Abstract

Tomographic phase microscopy is a laser interferometry technique in which a 3D refractive index map of a biological sample is constructed from quantitative phase images collected at a set of illumination angles. Although the resulting tomographic images provide valuable information, their resolution declines at axial distances beyond about 1μm from the focal plane. We describe an improved 3D reconstruction algorithm in which the field at the focal plane is numerically propagated to depths throughout the sample. Diffraction is thus incorporated, extending the depth of focus to more than 10μm. Tomograms with improved focal depth are demonstrated for single HT29 cells.

© 2008 Optical Society of America

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References

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  1. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Methods 4, 717 (2007).
    [CrossRef] [PubMed]
  2. C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, Opt. Lett. 32, 1572 (2007).
    [CrossRef] [PubMed]
  3. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).
  4. A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
    [CrossRef]
  5. F. Charriere, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, Opt. Express 14, 7005 (2006).
    [CrossRef] [PubMed]
  6. G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Image Process. 9, 1560 (2000).
    [CrossRef]
  7. K. Creath, Prog. Opt. 26, 349 (1988).
    [CrossRef]
  8. R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
    [CrossRef]

2007 (2)

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

C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, Opt. Lett. 32, 1572 (2007).
[CrossRef] [PubMed]

2006 (1)

2000 (2)

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Image Process. 9, 1560 (2000).
[CrossRef]

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

1988 (2)

K. Creath, Prog. Opt. 26, 349 (1988).
[CrossRef]

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

IEEE Trans. Image Process. (1)

G. A. Tsihrintzis and A. J. Devaney, IEEE Trans. Image Process. 9, 1560 (2000).
[CrossRef]

Nat. Methods (1)

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

Opt. Commun. (1)

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, Opt. Commun. 175, 329 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Prog. Opt. (1)

K. Creath, Prog. Opt. 26, 349 (1988).
[CrossRef]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

Other (1)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).

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Figures (3)

Fig. 1
Fig. 1

Tomographic phase microscope. GM, galvanometer scanning mirror; L1, lens, focal length f = 250 mm ; BF, back focal plane of condenser lens; C, condenser lens; OL, objective lens; L2, lens, 200 mm ; AOMs, acousto-optic modulators. The frequency-shifted reference laser beam is shown in blue online. The diagram (a) describes the phase projection geometry, with θ the illumination angle.

Fig. 2
Fig. 2

Effect of sampling depth on refractive index tomograms. (a) Phase image of a 10 μ m polystyrene bead with the focus 4 μ m above the center of the bead. (b) Quantitative phase image after applying the propagation correction, with the focus brought to the center of the bead. The color bar indicates phase in radians. (c) x y slice of the refractive index tomogram for the same focus as in (a). (d) x y slice of the refractive index tomogram after applying the propagation algorithm. The color bar indicates the refractive index measured at λ = 633 nm .

Fig. 3
Fig. 3

Refractive index tomogram of an HT29 cell before and after applying the propagation correction. (a)–(d) Successive x y slices of the refractive index tomogram at 2 μ m intervals in the axial direction, before applying the propagation correction. (f)–(h) x y slices corresponding to (a), (b), and (d) after applying the propagation algorithm. (e) and (i) x z slices along the dashed lines indicated in (d) and (h), respectively. The color bar indicates refractive index at λ = 633 nm . (j)–(m) Bright field images with the image focus corresponding to (a)–(d). Scale bar, 10 μ m .

Equations (3)

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I ( x , y ; θ , t ) = I R + I S ( x , y ) + 2 I R I S ( x , y ) cos ( 2 π Ω t + ϕ θ ( x , y ) + k m sin θ M x ) .
u θ ( x , y ) = [ ( I 4 I 2 ) + i ( I 3 I 1 ) ] ( 4 I R ) = I S ( x , y ) exp ( i ϕ θ ( x , y ) + i ( k m sin θ ) x M ) .
u θ ( x , y ; d ) = U θ ( k x , k y ; z = 0 ) e i k x x + i k y y + i d k m 2 k x 2 k y 2 d k x d k y .

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