Abstract

We describe the use of degree of polarization to discriminate unscattered and weakly scattered light from multiply scattered light in an optically turbid material. We use spatially resolved measurements of the degree of polarization to compare how well linearly and circularly polarized light survives in a sample. Experiments were performed on common tissue phantoms consisting of polystyrene and Intralipid microsphere suspensions and on adipose and arterial tissue. The results indicate that polarization is maintained even after unpolarized irradiance through each sample has been extinguished by several orders of magnitude. The results also show that polarized light propagation in common tissue phantoms is distinctly different from polarized light propagation in the two tissues investigated. Further, these experiments illustrate when polarization is an effective discrimination criterion and when it is not. The potential of a polarization-based discrimination scheme to image through the biological and nonbiological samples investigated here is also discussed.

© 1999 Optical Society of America

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References

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1996

O. Emile, F. Bretenaker, A. Le Floch, “Rotating polarization imaging in turbid media,” Opt. Lett. 21, 1706–1708 (1996).
[CrossRef] [PubMed]

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Topics Quantum Electron. 2, 898–905 (1996).
[CrossRef]

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

1994

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1993

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

1992

1991

1990

1989

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

1978

1977

1972

1969

1957

D. Maurice, “Structure and transparency of the cornea,” J. Physiol. 136, 263–287 (1957).
[PubMed]

Akatsuha, T.

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

Alberts, B.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Alfano, R. R.

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Bloom, W.

W. Bloom, D. W. Fawcett, A Textbook of Histology (Saunders, Philadelphia, Pa., 1986).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 7–136.

Bonner, R. F.

Bonnier, D.

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, New York, 1980).

Bray, D.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Bretenaker, F.

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Carswell, A. I.

Chan, K. P.

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

Cheong, W.-F.

W.-F. Cheong, “Summary of optical properties,” in Optical–Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert eds. (Plenum, New York, 1985), pp. 275–303.

Das, B. B.

Devaraj, B.

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

Dilworth, D. S.

Dunn, A.

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Topics Quantum Electron. 2, 898–905 (1996).
[CrossRef]

Eick, A. A.

Emile, O.

Farrell, R. A.

Fawcett, D. W.

W. Bloom, D. W. Fawcett, A Textbook of Histology (Saunders, Philadelphia, Pa., 1986).

Forand, J. L.

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

Fournier, G. R.

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

Freyer, J. P.

Gandbakhche, A. H.

Granatstein, V. L.

Hart, R. W.

Haskell, R. C.

Hielscher, A. H.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 7–136.

Johnson, T. M.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, San Diego, Calif., 1969).

Khong, M. P.

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), pp. 285–290.

Le Floch, A.

Leith, E. N.

Levine, A. M.

Lewis, J.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), pp. 285–290.

Lopez, J. L.

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Maffione, R. A.

R. A. Maffione, J. M. Voss, C. D. Mobley, “Theory and measurements of the complete beam spread function of sea ice,” Limnol. Oceanogr. 43, 34–43 (1998).
[CrossRef]

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Maurice, D.

D. Maurice, “Structure and transparency of the cornea,” J. Physiol. 136, 263–287 (1957).
[PubMed]

Mertens, L. E.

Mobley, C. D.

R. A. Maffione, J. M. Voss, C. D. Mobley, “Theory and measurements of the complete beam spread function of sea ice,” Limnol. Oceanogr. 43, 34–43 (1998).
[CrossRef]

Moes, C. J. M.

Morgan, S. P.

Mourant, J. R.

Pace, P. W.

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Prahl, S. A.

Raff, M.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), pp. 285–290.

Replogle, F. S.

Rhinewine, M.

Rhodin, J. A. G.

J. A. G. Rhodin, Histology: A Text and Atlas (Oxford U. Press, New York, 1974).

Richards-Kortum, R.

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Topics Quantum Electron. 2, 898–905 (1996).
[CrossRef]

Roberts, K.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Ryan, J. S.

Schmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

J. M. Schmitt, A. H. Gandbakhche, R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31, 6535–6546 (1992).
[CrossRef] [PubMed]

Shen, A.

Somekh, M. G.

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.-T.

Usa, M.

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Voss, J. M.

R. A. Maffione, J. M. Voss, C. D. Mobley, “Theory and measurements of the complete beam spread function of sea ice,” Limnol. Oceanogr. 43, 34–43 (1998).
[CrossRef]

Watson, J. D.

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

Weitz, D. A.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, New York, 1980).

Yoo, K. M.

Zhu, J. X.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Appl. Opt.

IEEE J. Sel. Topics Quantum Electron.

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Topics Quantum Electron. 2, 898–905 (1996).
[CrossRef]

B. Devaraj, M. Usa, K. P. Chan, T. Akatsuha, “Recent advances in coherent detection imaging (CDI) in biomedicine: laser tomography of human tissues in vivo and in vitro,” IEEE J. Sel. Topics Quantum Electron. 2, 1008–1016 (1996).
[CrossRef]

J. Opt. Soc. Am.

J. Physiol.

D. Maurice, “Structure and transparency of the cornea,” J. Physiol. 136, 263–287 (1957).
[PubMed]

Limnol. Oceanogr.

R. A. Maffione, J. M. Voss, C. D. Mobley, “Theory and measurements of the complete beam spread function of sea ice,” Limnol. Oceanogr. 43, 34–43 (1998).
[CrossRef]

Opt. Eng.

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

G. R. Fournier, D. Bonnier, J. L. Forand, P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng. 32, 2185–2190 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. B

F. C. MacKintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Phys. Rev. E

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Other

W.-F. Cheong, “Summary of optical properties,” in Optical–Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert eds. (Plenum, New York, 1985), pp. 275–303.

J. A. G. Rhodin, Histology: A Text and Atlas (Oxford U. Press, New York, 1974).

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell (Garland, New York, 1983).

W. Bloom, D. W. Fawcett, A Textbook of Histology (Saunders, Philadelphia, Pa., 1986).

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, New York, 1980).

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), pp. 285–290.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 7–136.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, San Diego, Calif., 1969).

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Figures (7)

Fig. 1
Fig. 1

Demonstration of imaging objects in optically turbid media with polarized light. A transparency slide with the letters LLNL printed in black ink was placed at the back edge of a 1-cm path-length glass cuvette. The cuvette was filled with 0.08% Intralipid (τ′ = 1.0). The images shown are 4 mm × 5 mm in dimensions. (a) No indication of the target is seen with unpolarized light. (b) With linearly polarized light [as described by Eq. (1) and Fig. 2(a)], the target is clearly identified.

Fig. 2
Fig. 2

Experimental setup. Aqueous samples are held in a 1-cm path-length glass cuvette between the two polarizers, whereas tissue samples are held between glass plates between the two polarizers. (a) The experimental setup for measuring the degree of linear polarization consists of a He–Ne laser and two linear polarizers. The degree of linear polarization is calculated from Eq. (1). (b) The experimental setup for measuring the degree of circular polarization consists of a He–Ne laser, two quarter-wave plates, and two linear polarizers. The degree of circular polarization is calculated from Eq. (4). The incident beam has a 1.5-mm 1/e 2 diameter and a Gaussian beam profile. The f/2.8, 55-mm focal-length camera lens is placed 4 cm from the back edge of the sample, resulting in a collection angle of 26°. The maximum degree of polarization with no sample present is 0.92.

Fig. 3
Fig. 3

Typical degrees of polarization of BSF’s at the back edge of the sample (labeled image plane in Fig. 2) for microsphere suspensions. For these data, μ s and g were calculated by use of Mie scattering cross sections for spheres and were used to calculate τ′ = μ s (1 - g)t, where t is the sample thickness.16,17 (a) 0.107-µm-diameter polystyrene spheres, linear polarization; (b) 1.072-µm-diameter polystyrene spheres, circular polarization.

Fig. 4
Fig. 4

Maximum degree of polarization for aqueous microsphere suspensions with diameters of (a) 0.107 µm, polystyrene; (b) 0.48 µm, polystyrene; (c) 1.072 µm polystyrene; (d) 25–675 nm, with a mean diameter of 97 ± 3 nm, Intralipid. Each point corresponds to an average taken from a 10 × 10 pixel area. The error bars represent the standard deviation. Points with nonvisible error bars have errors that are smaller than the symbol.

Fig. 5
Fig. 5

Maximum degree of polarization in tissue for (a) porcine fat and (b) porcine artery. Each point corresponds to an average taken from a 10 × 10 pixel area in the corresponding BSF image. The error bars represent the standard deviation. The values for μ s and g for each tissue were taken from the literature.19

Fig. 6
Fig. 6

Parameterization of BSF’s for tissue. (a) BSF’s for unpolarized and polarized light in a 0.26-mm-thick section of artery (τ′ = 1.06); (b) PP 0 versus ΔII 0 for fat and artery. The parameterization ΔPP 0 is shown here for linearly polarized light incident upon each sample; the results seen with circularly polarized light show similar trends. The exponential fit shown for each data set indicates how quickly ΔPP 0 and ΔII 0 decay.

Fig. 7
Fig. 7

Maximum degree of polarization in polystyrene and Intralipid suspensions and in porcine fat for (a) linear polarization and (b) circular polarization.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

pL=I1-I2I1+I2.
Iout=IinLP1QWP1SAMPLEQWP2LP2,
IOUT=I00.25p1+p cos2Ωt+α0.25 cos p2Ωt+α1+p cos2Ωt+α0.25p1+p cos2Ωt+αsin2Ωt+α0.
pC=VacVdc=IrcpItotal,

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