Abstract

Image formation in a turbid medium under a microscope is studied both theoretically and experimentally. In particular, the relationship of image resolution to scattered photons, which experience different numbers of scattering events, is explored in a scanning microscope. The effects of the numerical aperture of a microscope objective and the detector size on image resolution that is contributed by scattered photons are carefully investigated. The results show that for an object embedded in a turbid medium of a thickness of 12 scattering mean-free-path lengths, transverse resolution of an image contributed by scattered photons is much lower than the diffraction-limited resolution. A criterion for determining the efficiency of a gating method is proposed in terms of the relationship of resolution to signal strength.

© 1998 Optical Society of America

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1997 (4)

M. Gu, X. Gan, “Monte Carlo simulation for confocal microscopy through turbid media,” Cell Vision 4, 109–110 (1997).

X. Gan, S. Schilders, M. Gu, “Combination of annular aperture and polarization gating methods for efficient microscopic imaging through a turbid medium: theoretical analysis,” Microsc. Microanal. 3, 495–503 (1997).

M. Kempe, A. Z. Genack, W. Rudolph, P. Dorn, “Ballistic and diffuse light detection in confocal and heterodyne imaging systems,” J. Opt. Soc. Am. A 14, 216–223 (1997).
[CrossRef]

S. P. Morgan, M. P. Khong, M. G. Somekh, “Effects of polarization state and scatterer concentration on optical imaging through scattering media,” Appl. Opt. 36, 1560–1565 (1997).
[CrossRef] [PubMed]

1996 (3)

1995 (3)

1994 (1)

1992 (1)

1991 (3)

Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, “Monte Carlo simulation of light transmission through living tissue,” Appl. Opt. 30, 4515–4520 (1991).
[CrossRef] [PubMed]

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990 (2)

1989 (1)

1987 (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

1986 (1)

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

’t Hooft, G. W.

Alfano, R. R.

Anderson-Engels, S.

Baselman, J. J. M.

Ben-Letaief, K.

Berg, R.

Bohern, C. F.

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bonner, R. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Davis, E. R.

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

De Silvestri, S.

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Dorn, P.

Flock, S. T.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Flott, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Gan, X.

X. Gan, S. Schilders, M. Gu, “Combination of annular aperture and polarization gating methods for efficient microscopic imaging through a turbid medium: theoretical analysis,” Microsc. Microanal. 3, 495–503 (1997).

M. Gu, X. Gan, “Monte Carlo simulation for confocal microscopy through turbid media,” Cell Vision 4, 109–110 (1997).

Gandjbakhche, A. H.

Genack, A. Z.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gu, M.

M. Gu, X. Gan, “Monte Carlo simulation for confocal microscopy through turbid media,” Cell Vision 4, 109–110 (1997).

X. Gan, S. Schilders, M. Gu, “Combination of annular aperture and polarization gating methods for efficient microscopic imaging through a turbid medium: theoretical analysis,” Microsc. Microanal. 3, 495–503 (1997).

M. Gu, T. Tannous, C. J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1996).
[CrossRef] [PubMed]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Hasegawa, Y.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ho, P. P.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ippen, E. P.

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Jackson, P. C.

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Jacques, S. L.

Jarlmann, O.

Kempe, M.

Key, H.

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Khong, M. P.

Knüttel, A.

Liang, X.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Margolis, R.

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Minsky, M.

M. Minsky, “Microscopy apparatus,” U.S. patent3,012,467 (December19, 1961).

Morgan, S. P.

Nomura, Y.

Oseroff, A.

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Papaioannou, D. G.

Patterson, M. S.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Puliafito, C. A.

J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R. Margolis, A. Oseroff, “Femtosecond optical ranging in biological systems,” Opt. Lett. 3, 150–153 (1986).
[CrossRef]

Pulianfito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rudolph, W.

Schilders, S.

X. Gan, S. Schilders, M. Gu, “Combination of annular aperture and polarization gating methods for efficient microscopic imaging through a turbid medium: theoretical analysis,” Microsc. Microanal. 3, 495–503 (1997).

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Somekh, M. G.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Svanberg, S.

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tamura, M.

Tannous, T.

van Gemert, M. J. C.

Wang, L.

Wang, Q. Z.

Wells, P. N. T.

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Welsch, E.

Wilson, B. C.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Yadlowsky, M. J.

Yadlowsky, M. Y.

Yamada, Y.

Yoo, K. M.

Appl. Opt. (6)

Cell Vision (1)

M. Gu, X. Gan, “Monte Carlo simulation for confocal microscopy through turbid media,” Cell Vision 4, 109–110 (1997).

J. Opt. Soc. Am. A (4)

Med. Phys. (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Microsc. Microanal. (1)

X. Gan, S. Schilders, M. Gu, “Combination of annular aperture and polarization gating methods for efficient microscopic imaging through a turbid medium: theoretical analysis,” Microsc. Microanal. 3, 495–503 (1997).

Opt. Lett. (5)

Phys. Med. Biol. (1)

H. Key, E. R. Davis, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flott, K. Gregory, C. A. Pulianfito, J. G. Fujimoto, “Optical coherent tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (5)

M. Minsky, “Microscopy apparatus,” U.S. patent3,012,467 (December19, 1961).

C. F. Bohern, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a scanning optical microscope.

Fig. 2
Fig. 2

(a) Image resolution as a function of the number of scattering events N or the optical thickness n (NA=0.25, vd). In the case of ΓN versus N, n=12. (b) Normalized photon-number distribution ρN as a function of the number of scattering events N for different values of the optical thickness n (NA=0.25, vd).

Fig. 3
Fig. 3

Image resolution Γ as a function of the optical thickness n for different values of the numerical aperture of objectives (vd).

Fig. 4
Fig. 4

Image resolution ΓN for different values of the numerical aperture of the objective (n=12, vd).

Fig. 5
Fig. 5

Normalized photon-number distribution ρN as a function of the number of scattering events N for different values of the numerical aperture of objectives (n=12, vd).

Fig. 6
Fig. 6

Image resolution Γ as a function of the optical thickness n for different pinhole sizes (NA=0.25).

Fig. 7
Fig. 7

Image resolution ΓN for different pinhole sizes (n=12, NA=0.25).

Fig. 8
Fig. 8

Normalized photon-number distribution ρN as a function of the number of scattering events N for different pinhole sizes (n=12, NA=0.25).

Fig. 9
Fig. 9

Image resolution Γ as a function of signal strength for different values of the numerical aperture of objectives (n=12).

Fig. 10
Fig. 10

A comparison of the normalized photon-number distribution ρN and image resolution ΓN between cases A and B: (a) normalized photon-number distribution, (b) image resolution.

Fig. 11
Fig. 11

Measured images of a bar embedded in a turbid medium of an optical thickness of n=10.4: (a) NA=0.25, vd=4000 µm, Γ=24.1 µm; (b) NA=0.25, vd=150 µm, Γ=13.4 µm; (c) NA=0.75, vd=4000 µm, Γ=25.5 µm; (d) NA=0.75, vd=500 µm, Γ=15.6 µm; (e) NA=0.75, vd=150 µm, Γ=14 µm; (f) NA=0.75, vd=50 µm.

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