Abstract

Optical heterodyning is a detection scheme that permits the preferential detection of ballistic photons transmitted through a random medium, providing the imaging of absorbing structures within. We introduce a normalized cross-correlation function as a quantitative measure of image quality and employ it to investigate the effect of source coherence length on the ability of optical heterodyning to detect these absorbing structures. The ability to image in transmission is found to be greatly enhanced by use of a reduced-coherence-length source. The effect on image quality of the transport mean-free-path length is quantified and found to depend on source coherence length. The necessity of considering scatterer particle–particle correlations is also presented.

© 1995 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 401.
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    [CrossRef] [PubMed]
  3. S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, Opt. Lett. 15, 1179 (1990).
    [CrossRef] [PubMed]
  4. K. M. Yoo, Q. Xing, R. R. Alfano, Opt. Lett. 16, 1019 (1991).
    [CrossRef] [PubMed]
  5. M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Opt. Lett. 16, 1868 (1991).
    [CrossRef] [PubMed]
  6. M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, E. A. Swanson, Opt. Lett. 18, 950 (1993).
    [CrossRef] [PubMed]
  7. E. Leith, C. Chen, H. Chen, D. Dilworth, J. Lopez, J. Rudd, P.-C. Sun, J. Valdmanis, G. Vossler, J. Opt. Soc. Am. A 9, 1148 (1992).
    [CrossRef]
  8. K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
    [CrossRef] [PubMed]
  9. M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
    [CrossRef]
  10. D. S. Dilworth, E. N. Leith, J. L. Lopez, Appl. Opt. 29, 691 (1990).
    [CrossRef] [PubMed]
  11. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
  12. K. M. Yoo, R. R. Alfano, Opt. Lett. 15, 320 (1990).
    [CrossRef] [PubMed]
  13. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 477.
  14. J. K. Percus, G. J. Yevick, Phys. Rev. 110, 583 (1958).
    [CrossRef]
  15. M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).
    [CrossRef]
  16. P. Saulnier, M. Zinkin, G. Watson, Phys. Rev. B 42, 2621 (1990).
    [CrossRef]
  17. M. Lax, V. Nayaramamurti, R. C. Fulton, Laser Optics of Condensed Matter (Plenum, New York, 1987), p. 229.

1993 (1)

1992 (2)

1991 (4)

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

K. M. Yoo, Q. Xing, R. R. Alfano, Opt. Lett. 16, 1019 (1991).
[CrossRef] [PubMed]

M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Opt. Lett. 16, 1868 (1991).
[CrossRef] [PubMed]

1990 (4)

1989 (1)

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

1963 (1)

M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).
[CrossRef]

1958 (1)

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 583 (1958).
[CrossRef]

Abramson, N. H.

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

Alfano, R. R.

Andersson-Engels, S.

Berg, R.

Bjelkhagen, H.

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 477.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chen, C.

Chen, H.

Das, B. B.

Dilworth, D.

Dilworth, D. S.

Duncan, M. D.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, E. A. Swanson, Opt. Lett. 18, 950 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fulton, R. C.

M. Lax, V. Nayaramamurti, R. C. Fulton, Laser Optics of Condensed Matter (Plenum, New York, 1987), p. 229.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hee, M. R.

M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, E. A. Swanson, Opt. Lett. 18, 950 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 477.

Ichimura, T.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

Inaba, H.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

Izatt, J. A.

Jacobson, J. M.

Jarlman, O.

Kondo, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

Lax, M.

M. Lax, V. Nayaramamurti, R. C. Fulton, Laser Optics of Condensed Matter (Plenum, New York, 1987), p. 229.

Leith, E.

Leith, E. N.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Lopez, J.

Lopez, J. L.

Mahon, R.

Nayaramamurti, V.

M. Lax, V. Nayaramamurti, R. C. Fulton, Laser Optics of Condensed Matter (Plenum, New York, 1987), p. 229.

Percus, J. K.

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 583 (1958).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Reintjes, J.

Rudd, J.

Saulnier, P.

P. Saulnier, M. Zinkin, G. Watson, Phys. Rev. B 42, 2621 (1990).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Serafin, J.

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

Spears, K. G.

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Sun, P.-C.

Svanberg, S.

Swanson, E. A.

M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, E. A. Swanson, Opt. Lett. 18, 950 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tankersley, L. L.

Toida, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

Valdmanis, J.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 401.

Vossler, G.

Watson, G.

P. Saulnier, M. Zinkin, G. Watson, Phys. Rev. B 42, 2621 (1990).
[CrossRef]

Wertheim, M. S.

M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).
[CrossRef]

Xing, Q.

Yevick, G. J.

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 583 (1958).
[CrossRef]

Yoo, K. M.

Zhu, X.

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

Zinkin, M.

P. Saulnier, M. Zinkin, G. Watson, Phys. Rev. B 42, 2621 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

K. G. Spears, J. Serafin, N. H. Abramson, X. Zhu, H. Bjelkhagen, IEEE Trans. Biomed. Eng. 36, 1210 (1989).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Lett. (6)

Phys. Rev. (1)

J. K. Percus, G. J. Yevick, Phys. Rev. 110, 583 (1958).
[CrossRef]

Phys. Rev. B (1)

P. Saulnier, M. Zinkin, G. Watson, Phys. Rev. B 42, 2621 (1990).
[CrossRef]

Phys. Rev. Lett. (1)

M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other (3)

M. Lax, V. Nayaramamurti, R. C. Fulton, Laser Optics of Condensed Matter (Plenum, New York, 1987), p. 229.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 401.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 477.

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Figures (3)

Fig. 1
Fig. 1

Modified Mach–Zehnder interferometer used to image absorbing structures within a random medium in transmission by means of optical heterodyning. A diode laser (780 nm) and a He–Ne laser (633 nm) were used. BS1, BS2, beam splitters; AOM1, AOM2, acousto-optic modulators; BE1, BE2, beam expanders; TS1, TS2, one-and two-dimensional translation stages; PH1, PH2, 800- and 400-μm pinholes; PD1, PD2, photodiode detectors; SC, CC, sample and compensating cells.

Fig. 2
Fig. 2

Image quality expressed as a normalized correlation function γ versus optical thickness L/l, where L = 1 cm is the sample thickness and l is the extinction mean free path length. Also shown are scales that indicate the number of transport mean-free-path lengths l* across the sample L/l* for the two scatterer diameters of 0.997 and 0.107 μm. Except for the distribution shown by open diamonds, all mean free path lengths l and l* account for particle–particle correlations by inclusion of the hard-sphere Percus–Yevick structure factor into the Mie cross sections. The data were obtained with a 300-μm coherence-length source.

Fig. 3
Fig. 3

Same as in Fig. 2, except that the data were obtained with a 0.4-m coherence-length source. The inset shows the temporal distribution of transmitted photons for the two scatter sizes, each with L/l = 10 but differing L/l*.

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C g f ( i , j ) = n m g ( n , m ) f ( n + i , m + j ) ,

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