Abstract

We present a novel microscopy technique to measure the scattered wavefront emitted from an optically transparent microscopic object. The complex amplitude is decoded via phase stepping in a common-path interferometer, enabling high mechanical stability. We demonstrate theoretically and practically that the incoherent summation of multiple illumination directions into a single image increases the resolving power and facilitates image reconstruction in diffraction tomography. We propose a slice-by-slice object-scatter extraction algorithm entirely based in real space in combination with ordinary z-stepping. Thereby the computational complexity affiliated with tomographic methods is significantly reduced. Using the first order Born approximation for weakly scattering objects it is possible to obtain estimates of the scattering density from the exitwaves.

© 2009 OSA

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    [CrossRef]

2009

2008

M. van ’t Hoff, V. de Sars, and M. Oheim, “A programmable light engine for quantitative single molecule TIRF and HILO imaging,” Opt. Express 16(22), 18495–18504 (2008).
[CrossRef] [PubMed]

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

2007

2006

2005

O. Shimomura, “The discovery of aequorin and green fluorescent protein,” J. Microsc. 217(1), 3–15 (2005).
[CrossRef]

A. L. Mattheyses and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Biophys. J. 88, 341A–342A (2005).

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005).
[CrossRef] [PubMed]

2004

2002

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205(2), 165–176 (2002).
[CrossRef] [PubMed]

2000

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

1999

1995

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[CrossRef]

1994

1990

1988

G. W. Ellis, “An Annular Scan Phase-Contrast Scanned Aperture Microscope (Aspsam),” Cell Motil. Cytoskeleton 10, 342–342 (1988).

1969

R. D. Allen, G. B. David, and G. Nomarski, “The zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. 69(4), 193–221 (1969).
[PubMed]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[CrossRef]

1955

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[CrossRef] [PubMed]

Agard, D. A.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[CrossRef]

Allen, R. D.

R. D. Allen, G. B. David, and G. Nomarski, “The zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. 69(4), 193–221 (1969).
[PubMed]

Axelrod, D.

A. L. Mattheyses and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Biophys. J. 88, 341A–342A (2005).

Badizadegan, K.

Belyaev, Y.

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

Bevilacqua, F.

Boppart, S. A.

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, “Optical properties of tissues quantified by Fourier-transform light scattering,” Opt. Lett. 34(9), 1372–1374 (2009).
[CrossRef] [PubMed]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

Bredebusch, I.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Carl, D.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Charrière, F.

Choi, W.

Colomb, T.

Cuche, E.

Dasari, R. R.

David, G. B.

R. D. Allen, G. B. David, and G. Nomarski, “The zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. 69(4), 193–221 (1969).
[PubMed]

de Sars, V.

Debailleul, M.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

Deflores, L. P.

Delaunay, J.-J.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22-31 (2009).
[CrossRef]

Depeursinge, C.

Ding, H.

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, “Optical properties of tissues quantified by Fourier-transform light scattering,” Opt. Lett. 34(9), 1372–1374 (2009).
[CrossRef] [PubMed]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

Domschke, W.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Ellis, G. W.

G. W. Ellis, “An Annular Scan Phase-Contrast Scanned Aperture Microscope (Aspsam),” Cell Motil. Cytoskeleton 10, 342–342 (1988).

Emery, Y.

Ewers, H.

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

Fang-Yen, C.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Feld, M. S.

Fiolka, R.

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

Fukutake, N.

Georges, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

Gustafsson, M. G.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[CrossRef]

Haeberlé, O.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22-31 (2009).
[CrossRef]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

Ikeda, T.

Inoué, S.

Iwai, H.

Juptner, W. P.

Kawata, S.

Keefe, D. L.

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

Kemper, B.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Kou, S. S.

Kuehn, J.

Kühn, J.

Lauer, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205(2), 165–176 (2002).
[CrossRef] [PubMed]

Liu, L.

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

Lue, N.

Marian, A.

Marquet, P.

Mattheyses, A. L.

A. L. Mattheyses and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Biophys. J. 88, 341A–342A (2005).

Milster, T. D.

Minami, S.

Montfort, F.

Nguyen, F.

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, “Optical properties of tissues quantified by Fourier-transform light scattering,” Opt. Lett. 34(9), 1372–1374 (2009).
[CrossRef] [PubMed]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

Noda, T.

Nomarski, G.

R. D. Allen, G. B. David, and G. Nomarski, “The zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. 69(4), 193–221 (1969).
[PubMed]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Oheim, M.

Oldenbourg, R.

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

Popescu, G.

Schafer, M.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Schnars, U.

Schnekenburger, J.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Sedat, J. W.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[CrossRef]

Sheppard, C. J.

Shimomura, O.

O. Shimomura, “The discovery of aequorin and green fluorescent protein,” J. Microsc. 217(1), 3–15 (2005).
[CrossRef]

Shribak, M.

Simon, B.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

Stemmer, A.

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

Sung, Y.

Trimarchi, J. R.

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

van ’t Hoff, M.

Vaughan, J. C.

Vertu, S.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22-31 (2009).
[CrossRef]

von Bally, G.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

Wang, Z.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

Weible, K.

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[CrossRef]

Yamada, I.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22-31 (2009).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[CrossRef] [PubMed]

Appl. Opt.

Biol. Reprod.

L. Liu, J. R. Trimarchi, R. Oldenbourg, and D. L. Keefe, “Increased birefringence in the meiotic spindle provides a new marker for the onset of activation in living oocytes,” Biol. Reprod. 63(1), 251–258 (2000).
[CrossRef] [PubMed]

Biophys. J.

A. L. Mattheyses and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Biophys. J. 88, 341A–342A (2005).

Cell Motil. Cytoskeleton

G. W. Ellis, “An Annular Scan Phase-Contrast Scanned Aperture Microscope (Aspsam),” Cell Motil. Cytoskeleton 10, 342–342 (1988).

Cent. Eur. J. Phys.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22-31 (2009).
[CrossRef]

J. Biomed. Opt.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11(3), 034005–034008 (2006).
[CrossRef]

J. Microsc.

O. Shimomura, “The discovery of aequorin and green fluorescent protein,” J. Microsc. 217(1), 3–15 (2005).
[CrossRef]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205(2), 165–176 (2002).
[CrossRef] [PubMed]

Meas. Sci. Technol.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[CrossRef]

Microsc. Res. Tech.

R. Fiolka, Y. Belyaev, H. Ewers, and A. Stemmer, “Even illumination in total internal reflection fluorescence microscopy using laser light,” Microsc. Res. Tech. 71(1), 45–50 (2008).
[CrossRef]

Nat. Methods

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Opt. Commun.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. 101(23), 238102 (2008).
[CrossRef] [PubMed]

Proc. SPIE

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses,” Proc. SPIE 2412, 147–156 (1995).
[CrossRef]

Science

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[CrossRef] [PubMed]

Z. Wiss. Mikrosk.

R. D. Allen, G. B. David, and G. Nomarski, “The zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Z. Wiss. Mikrosk. 69(4), 193–221 (1969).
[PubMed]

Other

M. Born, and E. Wolf, Principles of optics,7th ed. (Cambridge University press, 2005).

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Figures (6)

Fig. 1
Fig. 1

Information transfer upon imaging a weakly scattering object: (a) Using coherent, axial illumination. (b) Using two oblique incoherent illumination directions. The solid line illustrates the transferred object information, the dotted line represents the corresponding complex conjugated information. (c) Sampling the reciprocal space using illumination directions with fixed incident angle but varying azimuth.

Fig. 2
Fig. 2

Optical train for rotating illumination and inline interferometry.

Fig. 3
Fig. 3

Simulated amplitude transfer functions (ATF) for rotating illumination under different incident angles. The ATF is rotationally symmetric around the kz axis.

Fig. 4
Fig. 4

Fourier transforms (kx-kz cross-sections) of a human cheek cell data set: (a) Raw data for axial illumination. (b) Raw data for rotating illumination. (c) Recovered object information for axial illumination after applying the phase stepping algorithm. (d) Recovered object information for rotating illumination after applying the phase stepping algorithm and (e) after rotational averaging around the kz axis.

Fig. 5
Fig. 5

Recovered phase image of groups of 100nm silica microspheres under (a) axial illumination and (b) under rotating illumination.

Fig. 6
Fig. 6

Human cheek cell as imaged in brightfield microscopy (a) and phase contrast microscopy (b). (c) Recovered phase information using rotating illumination. (d) Recovered phase information in an x-z plane. The image data is equally sampled in the x and z direction. (e) Magnified version of the boxed area in (d).

Equations (7)

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K=kki
I=|R+O|2=RR*+OO*+RO*+R*OR=r0ei(φ+k0ω)
I˜=R˜×R˜+O˜×O*˜+R˜×O˜+R*˜×O˜R˜=r0δ(kk0)eiφ
Or0=(eiφ1I1+eiφ2I2+eiφ3I3+eiφ4I4)*/4φ1=0;φ2=π/2;φ3=π;φ4=3π/2;
I1=|R1+O|2=|R1|2+|O|2+R1O*+OR1*;I2=|R2+O|2;I3=|R3+O|2;I4=|R4+O|2;Ri=r0eiφi
I1+eiφ2I2+eiφ3I3+eiφ4I4
4r0O*+(Or0)(1+e2iφ2+e2iφ3+e2iφ4)_+(|r0|2+|O|2)(1+eiφ2+eiφ3+eiφ4)_

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