Abstract

A reconstruction theory for multispectral intensity diffraction tomography (I-DT) is established and investigated for use with single material objects whose dispersion characteristics are known a priori. Instead of varying the object-to-detector distance, as prescribed by the original I-DT method and other classic in-line holographic reconstruction methods, the temporal frequency of the illuminating plane wave represents the degree of freedom of the imaging system that is varied to acquire two independent intensity measurements at each tomographic view angle. Unlike previous multispectral I-DT methods, the proposed method does not require a nondispersive assumption. A computer-simulation study is presented to demonstrate and corroborate the method.

© 2009 Optical Society of America

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2007 (3)

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

D. Shi and M. A. Anastasio, “Intensity diffraction tomography with fixed detector plane,” Opt. Eng. (Bellingham) 46, 107003 (2007).
[CrossRef]

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensiy diffraction tomography,” J. Opt. Soc. Am. A 24, 626-642 (2007).
[CrossRef]

2006 (3)

2005 (3)

2004 (3)

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960-2965 (2004).
[CrossRef] [PubMed]

D. Shi, M. A. Anastasio, Y. Huang, and G. Gbur, “Half-scan and single-plane intensity diffraction tomography for phase objects,” Phys. Med. Biol. 49, 2733-2752 (2004).
[CrossRef] [PubMed]

M. A. Anastasio and D. Shi, “On the relationship between intensity diffraction tomography and phase-contrast tomography,” Proc. SPIE 5535, 361-368 (2004).
[CrossRef]

2003 (3)

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

A. S. T. Beetz and C. Jacobsen, “Soft x-ray diffraction tomography: simulations and first experimerimental results,” J. Phys. IV 104, 31-34 (2003).

S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

2002 (4)

G. Gbur and E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194-2202 (2002).
[CrossRef]

G. Gbur and E. Wolf, “Diffraction tomography without phase information,” Opt. Lett. 27, 1890-1892 (2002).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

2001 (2)

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165-176 (2001).
[CrossRef]

2000 (2)

1999 (2)

M. A. Anastasio and X. Pan, “Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography,” Int. J. Imaging Syst. Technol. 10, 437-446 (1999).
[CrossRef]

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

1998 (3)

1995 (1)

T. Wedberg and J. Stamnes, “Quantitative imaging by optical diffraction tomography,” Opt. Rev. 2, 28-31 (1995).
[CrossRef]

1994 (1)

M. H. Maleki and A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. (Bellingham) 33, 3243-3253 (1994).
[CrossRef]

1993 (1)

1992 (1)

A. J. Devaney and A. Schatzberg, “The coherent optical tomographic microscope,” Proc. SPIE 1767, 62-71 (1992).
[CrossRef]

1991 (1)

1986 (1)

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161-183 (1986).
[CrossRef]

1983 (1)

S. Pan and A. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust., Speech, Signal Process. 31, 1262-1275 (1983).
[CrossRef]

1982 (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982).
[CrossRef] [PubMed]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153-156 (1969).
[CrossRef]

Anastasio, M. A.

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensiy diffraction tomography,” J. Opt. Soc. Am. A 24, 626-642 (2007).
[CrossRef]

D. Shi and M. A. Anastasio, “Intensity diffraction tomography with fixed detector plane,” Opt. Eng. (Bellingham) 46, 107003 (2007).
[CrossRef]

M. A. Anastasio, D. Shi, and G. Gbur, “Multispectral intensity diffraction tomography reconstruction theory: quasi-nondispersive objects,” J. Opt. Soc. Am. A 23, 1359-1368 (2006).
[CrossRef]

D. Shi and M. A. Anastasio, “Off-axis holographic tomography for diffracting scalar wavefields,” Phys. Rev. E 73, 016612 (2006).
[CrossRef]

G. Gbur, M. A. Anastasio, Y. Huang, and D. Shi, “Spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 230-238 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image reconstruction in spherical wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 2651-2661 (2005).
[CrossRef]

D. Shi, M. A. Anastasio, Y. Huang, and G. Gbur, “Half-scan and single-plane intensity diffraction tomography for phase objects,” Phys. Med. Biol. 49, 2733-2752 (2004).
[CrossRef] [PubMed]

M. A. Anastasio and D. Shi, “On the relationship between intensity diffraction tomography and phase-contrast tomography,” Proc. SPIE 5535, 361-368 (2004).
[CrossRef]

M. A. Anastasio and X. Pan, “Computationally efficient and statistically robust image reconstruction in 3D diffraction tomography,” J. Opt. Soc. Am. A 17, 391-400 (2000).
[CrossRef]

M. A. Anastasio and X. Pan, “Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography,” Int. J. Imaging Syst. Technol. 10, 437-446 (1999).
[CrossRef]

Arsenault, H. H.

Barrett, H. H.

E. Clarkson and H. H. Barrett, “Symmetry properties of an imaging transform and consistency conditions in image space,” Phys. Med. Biol. 43, 1039-1048 (1998).
[CrossRef] [PubMed]

Barty, A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Beetz, A. S. T.

A. S. T. Beetz and C. Jacobsen, “Soft x-ray diffraction tomography: simulations and first experimerimental results,” J. Phys. IV 104, 31-34 (2003).

Bernier, R.

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
[CrossRef]

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
[CrossRef]

Boppart, S. A.

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Carney, P. S.

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

Charrire, F.

Chen, B.

Clarkson, E.

E. Clarkson and H. H. Barrett, “Symmetry properties of an imaging transform and consistency conditions in image space,” Phys. Med. Biol. 43, 1039-1048 (1998).
[CrossRef] [PubMed]

Colomb, T.

Davis, T.

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

Depeursinge, C.

Devaney, A. J.

P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338-2347 (2005).
[CrossRef]

M. H. Maleki and A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. (Bellingham) 33, 3243-3253 (1994).
[CrossRef]

M. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086-1092 (1993).
[CrossRef]

A. J. Devaney and A. Schatzberg, “The coherent optical tomographic microscope,” Proc. SPIE 1767, 62-71 (1992).
[CrossRef]

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161-183 (1986).
[CrossRef]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982).
[CrossRef] [PubMed]

Dhal, B.

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Dover, 1989).

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

Gbur, G.

Guo, P.

Gureyev, T.

Gureyev, T. E.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

Hayes, J.

Heger, T. J.

Huang, Y.

Jacobsen, C.

A. S. T. Beetz and C. Jacobsen, “Soft x-ray diffraction tomography: simulations and first experimerimental results,” J. Phys. IV 104, 31-34 (2003).

Kak, A.

S. Pan and A. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust., Speech, Signal Process. 31, 1262-1275 (1983).
[CrossRef]

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165-176 (2001).
[CrossRef]

Maleki, M.

Maleki, M. H.

M. H. Maleki and A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. (Bellingham) 33, 3243-3253 (1994).
[CrossRef]

Mancuso, A.

Marks, D. L.

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

Marquet, P.

Mayo, S.

S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

McMahon, P.

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

Miller, P.

Miller, P. R.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Mitchell, E. A. D.

Nugent, K.

Nugent, K. A.

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Paganin, D.

S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Paganin, D. M.

D. M. Paganin, Coherent X-Ray Optics (Oxford U. Press, 2006).
[CrossRef]

Pan, S.

S. Pan and A. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust., Speech, Signal Process. 31, 1262-1275 (1983).
[CrossRef]

Pan, X.

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

Paterson, D.

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960-2965 (2004).
[CrossRef] [PubMed]

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

Pavillon, N.

Peele, A.

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960-2965 (2004).
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P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

Pogany, A.

S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

Ralston, T.

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

Rappaz, B.

Rau, C.

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

Raven, C.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

Roberts, A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Schatzberg, A.

A. J. Devaney and A. Schatzberg, “The coherent optical tomographic microscope,” Proc. SPIE 1767, 62-71 (1992).
[CrossRef]

Scholten, R.

Shi, D.

D. Shi and M. A. Anastasio, “Intensity diffraction tomography with fixed detector plane,” Opt. Eng. (Bellingham) 46, 107003 (2007).
[CrossRef]

M. A. Anastasio, D. Shi, and G. Gbur, “Multispectral intensity diffraction tomography reconstruction theory: quasi-nondispersive objects,” J. Opt. Soc. Am. A 23, 1359-1368 (2006).
[CrossRef]

D. Shi and M. A. Anastasio, “Off-axis holographic tomography for diffracting scalar wavefields,” Phys. Rev. E 73, 016612 (2006).
[CrossRef]

G. Gbur, M. A. Anastasio, Y. Huang, and D. Shi, “Spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 230-238 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image reconstruction in spherical wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 2651-2661 (2005).
[CrossRef]

D. Shi, M. A. Anastasio, Y. Huang, and G. Gbur, “Half-scan and single-plane intensity diffraction tomography for phase objects,” Phys. Med. Biol. 49, 2733-2752 (2004).
[CrossRef] [PubMed]

M. A. Anastasio and D. Shi, “On the relationship between intensity diffraction tomography and phase-contrast tomography,” Proc. SPIE 5535, 361-368 (2004).
[CrossRef]

Snigirev, A.

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

Snigireva, I.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

Spanne, P.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

Stamnes, J.

Stevenson, A.

Stevenson, A. W.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

Tran, C.

Turner, L.

Wedberg, T.

T. Wedberg and J. Stamnes, “Quantitative imaging by optical diffraction tomography,” Opt. Rev. 2, 28-31 (1995).
[CrossRef]

Weitkamp, T.

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

Wilkins, S.

Wilkins, S. W.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

Wolf, E.

G. Gbur and E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194-2202 (2002).
[CrossRef]

G. Gbur and E. Wolf, “Diffraction tomography without phase information,” Opt. Lett. 27, 1890-1892 (2002).
[CrossRef]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153-156 (1969).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A.Consortini, ed. (Academic, 1996), pp. 83-110.
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

P. McMahon, A. Peele, D. Paterson, K. A. Nugent, A. Snigirev, T. Weitkamp, and C. Rau, “X-ray tomographic imaging of the complex refractive index,” Appl. Phys. Lett. 83, 1480-1482 (2003).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (1)

S. Pan and A. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust., Speech, Signal Process. 31, 1262-1275 (1983).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

M. A. Anastasio and X. Pan, “Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography,” Int. J. Imaging Syst. Technol. 10, 437-446 (1999).
[CrossRef]

Inverse Probl. (1)

A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161-183 (1986).
[CrossRef]

J. Microsc. (3)

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165-176 (2001).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79-96 (2002).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (9)

X. Pan, “A unified reconstruction theory for diffraction tomography with considerations of noise control,” J. Opt. Soc. Am. A 15, 2312-2326 (1998).
[CrossRef]

M. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086-1092 (1993).
[CrossRef]

M. A. Anastasio and X. Pan, “Computationally efficient and statistically robust image reconstruction in 3D diffraction tomography,” J. Opt. Soc. Am. A 17, 391-400 (2000).
[CrossRef]

G. Gbur and E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194-2202 (2002).
[CrossRef]

G. Gbur, M. A. Anastasio, Y. Huang, and D. Shi, “Spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 230-238 (2005).
[CrossRef]

P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338-2347 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image reconstruction in spherical wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 2651-2661 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, and G. Gbur, “Multispectral intensity diffraction tomography reconstruction theory: quasi-nondispersive objects,” J. Opt. Soc. Am. A 23, 1359-1368 (2006).
[CrossRef]

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensiy diffraction tomography,” J. Opt. Soc. Am. A 24, 626-642 (2007).
[CrossRef]

J. Phys. IV (1)

A. S. T. Beetz and C. Jacobsen, “Soft x-ray diffraction tomography: simulations and first experimerimental results,” J. Phys. IV 104, 31-34 (2003).

Nat. Phys. (1)

T. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129-134 (2007).
[CrossRef]

Opt. Commun. (2)

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329-336 (2000).
[CrossRef]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153-156 (1969).
[CrossRef]

Opt. Eng. (Bellingham) (2)

M. H. Maleki and A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. (Bellingham) 33, 3243-3253 (1994).
[CrossRef]

D. Shi and M. A. Anastasio, “Intensity diffraction tomography with fixed detector plane,” Opt. Eng. (Bellingham) 46, 107003 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Rev. (1)

T. Wedberg and J. Stamnes, “Quantitative imaging by optical diffraction tomography,” Opt. Rev. 2, 28-31 (1995).
[CrossRef]

Phys. Med. Biol. (3)

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741-750 (1999).
[CrossRef] [PubMed]

E. Clarkson and H. H. Barrett, “Symmetry properties of an imaging transform and consistency conditions in image space,” Phys. Med. Biol. 43, 1039-1048 (1998).
[CrossRef] [PubMed]

D. Shi, M. A. Anastasio, Y. Huang, and G. Gbur, “Half-scan and single-plane intensity diffraction tomography for phase objects,” Phys. Med. Biol. 49, 2733-2752 (2004).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. Shi and M. A. Anastasio, “Off-axis holographic tomography for diffracting scalar wavefields,” Phys. Rev. E 73, 016612 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86, 5827-5830 (2001).
[CrossRef] [PubMed]

Proc. SPIE (2)

A. J. Devaney and A. Schatzberg, “The coherent optical tomographic microscope,” Proc. SPIE 1767, 62-71 (1992).
[CrossRef]

M. A. Anastasio and D. Shi, “On the relationship between intensity diffraction tomography and phase-contrast tomography,” Proc. SPIE 5535, 361-368 (2004).
[CrossRef]

Ultrason. Imaging (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982).
[CrossRef] [PubMed]

Other (5)

D. M. Paganin, Coherent X-Ray Optics (Oxford U. Press, 2006).
[CrossRef]

E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A.Consortini, ed. (Academic, 1996), pp. 83-110.
[CrossRef]

G. R. Fowles, Introduction to Modern Optics (Dover, 1989).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Rotated coordinate system employed to describe the tomographic measurement geometry. (b) A schematic of the 3D measurement geometry.

Fig. 2
Fig. 2

2D I-DT measurement geometry employed in the computer-simulation studies.

Fig. 3
Fig. 3

Real-valued component of the true phantom at temporal frequencies (a) ω 1 and (b) ω 2 . Profiles through the central rows of the images in (a) and (b) are shown in (c) and (d).

Fig. 4
Fig. 4

Imaginary-valued component of the true phantom at temporal frequencies (a) ω 1 and (b) ω 2 . Profiles through the central rows of the images in (a) and (b) are shown in (c) and (d).

Fig. 5
Fig. 5

Images reconstructed from noiseless simulation data that depict the (a) real- and (b) imaginary-valued components of the refractive index distribution at temporal frequency ω 2 . Profiles through the central rows of the reconstructed images in (a) and (b) are denoted by dashed lines in (c) and (d). The true profiles are superimposed as solid lines.

Fig. 6
Fig. 6

Images reconstructed from noisy simulation data that depict the (a) real- and (b) imaginary-valued components of the refractive index distribution at temporal frequency ω 2 . Profiles through the central rows of the reconstructed images in (a) and (b) are denoted by dashed lines in (c) and (d). The true profiles are superimposed as solid lines.

Equations (38)

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f ω ( r ) [ n ω ( r ) ] 2 1 .
U ( r ; ω ) U i ( r ; ω ) exp [ ψ ( r ; ω ) ] ,
ψ ( r ; ω ) = k 2 4 π U i ( r ; ω ) V d r f ω ( r ) U i ( r ; ω ) exp ( i k r r ) r r .
I ( x , y r ; d , ϕ , ω ) = U ( x , y r ; d , ϕ , ω ) 2 = exp [ ψ ( x , y r ; d , ϕ , ω ) + ψ * ( x , y r ; d , ϕ , ω ) ] ,
D ( x , y r ; d , ϕ , ω ) = log [ I ( x , y r ; d , ϕ , ω ) ] = ψ ( x , y r ; d , ϕ , ω ) + ψ * ( x , y r ; d , ϕ , ω ) .
D ̂ ( u , v r ; d , ϕ , ω ) = 1 ( 2 π ) 2 d x d y r D ( x , y r ; d , ϕ , ω ) exp [ i ( u x + v r y r ) ] ,
F ̂ ω ( K ) = 1 ( 2 π ) 3 V d r f ω ( r ) exp [ i K r ] ,
K E [ u , v r , ϕ , ω j ] = u s 1 + v r s 2 , r ( ϕ ) + ( ν j k j ) s 0 , r ( ϕ ) ,
ν j ( ω j c 0 ) 2 u 2 v r 2 ,
F ̂ ω [ u , v r ; ϕ , ω j ] F ̂ ω ( K E [ u , v r , ϕ , ω j ] ) .
D ̂ ( u , v r ; d , ϕ , ω ) = i π k 2 ν { F ̂ ω [ u , v r ; ϕ , ω ] exp [ i ( ν k ) d ] ( F ̂ ω [ u , v r ; ϕ , ω ] ) * exp [ i ( ν k ) d ] } ,
F ̂ ω 1 [ u , v r ; ϕ + ϕ , ω 2 ] = F ̂ ω 1 [ u , v r ; ϕ , ω 1 ] ,
v r = [ R 2 ( R 2 + u 2 ) 2 4 k 1 2 ] 1 2 sgn ( v r ) ,
R [ v r 2 + ( ν 2 k 2 ) 2 ] 1 2 .
ϕ = arctan ( v r ν 1 k 1 ) + arctan ( v r ν 2 k 2 ) ,
ν 1 = [ k 1 2 u 2 ( v r ) 2 ] 1 2 .
[ n ω ( r ) ] 2 = 1 + N e 2 m ϵ 0 n ( f n Ω n 2 ω 2 i γ n ω ) ,
f ω ( r ) = N e 2 m ϵ 0 n ( f n Ω n 2 ω 2 i γ n ω ) .
f ω ( r ) = S ( r ) h ( ω ) ,
S ( r ) N ( r ) e 2 m ϵ 0 ,
h ( ω ) n ( f n Ω n 2 ω 2 i γ n ω ) .
f ω 2 ( r ) = f ω 1 ( r ) h ( ω 2 ) h ( ω 1 ) ,
F ̂ ω 2 ( K ) = F ̂ ω 1 ( K ) h ( ω 2 ) h ( ω 1 ) .
F ̂ ω 2 [ u , v r ; ϕ + ϕ , ω 2 ] = F ̂ ω 1 [ u , v r ; ϕ , ω 1 ] h ( ω 2 ) h ( ω 1 ) .
D ̂ ( u , v r ; d , ϕ , ω 1 ) = i π k 1 2 ν 1 { F ̂ ω 1 [ u , v r ; ϕ , ω 1 ] exp [ i ( ν 1 k 1 ) d ] ( F ̂ ω 1 [ u , v r ; ϕ , ω 1 ] ) * exp [ i ( ν 1 k 1 ) d ] } ,
D ̂ ( u , v r ; d , ϕ , ω 2 ) = i π k 2 2 ν 2 { F ̂ ω 2 [ u , v r ; ϕ , ω 2 ] exp [ i ( ν 2 k 2 ) d ] ( F ̂ ω 2 [ u , v r ; ϕ , ω 2 ] ) * exp [ i ( ν 2 k 2 ) d ] } ,
D ̂ ( u , v r ; d , ϕ , ω 1 ) = i π k 1 2 ν 1 { h ( ω 1 ) h ( ω 2 ) F ̂ ω 2 [ u , v r ; ϕ + ϕ , ω 2 ] exp [ i ( ν 1 k 1 ) d ] h * ( ω 1 ) h * ( ω 2 ) ( F ̂ ω 2 [ u , v r ; ϕ + ϕ , ω 2 ] ) * exp [ i ( ν 1 k 1 ) d ] } .
D ̂ ( u , v r ; d , ϕ , ω j ) = n = D ̂ n ( u , v r ; d , ω j ) exp [ i n ϕ ] ,
F ̂ ω 2 [ u , v r ; ϕ , ω 2 ] = n = F ̂ n ω 2 [ u , v r ; ω 2 ] exp [ i n ϕ ] ,
D ̂ n ( u , v r ; d , ω j ) = 1 2 π 0 2 π d ϕ D ̂ ( u , v r ; d , ϕ , ω j ) exp [ i n ϕ ] ,
F ̂ n ω 2 [ u , v r ; ω 2 ] = 1 2 π 0 2 π d ϕ F ̂ ω 2 [ u , v r ; ϕ , ω 2 ] exp [ i n ϕ ] .
D ̂ n ( u , v r ; d , ω 1 ) = i π k 1 2 ν 1 { h ( ω 1 ) h ( ω 2 ) F ̂ n ω 2 [ u , v r ; ω 2 ] exp [ i n ϕ ( v r ) + i ( ν 1 k 1 ) d ] h * ( ω 1 ) h * ( ω 2 ) ( F ̂ n ω 2 [ u , v r ; ω 2 ] ) * exp [ i n ϕ ( v r ) i ( ν 1 k 1 ) d ] } .
D ̂ n ( u , v r ; d , ω 2 ) = i π k 2 2 ν 2 { F ̂ n ω 2 [ u , v r ; ω 2 ] exp [ i ( ν 2 k 2 ) d ] ( F ̂ n ω 2 [ u , v r ; ω 2 ] ) * exp [ i ( ν 2 k 2 ) d ] } .
F ̂ n ω 2 [ u , v r ; ω 2 ] = 1 M ν 1 i π k 1 2 D ̂ n ( u , v r ; d , ω 1 ) h * ( ω 1 ) h * ( ω 2 ) exp [ i n ϕ ( v r ) i ( ν 1 k 1 ) d ] ν 2 i π k 2 2 D ̂ n ( u , v r ; d , ω 2 ) exp [ i ( ν 2 k 2 ) d ] ,
M = h ( ω 1 ) h ( ω 2 ) exp [ i n ϕ ( v r ) + i ( ν 1 k 1 ) d ] h * ( ω 1 ) h * ( ω 2 ) exp [ i n ϕ ( v r ) i ( ν 1 k 1 ) d ] exp [ i ( ν 2 k 2 ) d ] exp [ i ( ν 2 k 2 ) d ] ,
h ( ω 1 ) h ( ω 2 ) exp [ 2 i ( n ϕ + ( ν 1 ν 2 k 1 + k 2 ) d ) ] = h * ( ω 1 ) h * ( ω 2 ) .
n ϕ + ( ν 1 ν 2 k 1 + k 2 ) d = ϴ + π l ,
ϴ arctan ( Im [ h ( ω 1 ) h ( ω 2 ) ] Re [ h ( ω 1 ) h ( ω 2 ) ] ) ,

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