Abstract

We present a technique for 3D imaging of live cells in translational motion without need of axial scanning of objective lens. A set of transmitted electric field images of cells at successive points of transverse translation is taken with a focused beam illumination. Based on Hyugens’ principle, angular plane waves are synthesized from E-field images of a focused beam. For a set of synthesized angular plane waves, we apply a filtered back-projection algorithm and obtain 3D maps of refractive index of live cells. This technique, which we refer to as synthetic aperture tomographic phase microscopy, can potentially be combined with flow cytometry or microfluidic devices, and will enable high throughput acquisition of quantitative refractive index data from large numbers of cells.

© 2008 Optical Society of America

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References

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  1. B. E. Bouma and G. J. Tearney, Handbook of optical coherent tomography (2001).
  2. W. Tan, A. L. Oldenburg, J. J. Norman, T. A. Desai, and S. A. Boppart, "Optical coherence tomography of cell dynamics in three-dimensional tissue models," Opt. Express 14, 7159-7171 (2006).
    [CrossRef] [PubMed]
  3. J. B. Pawley, Handbook of biological confocal microscopy (2006).
    [CrossRef]
  4. M. Slaney and A. C. Kak, "Diffraction tomography," Proc. Soc. Photo. Opt. Instrum. Eng. 413, 2-19 (1983).
  5. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, "Tomographic phase microscopy," Nature Methods 4, 717-719 (2007).
    [CrossRef] [PubMed]
  6. G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
    [CrossRef]
  7. F. Charriere, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
    [CrossRef] [PubMed]
  8. 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 (2002).
    [CrossRef] [PubMed]
  9. M. Zysk, J. J. Reynolds, D. L. Marks, P. S. Carney, and S. A. Boppart, "Projected index computed tomography," Opt. Lett. 28, 701-703 (2003).
    [CrossRef] [PubMed]
  10. D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
    [CrossRef]
  11. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, "Interferometric synthetic aperture microscopy," Nature Phys. 3, 129-134 (2007).
    [CrossRef]
  12. N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
    [CrossRef] [PubMed]
  13. N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of optics (1999).
  15. C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, "Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy," Opt. Lett. 32, 1572-1574 (2007).
    [CrossRef] [PubMed]
  16. X. Zhong, "A four-frame phase shift method insensitive to phase shifter nonlinearity," J. Opt. A: Pure Appl. Opt. 8, 300-303 (2006).
  17. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (1988).

2008 (1)

2007 (3)

C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, "Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy," Opt. Lett. 32, 1572-1574 (2007).
[CrossRef] [PubMed]

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

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

2006 (4)

2003 (1)

2002 (1)

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 (2002).
[CrossRef] [PubMed]

1998 (1)

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

1984 (1)

D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
[CrossRef]

1983 (1)

M. Slaney and A. C. Kak, "Diffraction tomography," Proc. Soc. Photo. Opt. Instrum. Eng. 413, 2-19 (1983).

Badizadegan, K.

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
[CrossRef] [PubMed]

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

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Boppart, S. A.

Carney, P. S.

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

M. Zysk, J. J. Reynolds, D. L. Marks, P. S. Carney, and S. A. Boppart, "Projected index computed tomography," Opt. Lett. 28, 701-703 (2003).
[CrossRef] [PubMed]

Charriere, F.

Choi, W.

Colomb, T.

Cuche, E.

Dasari, R. R.

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
[CrossRef] [PubMed]

C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, "Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy," Opt. Lett. 32, 1572-1574 (2007).
[CrossRef] [PubMed]

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

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Depeursinge, C.

Desai, T. A.

Fang-Yen, C.

Feld, M. S.

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
[CrossRef] [PubMed]

C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, "Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy," Opt. Lett. 32, 1572-1574 (2007).
[CrossRef] [PubMed]

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

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Ikeda, T.

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Kak, A. C.

D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
[CrossRef]

M. Slaney and A. C. Kak, "Diffraction tomography," Proc. Soc. Photo. Opt. Instrum. Eng. 413, 2-19 (1983).

Kozinets, G. I.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Kuehn, J.

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 (2002).
[CrossRef] [PubMed]

Levin, G. G.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Likhachov, A. V.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Lue, N.

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
[CrossRef] [PubMed]

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

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Marian, A.

Marks, D. L.

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

M. Zysk, J. J. Reynolds, D. L. Marks, P. S. Carney, and S. A. Boppart, "Projected index computed tomography," Opt. Lett. 28, 701-703 (2003).
[CrossRef] [PubMed]

Marquet, P.

Montfort, F.

Nahamoo, D.

D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
[CrossRef]

Norman, J. J.

Novoderzhkina, J. K.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Oh, S.

Oldenburg, A. L.

Pan, S. X.

D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
[CrossRef]

Park, Y.

Pickalov, V. V.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Popescu, G.

N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Confocal diffraction phase microscopy of live cells," Opt. Lett. 33, 2074-2076 (2008).
[CrossRef] [PubMed]

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, Live cell refractometry using microfluidic devices, Opt. Lett. 31, 2579 (2006).
[CrossRef]

Ralston, T. S.

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

Reynolds, J. J.

Seung, H. S.

Slaney, M.

M. Slaney and A. C. Kak, "Diffraction tomography," Proc. Soc. Photo. Opt. Instrum. Eng. 413, 2-19 (1983).

Song, S.

Streletskaya, E. A.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Tan, W.

Vishnyakov, G. N.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Zakarian, C. S.

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Zhong, X.

X. Zhong, "A four-frame phase shift method insensitive to phase shifter nonlinearity," J. Opt. A: Pure Appl. Opt. 8, 300-303 (2006).

Zysk, M.

IEEE Trans. Sonics and Ultrason. (1)

D. Nahamoo, S. X. Pan, and A. C. Kak, "Synthetic aperture diffraction tomography and its interpolation -free computer implementation," IEEE Trans. Sonics and Ultrason. 31, 218-229 (1984).
[CrossRef]

J. Microsc. (1)

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 (2002).
[CrossRef] [PubMed]

J. Opt. A: Pure Appl. Opt. (1)

X. Zhong, "A four-frame phase shift method insensitive to phase shifter nonlinearity," J. Opt. A: Pure Appl. Opt. 8, 300-303 (2006).

Nature Methods (1)

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

Nature Phys. (1)

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

Opt. Express (1)

Opt. Lett. (5)

Proc. Soc. Photo. Opt. Instrum. Eng. (1)

M. Slaney and A. C. Kak, "Diffraction tomography," Proc. Soc. Photo. Opt. Instrum. Eng. 413, 2-19 (1983).

Proc. SPIE (1)

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, "Three-dimensional limited-angle microtomography of blood cells: experimental results," Proc. SPIE 3261, 159-164 (1998).
[CrossRef]

Other (4)

B. E. Bouma and G. J. Tearney, Handbook of optical coherent tomography (2001).

J. B. Pawley, Handbook of biological confocal microscopy (2006).
[CrossRef]

M. Born and E. Wolf, Principles of optics (1999).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (1988).

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Figures (3)

Fig 1.
Fig 1.

Experimental setup. Two views depend on the axes of cylindrical lenses are shown: (a) Imaging axis in which the illumination beam is a plane wave, (b) Fourier axis in which the illumination is a focused beam. C1-4 are cylindrical lenses with focal lengths 10, 20, 40 and 20 cm. L1 is a 1.4 NA condenser lens (Nikon). L2 is a 100× objective lens (Zeiss). L3 a tube lens, and L4 is the image lens with focal length of 20 cm. B1 and B2 are beam splitters. M1 is the CCD camera (Fastcam 1024PCI, Photron) and M2 is the video camera (TC-84, Sony). (c) Bright field image of a 10 µm polystyrene bead. (d) Line focus beam through a bead imaged at camera M1. (e) Four consecutive π/2 phase-shifted interferometric images of the bead imaged at camera M2. (f) Quantitative phase image of the bead processed from (e).

Fig. 2.
Fig. 2.

Quantitative E-field images for a focused beam illumination. (a) Series of phase images while translating a HeLa cell. (b) Amplitude images at the image plane. (c–e) Synthesized quantitative phase images of a HeLa cell, equivalent to angular plane wave at -30°, 0° and +35°, respectively. Color bars indicate phase in radians.

Fig. 3.
Fig. 3.

Refractive index tomogram of a live HeLa cell. (a)–(c) Lateral slices of tomogram images for a HeLa cell in 2 µm steps from top to bottom. (d) Bright field image of the same HeLa cell. Color bar indicates refractive index at λ=632.8 nm.

Equations (6)

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E ( x , z ) = A ( k x ) exp ( ik x x + ik z z ) dk x ,
E ( x , z ) = A ( k x ) exp [ i { k x x + k z z + ϕ ( x ; k x ) } ] dk x ,
E ( x ; η , z ) = E ( x η , z ) = ( A ( k x ) exp ( ik x η ) ) exp [ i { k x x + k z z + ϕ ( x ; k x ) } ] dk x .
E ( x ; η , z ' ) e i k η η d η = [ exp { i ( k η k x ) η } d η ] A ( k x ) exp [ i { k x x + k z z + ϕ ( x ; k x ) } ] dk x ,
= A ( k η ) exp [ i { k η x + ( k 0 2 k η 2 ) 1 2 z ' + ϕ ( x ; k η ) } ] .
E ( x ; k η , y , z ) = E ( x ; η , y , z ) exp ( i k η η ) d η = A ( k η ) exp [ i { k η x + k 0 2 k η 2 z + ϕ ( x , y ; k η ) } ] .

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