Abstract

Recent methods of phase imaging in x-ray tomography allow the visualization of features that are not resolved in conventional absorption microtomography. Of these, the relatively simple setup needed to produce Fresnel-propagated tomograms appears to be well suited to probe tooth-dentin where composition as well as microstructure vary in a graded manner. By adapting analytical propagation approximations we provide predictions of the form of the interference patterns in the 3D images, which we compare to numerical simulations as well as data obtained from measurements of water immersed samples. Our observations reveal details of the tubular structure of dentin, and may be evaluated similarly to conventional absorption tomograms. We believe this exemplifies the power of Fresnel-propagated imaging as a form of 3D microscopy, well suited to quantify gradual microstructural-variations in teeth and similar tissues.

© 2006 Optical Society of America

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2006

P. Zaslansky, A. A. Friesem, and S. Weiner, "Structure and mechanical properties of the soft zone separating bulk dentin and enamel in crowns of human teeth: Insight into tooth function," J. Struct. Biol. 153, 188-199 (2006).
[CrossRef] [PubMed]

2005

X. Wu, H. Liu, and A. Yan, "X-ray phase-attenuation duality and phase retrieval," Opt. Lett. 30, 379-381 (2005).
[CrossRef] [PubMed]

S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard x rays," Rev. Sci. Instrum. 76, 0737051-0737057 (2005).
[CrossRef]

2004

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

2003

2001

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

A. V. Bronnikov, "Theory of quantitative phase-contrast computed tomography," J. Opt. Soc. Am. A 19, 472-480 (2001).
[CrossRef]

2000

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

1999

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

A. V. Bronnikov, "Reconstruction formulas in phase-contrast tomography," Opt. Commun. 171, 239-244 (1999).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

1998

P. Roschger, P. Fratzl, J. Eschberger, and K. Klaushofer, "Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies," Bone 23, 319-326 (1998).
[CrossRef] [PubMed]

R. Wang, and S. Weiner, "Strain-structure relations in human teeth using Moire fringes," J. Biomech. 31, 135-141 (1998).
[CrossRef] [PubMed]

S. Weiner, and H. D. Wagner, "The material bone: structure- mechanical function relations," Ann. Rev. Mat. Sci. 28, 271-298 (1998).
[CrossRef]

A. Koch, C. Raven, P. Spanne, A. Snigirev, "X-ray imaging with submicrometer resolution employing transparent luminescent screens," J. Opt. Soc. Am. A 15, 1940-1951 (1998).
[CrossRef]

1997

J. C. Elliott, "Structure, crystal chemistry and density of enamel apatites," Dental Enamel 205, 54-72 (1997).

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

1996

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

U. Bonse, F. Busch, "X-ray computed microtomography (µCT) using synchrotron radiation (SR)," Prog. Biophys. Mol. Bio. 65, 133-169 (1996).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-constrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

1995

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature 373, 595-598 (1995).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

1994

J.H. Kinney, G. W. MarshallJr., S.J. Marshall, "Three-dimensional mapping of mineral densities in carious dentin: Theory and Method," Scanning Microsc. 8, 197-205 (1994).
[PubMed]

1993

T. Malzbender, "Fourier Volume Rendering," ACM T.Graphic. 12, 233-250 (1993).
[CrossRef]

1989

D. H. Pashley, "Dentin: a dynamic substrate: a review," Scanning Microsc. 3, 161-174 (1989).
[PubMed]

1980

E. Spiller, "Recent developements towards high resolution x-ray imaging," Nucl. Instrum. Methods 177, 187-192 (1980).
[CrossRef]

1969

R. S. Gilmore, R. P. Pollack, and J. L. Katz, "Elastic properties of bovine dentine and enamel," Arch. Oral Biol. 15, 787-796 (1969).
[CrossRef]

1959

R. Craig, P. Gehring, and F. Peyton, "Relation of structure to the microhardness of human dentin," J. Dent. Res. 38, 624-630 (1959).
[CrossRef] [PubMed]

1956

R. N. Bracewell, "Strip Integration in Radio Astronomy," Aust. J. Phys. 9, 198-215 (1956).
[CrossRef]

1954

L. G. Parratt, "Surface studies of solids by total reflection of x-rays," Phys. Rev. 95, 359-369 (1954).
[CrossRef]

Arad, T.

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

Baruchel, J.

S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard x rays," Rev. Sci. Instrum. 76, 0737051-0737057 (2005).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

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

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

Beniash, E.

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

Bonse, U.

U. Bonse, F. Busch, "X-ray computed microtomography (µCT) using synchrotron radiation (SR)," Prog. Biophys. Mol. Bio. 65, 133-169 (1996).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, "Strip Integration in Radio Astronomy," Aust. J. Phys. 9, 198-215 (1956).
[CrossRef]

Bronnikov, A. V.

A. V. Bronnikov, "Theory of quantitative phase-contrast computed tomography," J. Opt. Soc. Am. A 19, 472-480 (2001).
[CrossRef]

A. V. Bronnikov, "Reconstruction formulas in phase-contrast tomography," Opt. Commun. 171, 239-244 (1999).
[CrossRef]

Busch, F.

U. Bonse, F. Busch, "X-ray computed microtomography (µCT) using synchrotron radiation (SR)," Prog. Biophys. Mol. Bio. 65, 133-169 (1996).
[CrossRef]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Chiba, H.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Cloetens, P.

S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard x rays," Rev. Sci. Instrum. 76, 0737051-0737057 (2005).
[CrossRef]

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

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

Craig, R.

R. Craig, P. Gehring, and F. Peyton, "Relation of structure to the microhardness of human dentin," J. Dent. Res. 38, 624-630 (1959).
[CrossRef] [PubMed]

Davis, T. J.

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

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature 373, 595-598 (1995).
[CrossRef]

Diete, W.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Dillon, J. W.

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

Dubini, B.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

Dyck, D. V.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

Eidelman, N.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

Elliott, J. C.

J. C. Elliott, "Structure, crystal chemistry and density of enamel apatites," Dental Enamel 205, 54-72 (1997).

Eschberger, J.

P. Roschger, P. Fratzl, J. Eschberger, and K. Klaushofer, "Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies," Bone 23, 319-326 (1998).
[CrossRef] [PubMed]

Frahm, R.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Fratzl, P.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

P. Roschger, P. Fratzl, J. Eschberger, and K. Klaushofer, "Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies," Bone 23, 319-326 (1998).
[CrossRef] [PubMed]

Friesem, A. A.

P. Zaslansky, A. A. Friesem, and S. Weiner, "Structure and mechanical properties of the soft zone separating bulk dentin and enamel in crowns of human teeth: Insight into tooth function," J. Struct. Biol. 153, 188-199 (2006).
[CrossRef] [PubMed]

Gao, D.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-constrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature 373, 595-598 (1995).
[CrossRef]

Gehring, P.

R. Craig, P. Gehring, and F. Peyton, "Relation of structure to the microhardness of human dentin," J. Dent. Res. 38, 624-630 (1959).
[CrossRef] [PubMed]

Gilmore, R. S.

R. S. Gilmore, R. P. Pollack, and J. L. Katz, "Elastic properties of bovine dentine and enamel," Arch. Oral Biol. 15, 787-796 (1969).
[CrossRef]

Girardin, E.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

Gmuer, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Goldenberg, F.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

Gorner, W.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Guigay, J. P.

S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard x rays," Rev. Sci. Instrum. 76, 0737051-0737057 (2005).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

Guigay, J.-P.

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

Gureyev, T. E.

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

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-constrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature 373, 595-598 (1995).
[CrossRef]

Hentschel, M. P.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Horikoshi, T.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Katz, J. L.

R. S. Gilmore, R. P. Pollack, and J. L. Katz, "Elastic properties of bovine dentine and enamel," Arch. Oral Biol. 15, 787-796 (1969).
[CrossRef]

Kinney, J.H.

J.H. Kinney, G. W. MarshallJr., S.J. Marshall, "Three-dimensional mapping of mineral densities in carious dentin: Theory and Method," Scanning Microsc. 8, 197-205 (1994).
[PubMed]

Klaushofer, K.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

P. Roschger, P. Fratzl, J. Eschberger, and K. Klaushofer, "Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies," Bone 23, 319-326 (1998).
[CrossRef] [PubMed]

Klein, U.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Koch, A.

Kohn, V.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Krumrey, M.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Kumagai, S.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Landuyt, J. V.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

Liu, H.

Ludwig, W.

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

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

Malzbender, T.

T. Malzbender, "Fourier Volume Rendering," ACM T.Graphic. 12, 233-250 (1993).
[CrossRef]

Marshall, G. W.

J.H. Kinney, G. W. MarshallJr., S.J. Marshall, "Three-dimensional mapping of mineral densities in carious dentin: Theory and Method," Scanning Microsc. 8, 197-205 (1994).
[PubMed]

Marshall, S.J.

J.H. Kinney, G. W. MarshallJr., S.J. Marshall, "Three-dimensional mapping of mineral densities in carious dentin: Theory and Method," Scanning Microsc. 8, 197-205 (1994).
[PubMed]

Mayo, S. C.

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Miller, P. R.

Mitsui, T.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Momose, A.

Muller, B. R.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Nugent, K. A.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

Paganin, D.

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

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," J. Appl. Phys. 81, 110-116 (1997).

Parratt, L. G.

L. G. Parratt, "Surface studies of solids by total reflection of x-rays," Phys. Rev. 95, 359-369 (1954).
[CrossRef]

Pashley, D. H.

D. H. Pashley, "Dentin: a dynamic substrate: a review," Scanning Microsc. 3, 161-174 (1989).
[PubMed]

Peyton, F.

R. Craig, P. Gehring, and F. Peyton, "Relation of structure to the microhardness of human dentin," J. Dent. Res. 38, 624-630 (1959).
[CrossRef] [PubMed]

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Pogany, A.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-constrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Pollack, R. P.

R. S. Gilmore, R. P. Pollack, and J. L. Katz, "Elastic properties of bovine dentine and enamel," Arch. Oral Biol. 15, 787-796 (1969).
[CrossRef]

Raven, C.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

A. Koch, C. Raven, P. Spanne, A. Snigirev, "X-ray imaging with submicrometer resolution employing transparent luminescent screens," J. Opt. Soc. Am. A 15, 1940-1951 (1998).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

Riesemeier, H.

W. Gorner, M. P. Hentschel, B. R. Muller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, and R. Frahm, "BAMline: the first hard X-ray beamline at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467, 703-706 (2001).
[CrossRef]

Rizzi, G.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

Romanzetti, S.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

Roschger, P.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

P. Roschger, P. Fratzl, J. Eschberger, and K. Klaushofer, "Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies," Bone 23, 319-326 (1998).
[CrossRef] [PubMed]

Rustichelli, F.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

Sabsay, B.

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Schlenker, M.

S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard x rays," Rev. Sci. Instrum. 76, 0737051-0737057 (2005).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. 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]

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

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
[CrossRef]

Shoutsu, D.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Siddiqui, F.

S. Weiner, A. Veis, E. Beniash, T. Arad, J. W. Dillon, B. Sabsay, and F. Siddiqui, "Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth," J. Struct. Biol. 126, 27-41 (1999).
[CrossRef] [PubMed]

Snigirev, A.

F. Rustichelli, B. Dubini, S. Romanzetti, E. Girardin, C. Raven, A. Snigirev, G. Rizzi, "Phase-contrast miroctomography of thin biomaterials," J. Mater. Sci. -Mater. M. 15, 1053-1057 (2004).
[CrossRef]

A. Koch, C. Raven, P. Spanne, A. Snigirev, "X-ray imaging with submicrometer resolution employing transparent luminescent screens," J. Opt. Soc. Am. A 15, 1940-1951 (1998).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Snigireva, I.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Souvorov, A.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

Spanne, P.

A. Koch, C. Raven, P. Spanne, A. Snigirev, "X-ray imaging with submicrometer resolution employing transparent luminescent screens," J. Opt. Soc. Am. A 15, 1940-1951 (1998).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, "Phase-contrast microtomography with coherent high-energy synchrotron x rays," Appl. Phys. Lett. 69, 1826-1828 (1996).
[CrossRef]

Spiller, E.

E. Spiller, "Recent developements towards high resolution x-ray imaging," Nucl. Instrum. Methods 177, 187-192 (1980).
[CrossRef]

Stevenson, A. W.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-constrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature 373, 595-598 (1995).
[CrossRef]

Takahashi, K.

H. Yoshimura, D. Shoutsu, T. Horikoshi, H. Chiba, S. Kumagai, K. Takahashi, and T. Mitsui, "Application of SEM-modified X-ray microscope to entomology and histology, and effects of X-ray coherence in imaging," J. Electron. Microsc. 49, 621-628 (2000).
[CrossRef]

Tesch, W.

W. Tesch, N. Eidelman, P. Roschger, F. Goldenberg, K. Klaushofer, and P. Fratzl, "Graded microstructure and mechanical properties of human crown dentin," Calcif. Tissue Int. 69, 147-157 (2001).
[CrossRef] [PubMed]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmuer, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
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Figures (8)

Fig. 1.
Fig. 1.

Schematic representation of x-ray propagation through a material containing dense tubular structures. A full tomographic dataset is obtained from 900 projection images of the sample, viewed from 180 degrees. The large source-to-sample distance coupled with a small beam divergence allow imaging of interference patterns of discontinuities due to propagation. Tomograms are produced by placing the detector in the standard absorption regime (d0) and at multiple propagation distances ranging from the near Fresnel to the far Fresnel regimes (d1–d3).

Fig. 2.
Fig. 2.

Model of the distribution of the refractive index n(r) in a single tubule and resulting fresnel propagated images. (a) Schematic of tubule (b) Schematic illustration of the real component of the refractive indices of void, PTD and matrix (c) The outcomes of propagation of a tubule with only a void (constructive interference), only PTD without void (destructive interference) and the sum of both. When the interference patterns overlap, image contrast vanishes. The analytical model (Eq. 12) was used to construct both contributions in Fourier space using Bessel functions. Propagation over d=433 mm was assumed, and the tubule was set to have a radius of rtubule =1.67×rvoid with rvoid =0.8 µm. Pictures show the squared modulus of the inverse Fourier transform of the Bessel functions.

Fig. 3.
Fig. 3.

Sample of human crown dentin with attached enamel: (a) Schematic illustration of the position and form of typical samples cut out of the intact tooth. (b) An experimental contact (absorption) radiogram of a sample prepared as shown in (a). The denser enamel appears brighter due to the convention of representing absorption images using a (-log) scale.

Fig. 4.
Fig. 4.

Tubules in dentin as seen in scanning electron microscopy. (a) An image of 244 tubules seen in one of the backscattered SEM images of a polished slice of dentin. The inset shows a magnified tubule which includes a void and a dense peritubular sheath. (b) Distribution of sizes of void radii and (c) tubule radii. (d) Histogram of ratios of tubule and void radii. <rvoid >=0.8 µm, <rtubule >=1.9 µm. The highest frequency of rtubule/rvoid is a ratio of 2.4.

Fig. 5.
Fig. 5.

Simulation of the evolution of the interference pattern of a tubule as a function tubule/void radii ratios. The rtubule/rvoid ratio is calculated from 1 (corresponding to no PTD) to 5. Three characteristic line profiles are plotted for ratios of (a) 1, (b) 1.67 and (c) 2.5. With no PTD surrounding the void (a) we note a bright interference peak forms at the tubule centre while tubules with a very thick PTD (c) will cause a dark central interference. For a very critical ratio rtubule/rvoid ~1.67 we note that the interference pattern almost vanishes (b).

Fig. 6.
Fig. 6.

Simulated Fresnel propagation of tubules at various distances. The two graphs (a) and (b) show the effect the propagation distance has on the measured interferences. Graph (a) shows the evolution of contrast produced by a simple void of rvoid =0.8 µm while in (b) a PTD sheath of 1.6 µm thickness was added (rtubule/rvoid=3). The three plots on the left show explicitly the interference patterns at (1) d=144 mm, (2) d=433 mm and (3) d=720 mm.

Fig. 7.
Fig. 7.

Slice across a Fresnel propagated tomogram compared with a propagated SEM image. (a) A magnified region from a recorded Fresnel propagated micro tomogram approx. 0.5 mm below the DEJ (experimental data) shows striking similarity to the simulated picture (b) obtained by virtual Fresnel propagation of the SEM image from Fig. 4. Both pictures correspond to a propagation distance of d=433 mm.

Fig. 8.
Fig. 8.

The effect of increasing propagation distance on image quality. Identical regions from Fresnel-propagated micro tomograms of dentin showing a close packing of tubules. The images recorded at (a) d=144 mm and (b) d=433 mm reveal clear details of the microstructure. At d=720 mm (c) tubules lose detail in the image due to the overlapping interference patterns.

Tables (1)

Tables Icon

Table 1. Values for the density and refractive index used for the numerical simulations

Equations (13)

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n = 1 δ + i β
u inc ( r ) = e i 2 π λ r r u inc ( x , y ) e i 2 π λ l l · e i π λ l ( x 2 + y 2 )
L t = λ 2 s α = λ l 2 s
u 0 ( x , y ) = u inc ( x , y ) · T ( x , y ) with T ( x , y ) = e B ( x , y ) e i ϕ ( x , y )
B ( x , y ) = 2 π λ . β ( x , y , z ) dz
ϕ ( x , y ) = 2 π λ · [ 1 δ ( x , y , z ) ] dz = ϕ 0 2 π λ · δ ( x , y , z ) dz
u d ( x , y ) = 1 i λ d + u 0 ( η , ξ ) · e i π λ d [ ( x η ) 2 + ( y ξ ) 2 ] d η d ξ
= 1 i λ dl e i 2 π λ l + T ( η , ξ ) · e i π λ l ( η 2 + ξ 2 ) · e i π λ d [ ( x η ) 2 + ( y ξ ) 2 ] d η d ξ
u D ( X , Y ) = ( P D * T ) X , Y with P D ( X , Y ) = 1 i λ D e i π λ D ( X 2 + Y 2 )
u ˜ D ( f X , f Y ) = P ˜ D ( f X , f Y ) · T ˜ ( f X , f Y ) with P ˜ D ( f X , f Y ) = e i π λ D ( f X 2 + f Y 2 )
n ( x , y , z ) = n ( r ) = n Matrix + ( n PTD n Matrix ) · circ ( r r tubule ) + ( n void n PTD ) · circ ( r r void )
n ˜ ( ρ ) = 2 π 0 r · n ( r ) · J 0 ( 2 π r ρ ) dr
n ˜ ( ρ ) = n Matrix δ Dirac + ( n PID n Matrix ) · r tubule · J 1 ( 2 π ρ · r tubule ) ρ + ( n Void n PTD ) · r Void · J 1 ( 2 π ρ · r Void ) ρ

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