “Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math.-Nat. Kl 69, 262–277 (1917).

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V. Sankaran, A. Kalukin, and R. Kraft, “Improvements to X-ray laminography for automated inspection of solder joints,” IEEE Compon. Pack. C 21, 148–154 (2002).

IEEE Compon. Pack. T (1)

T. Moore, D. Vanderstraeten, and P. Forssell, “Three-dimensional x-ray laminography as a tool for detection and characterization of BGA package defects,” IEEE Compon. Pack. T 25, 224–229 (2002).
[CrossRef]

IEEE T. Compon. Pack. A (1)

A. Kalukin and V. Sankaran, “Three-dimensional visualization of multilayered assemblies using X-ray laminography,” IEEE T. Compon. Pack. A 20, 361–366 (2002).
[CrossRef]

IEEE. Compon. Pack. A (1)

S. Rooks, B. Benhabib, and K. Smith, “Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE. Compon. Pack. A 18, 851–861 (2002).

J. Struct. Biol. (1)

S. Lanzavecchia, F. Cantele, P. Bellon, L. Zampighi, M. Kreman, E. Wright, and G. Zampighi, “Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers,” J. Struct. Biol. 149, 87–98 (2005).
[CrossRef] [PubMed]

J. Synchrotron Radiat. (1)

F. Xu, L. Helfen, A. Moffat, G. Johnson, I. Sinclair, and T. Baumbach, “Synchrotron radiation computed laminography for polymer composite failure studies,” J. Synchrotron Radiat. 17, 222–226 (2010).
[CrossRef] [PubMed]

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G. Wang and M. Jiang, “Ordered-subset simultaneous algebraic reconstruction techniques (OS-SART),” J. X-ray Sci. Technol. 12, 169–177 (2004).

Nucl. Instrum. Meth. A (2)

L. Helfen, A. Myagotin, P. Pernot, M. DiMichiel, P. Mikulík, A. Berthold, and T. Baumbach, “Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging,” Nucl. Instrum. Meth. A 563, 163–166 (2006).
[CrossRef]

L. Helfen, F. Xu, B. Schillinger, E. Calzada, I. Zanette, T. Weitkamp, and T. Baumbach, “Neutron laminography–a novel approach to three-dimensional imaging of flat objects with neutrons,” Nucl. Instrum. Meth. A (2011).
[CrossRef]

Phys. Med. Biol. (1)

S. Siltanen, V. Kolehmainen, S. Järvenpää, J. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, “Statistical inversion for medical x-ray tomography with few radiographs: I. General theory,” Phys. Med. Biol. 48, 1437 (2003).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

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 A 204, 2760–2765 (2007).
[CrossRef]

Proc. SPIE (1)

L. Helfen, T. Baumbach, P. Pernot, P. Mikulík, M. DiMichiel, and J. Baruchel, “High-resolution three-dimensional imaging by synchrotron-radiation computed laminography,” Proc. SPIE 6318, 63180N (2006).
[CrossRef]

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L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82, 063702 (2011).
[CrossRef] [PubMed]

P. Bleuet, P. Cloetens, P. Gergaud, D. Mariolle, N. Chevalier, R. Tucoulou, J. Susini, and A. Chabli, “A hard x-ray nanoprobe for scanning and projection nanotomography,” Rev. Sci. Instrum. 80, 056101 (2009).
[CrossRef] [PubMed]

Scripta Mater. (1)

A. Moffat, P. Wright, L. Helfen, T. Baumbach, G. Johnson, S. Spearing, and I. Sinclair, “In situ synchrotron computed laminography of damage in carbon fibre–epoxy [90/0]s laminates,” Scripta Mater. 62, 97–100 (2010).
[CrossRef]

The 10th International Conference on X-Ray Microscopy (1)

P. Krüger, S. Niese, E. Zschech, J. Gelb, M. Feser, I. McNulty, C. Eyberger, and B. Lai, “Improved scanning geometry to collect 3D-Geometry data in flat samples,” in The 10th International Conference on X-Ray Microscopy, (2011), pp. 258–260.

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Other (2)

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3d imaging of structure and composition in extended objects,” (2011). Submitted.

J. Hsieh, Computed tomography: Principles, design, artifacts, and recent advances (SPIE Press, 2003).

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Figures (6)

Fig. 1
Fig. 1

(a) Illustration of the two scanning geometries for the parallel-beam case. Here ωCT is the tomographic rotation axis and ωCL is the laminographic rotation axis. The specimen coordinate frame (x,y,z′) is defined with (x,y′) spanning the in-plane direction and z′ being parallel to the specimen surface normal. (b,c) Sketch of the filling of Fourier space in CL and CT, respectively, for Ψ = 30°. (d) Sketch of the difference in the filling of the Fourier space for the two methods, with parts cut away for better visualization.

Fig. 2
Fig. 2

Experimental images of a Siemens star test pattern recorded with CT and CL. The central in-plane slices shown for CT (a) and CL (b). (c,d) Through-plane slices along the horizontal line shown in (a) and (b). (e,f) Through-plane slices along the vertical line shown in (a) and (b). (g) A profile plot along the semi circle depicted in (a) and (b) for CT (dashed line) and CL (solid line). All of the images were equally normalized for good visualization. The white numbered arrows in (a) and (b) indicate features that are discussed in the text. The missing information angle Ψ was 30°.

Fig. 3
Fig. 3

(a) Illustration showing the sample geometry and the two planes that we choose for inspection. The substrate extends infinitely in the x′ and y′-directions, but only a portion of the substrate is shown. (b) Through-plane and in-plane slices of reconstructed single sphere for Ψ = 30°. (c) A plot of the profiles through the middle of the sphere along the CL rotation axis for Ψ = 25°. (d) A plot of measured height, as a full-width half-maximum (FWHM) of the central vertical profile, as a fraction of the real radius of the sphere for CT (crosses) and CL (open circles).

Fig. 4
Fig. 4

Resolution test pattern aligned along the CT rotation axis (a), perpendicular to the CT rotation axis in the sample plane (b), and along the sample surface normal (c). On the left are shown the reconstructed central slices of the test pattern, in the middle are shown plots through the middle of the test pattern, and on the right are illustrations of the geometry. Note that the profile plot in (c) has a different scale on the horizontal axis than the other two profile plots.

Fig. 5
Fig. 5

An arrangement of boxes where the two larger boxes go beyond the field of view. Result for CL (a), for CT when the long structures are perpendicular to the rotation axis (b), for CT after rotating the structure by 5° (c). The images at the top show an in-plane slice, and the images at the bottom show a through-plane slice taken along the dashed lines depicted in the top images.

Fig. 6
Fig. 6

The transmitted intensity as a function of the angle Ψ for differently transmitting flat objects (a). Simulated images of the resolution test pattern with noise for CT (b) and CL (c) at Ψ = 30°. Simulated images of the resolution test pattern with noise for CT (d) and CL (e) at Ψ = 1.8°. The values for signal-to-noise ratios have been calculated for the feature indicated by the arrow in panel (b).

Equations (3)

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h i = ( h max h min ) x i L + h min
x i + 1 = x i + 2 h i
x 0 = 0.

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