Abstract

We report on the development of a method that records spatially dependent intensity patterns of polarized light that is diffusely backscattered from highly scattering media. It is demonstrated that these intensity patterns can be used to differentiate turbid media, such as polystyrene-sphere and biological-cell suspensions. Our technique employs polarized light from a He-Ne laser (λ = 543 nm), which is focused onto the surface of the scattering medium. A surface area of approximately 4x4 cm centered on the light input point is imaged through polarization-analysis optics onto a CCD camera. One can observe a large variety of intensity patterns by varying the polarization state of the incident laser light and changing the analyzer configuration to detect different polarization components of the backscattered light. Introducing the Mueller-matrix concept for diffusely backscattered light, a framework is provided to select a subset of measurements that comprehensively describe the optical properties of backscattering media.

© 1997 Optical Society of America

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  1. J.M. Schmitt, A.H. Gandjbakhche, and 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]
  2. R.R. Anderson, “Polarized-light examination and photography of the skin,“ Arch. Dermatol. 127, 1000–1005 (1991).
    [Crossref] [PubMed]
  3. S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
    [Crossref]
  4. S.G. Demos and R.R. Alfano, “Optical polarization imaging,“ Appl. Opt. 36, 150–155 (1997).
    [Crossref] [PubMed]
  5. A.H. Hielscher, J.R. Mourant, and I.J. Bigio, “Diffuse polarization spectroscopy on tissue phantoms and biological cell suspensions”, in Optical Biopsies and Microscopic Techniques, I.J. Bigio, W.S. Grundfest, H. Schneckenburger, K. Svanberg, and P.M. Viallet, eds., Proc. SPIE 2926, pp. 67–76 (1996).
    [Crossref]
  6. A.H. Hielscher, J.R. Mourant, and I.J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,“ Appl. Opt. 36, 125–135 (1997).
    [Crossref] [PubMed]
  7. W.S. Bickel and W.M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,“ Am. J. Phys. 53, 468–478 (1985).
    [Crossref]
  8. H.C. van de Hulst, Light Scattering by Small Particles (John Wiley&Sons, New York, NY, 1957)
  9. W.S. Bickel, A.J. Watkins, and G. Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,“ Am. J. Phys. 55, 559–561 (1987).
    [Crossref]
  10. L.C. Junqueira, J. Carneiro, and R.O. Kelley, Basic Histology (Appleton&Lange, Norwalk, Connecticut, 1992), pp. 108–110.
  11. L.A. Kunz-Schugart, K. Groebe, and W. Mueller-Klieser, “Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation,“ Int. J. Cancer. 66, 578–586 (1996).
    [Crossref]
  12. K.E. LaRue, E.M. Bradbury, and J.P. Freyer, “Regulation of G1 transit by cyclin kinase inhibitors in multicellular spheroid cultures of rat embryo fibroblast cells transformed to different extents,“ Cancer Res., in press (1998).
    [PubMed]
  13. S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.
  14. A. Kienle, L. Lilge, M.S. Patterson, R. Hibst, R. Steiner, and B.C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,“ Appl. Opt. 35, 2304–2314 (1996).
    [Crossref] [PubMed]
  15. T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,“ Med. Phys. 19, 879–888 (1992).
    [Crossref] [PubMed]
  16. J.R. Mourant, T. Fuselier, J. Boyer, T. M.. Johnsons, and I.J. Bigio, “Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms,“ Appl. Opt. 36, 949–957 (1997).
    [Crossref] [PubMed]
  17. M.G. Nichols, E.L. Hull, and T.H. Foster, “Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,“ Appl. Opt. 36, 93–104 (1997).
    [Crossref] [PubMed]
  18. J.T. Bruulsema, J.E. Hayward, T.J. Farrel, M.S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, and H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficients,“ Opt. Lett. 22, 190–192 (1997).
    [Crossref] [PubMed]
  19. A. Kienle and M.S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equation for reflectance from a semi-infinite turbid medium,“ J. Opt. Soc. of Am. A 14, 246–254 (1997).
    [Crossref]
  20. R. Bays, G. Wagnieres, D. Robert, D. Braichotte, J.F. Savary, P. Monnier, and H. Vandenbergh, “Clinical determination of tissue optical properties by endoscopic spatially-resolved reflectometry,“ Appl. Opt. 35, 1756–1766 (1996).
    [Crossref] [PubMed]
  21. H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
    [Crossref] [PubMed]
  22. P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
    [Crossref]
  23. L.H. Wang and S.L. Jaques, “Hybrid model of Monte Carlo simulations and diffusion theory for light flectance by turbid media,“ J. Opt. Soc. Am. A 10, 1746–1752 (1993).
    [Crossref]
  24. T.J. Farrell, B.C. Wilson, and M.S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance mesurements.,“ Phys. Med. Biol. 37, 2281–2286 (1992).
    [Crossref] [PubMed]

1998 (1)

K.E. LaRue, E.M. Bradbury, and J.P. Freyer, “Regulation of G1 transit by cyclin kinase inhibitors in multicellular spheroid cultures of rat embryo fibroblast cells transformed to different extents,“ Cancer Res., in press (1998).
[PubMed]

1997 (6)

1996 (5)

R. Bays, G. Wagnieres, D. Robert, D. Braichotte, J.F. Savary, P. Monnier, and H. Vandenbergh, “Clinical determination of tissue optical properties by endoscopic spatially-resolved reflectometry,“ Appl. Opt. 35, 1756–1766 (1996).
[Crossref] [PubMed]

S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
[Crossref]

A.H. Hielscher, J.R. Mourant, and I.J. Bigio, “Diffuse polarization spectroscopy on tissue phantoms and biological cell suspensions”, in Optical Biopsies and Microscopic Techniques, I.J. Bigio, W.S. Grundfest, H. Schneckenburger, K. Svanberg, and P.M. Viallet, eds., Proc. SPIE 2926, pp. 67–76 (1996).
[Crossref]

A. Kienle, L. Lilge, M.S. Patterson, R. Hibst, R. Steiner, and B.C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,“ Appl. Opt. 35, 2304–2314 (1996).
[Crossref] [PubMed]

L.A. Kunz-Schugart, K. Groebe, and W. Mueller-Klieser, “Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation,“ Int. J. Cancer. 66, 578–586 (1996).
[Crossref]

1995 (2)

H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
[Crossref] [PubMed]

P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
[Crossref]

1993 (1)

1992 (4)

T.J. Farrell, B.C. Wilson, and M.S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance mesurements.,“ Phys. Med. Biol. 37, 2281–2286 (1992).
[Crossref] [PubMed]

J.M. Schmitt, A.H. Gandjbakhche, and 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]

T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,“ Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

1991 (1)

R.R. Anderson, “Polarized-light examination and photography of the skin,“ Arch. Dermatol. 127, 1000–1005 (1991).
[Crossref] [PubMed]

1987 (1)

W.S. Bickel, A.J. Watkins, and G. Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,“ Am. J. Phys. 55, 559–561 (1987).
[Crossref]

1985 (1)

W.S. Bickel and W.M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,“ Am. J. Phys. 53, 468–478 (1985).
[Crossref]

Alfano, R.R.

Anderson, R.R.

R.R. Anderson, “Polarized-light examination and photography of the skin,“ Arch. Dermatol. 127, 1000–1005 (1991).
[Crossref] [PubMed]

Bailey, W.M.

W.S. Bickel and W.M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,“ Am. J. Phys. 53, 468–478 (1985).
[Crossref]

Bays, R.

Berger, M.

Bevilacqua, F.

P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
[Crossref]

Bickel, W.S.

W.S. Bickel, A.J. Watkins, and G. Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,“ Am. J. Phys. 55, 559–561 (1987).
[Crossref]

W.S. Bickel and W.M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,“ Am. J. Phys. 53, 468–478 (1985).
[Crossref]

Bigio, I.J.

Boas, D.A.

H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
[Crossref] [PubMed]

Bonner, R.F.

Boyer, J.

Bradbury, E.M.

K.E. LaRue, E.M. Bradbury, and J.P. Freyer, “Regulation of G1 transit by cyclin kinase inhibitors in multicellular spheroid cultures of rat embryo fibroblast cells transformed to different extents,“ Cancer Res., in press (1998).
[PubMed]

Braichotte, D.

Bruulsema, J.T.

Carneiro, J.

L.C. Junqueira, J. Carneiro, and R.O. Kelley, Basic Histology (Appleton&Lange, Norwalk, Connecticut, 1992), pp. 108–110.

Chance, B.

H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
[Crossref] [PubMed]

Dehaller, E.B.

P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
[Crossref]

Demos, S.G.

Depeursinge, C.

P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
[Crossref]

Farrel, T.J.

Farrell, T.J.

T.J. Farrell, B.C. Wilson, and M.S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance mesurements.,“ Phys. Med. Biol. 37, 2281–2286 (1992).
[Crossref] [PubMed]

T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,“ Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Foster, T.H.

Freyer, J.P.

K.E. LaRue, E.M. Bradbury, and J.P. Freyer, “Regulation of G1 transit by cyclin kinase inhibitors in multicellular spheroid cultures of rat embryo fibroblast cells transformed to different extents,“ Cancer Res., in press (1998).
[PubMed]

Fuselier, T.

Gandjbakhche, A.H.

Groebe, K.

L.A. Kunz-Schugart, K. Groebe, and W. Mueller-Klieser, “Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation,“ Int. J. Cancer. 66, 578–586 (1996).
[Crossref]

Gutsche, A.

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

Hayward, J.E.

Heinemann, L.

Hibst, R.

Hielscher, A.H.

A.H. Hielscher, J.R. Mourant, and I.J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,“ Appl. Opt. 36, 125–135 (1997).
[Crossref] [PubMed]

A.H. Hielscher, J.R. Mourant, and I.J. Bigio, “Diffuse polarization spectroscopy on tissue phantoms and biological cell suspensions”, in Optical Biopsies and Microscopic Techniques, I.J. Bigio, W.S. Grundfest, H. Schneckenburger, K. Svanberg, and P.M. Viallet, eds., Proc. SPIE 2926, pp. 67–76 (1996).
[Crossref]

Hull, E.L.

Jacques, S.L.

S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
[Crossref]

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

Jaques, S.L.

Johnsons, T. M..

Junqueira, L.C.

L.C. Junqueira, J. Carneiro, and R.O. Kelley, Basic Histology (Appleton&Lange, Norwalk, Connecticut, 1992), pp. 108–110.

Kelley, R.O.

L.C. Junqueira, J. Carneiro, and R.O. Kelley, Basic Histology (Appleton&Lange, Norwalk, Connecticut, 1992), pp. 108–110.

Kienle, A.

A. Kienle and M.S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equation for reflectance from a semi-infinite turbid medium,“ J. Opt. Soc. of Am. A 14, 246–254 (1997).
[Crossref]

A. Kienle, L. Lilge, M.S. Patterson, R. Hibst, R. Steiner, and B.C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,“ Appl. Opt. 35, 2304–2314 (1996).
[Crossref] [PubMed]

Koschinsky, T.

Kunz-Schugart, L.A.

L.A. Kunz-Schugart, K. Groebe, and W. Mueller-Klieser, “Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation,“ Int. J. Cancer. 66, 578–586 (1996).
[Crossref]

LaRue, K.E.

K.E. LaRue, E.M. Bradbury, and J.P. Freyer, “Regulation of G1 transit by cyclin kinase inhibitors in multicellular spheroid cultures of rat embryo fibroblast cells transformed to different extents,“ Cancer Res., in press (1998).
[PubMed]

Lilge, L.

Liu, H.L.

H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
[Crossref] [PubMed]

Marquet, P.

P. Marquet, F. Bevilacqua, C. Depeursinge, and E.B. Dehaller, “Determination of reduced scattering and absorption coefficients by a single charged coupled device array measurement: 1. Comparison between experiments and simulations,“ Opt. Eng. 34, 2055–2063 (1995).
[Crossref]

Monnier, P.

Mourant, J.R.

Mueller-Klieser, W.

L.A. Kunz-Schugart, K. Groebe, and W. Mueller-Klieser, “Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation,“ Int. J. Cancer. 66, 578–586 (1996).
[Crossref]

Nichols, M.G.

Orskov, H.

Ostermeyer, M.

S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
[Crossref]

Patterson, M.S.

A. Kienle and M.S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equation for reflectance from a semi-infinite turbid medium,“ J. Opt. Soc. of Am. A 14, 246–254 (1997).
[Crossref]

J.T. Bruulsema, J.E. Hayward, T.J. Farrel, M.S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahlchristiansen, and H. Orskov, “Correlation between blood-glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficients,“ Opt. Lett. 22, 190–192 (1997).
[Crossref] [PubMed]

A. Kienle, L. Lilge, M.S. Patterson, R. Hibst, R. Steiner, and B.C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,“ Appl. Opt. 35, 2304–2314 (1996).
[Crossref] [PubMed]

T.J. Farrell, B.C. Wilson, and M.S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance mesurements.,“ Phys. Med. Biol. 37, 2281–2286 (1992).
[Crossref] [PubMed]

T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,“ Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Robert, D.

Sandahlchristiansen, J.

Savary, J.F.

Schmitt, J.M.

Schwartz, J.

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

Steiner, R.

Stephens, D.V.

S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
[Crossref]

Tittel, F.K.

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

van de Hulst, H.C.

H.C. van de Hulst, Light Scattering by Small Particles (John Wiley&Sons, New York, NY, 1957)

Vandenbergh, H.

Videen, G.

W.S. Bickel, A.J. Watkins, and G. Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,“ Am. J. Phys. 55, 559–561 (1987).
[Crossref]

Wagnieres, G.

Wang, L.

S.L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F.K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,“ in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R.R. Alfano, S.R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B.R. Masters, S. Svanberg, and P. van der Zee, eds.,  Vol. ISII of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, WA, 1992) pp. 211–226.

Wang, L.H.

S.L. Jacques, L.H. Wang, D.V. Stephens, and M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,“ in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE 2671, pp. 199–220 (1996).
[Crossref]

L.H. Wang and S.L. Jaques, “Hybrid model of Monte Carlo simulations and diffusion theory for light flectance by turbid media,“ J. Opt. Soc. Am. A 10, 1746–1752 (1993).
[Crossref]

Watkins, A.J.

W.S. Bickel, A.J. Watkins, and G. Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,“ Am. J. Phys. 55, 559–561 (1987).
[Crossref]

Wilson, B.

T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,“ Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Wilson, B.C.

A. Kienle, L. Lilge, M.S. Patterson, R. Hibst, R. Steiner, and B.C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,“ Appl. Opt. 35, 2304–2314 (1996).
[Crossref] [PubMed]

T.J. Farrell, B.C. Wilson, and M.S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance mesurements.,“ Phys. Med. Biol. 37, 2281–2286 (1992).
[Crossref] [PubMed]

Yodh, A.G.

H.L. Liu, D.A. Boas, Y.T Zhang, A.G. Yodh, and B. Chance, “Determination of optical-properties and bloodoxygenation in tissue using continous NIR light,“ Phys. Med. Biol. 40, 1983–1993 (1995).
[Crossref] [PubMed]

Zhang, Y.T

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup for measuring diffusely backscattered polarized light.

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Fig. 2.
Fig. 2.

Two examples of images taken with the experimental setup depicted in Fig.1. The scattering medium was a suspension of polystyrene-spheres with a diameter of 204 nm at a concentration of 0.05% by weight. Using Mie-theory8 the scattering coefficient of the suspension was calculated to be μs' = 1.9 cm-1. In Fig. 2a (left) the incident beam was linearly polarized at +45° with respect to the x-axis and the analyzer consisted of a linear polarizer oriented along the y-axis. Fig. 2b (right) was obtained with a right-hand circularly polarized incident beam and the linear polarization analyzer oriented along x-axis. The line that enters the images from the right is caused by the needle that holds the optical mask, which obscures the center of the images. To better illustrate the azimuthal dependence of the intensity decay the images are shown in a false-color depiction. The yellow areas in the corner of the images are outside the cylindrical beaker that contains the particle suspensions.

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Fig. 3.
Fig. 3.

This chart shows how to measure the various Mueller matrix elements. A two letter combination stands for one measurement. For example the combination (HV) means that the incoming light is linearly polarized along the horizontal axis (x-axis, see Fig. 2) and the analyzer is set to transmit light that is linearly polarized along the vertical axis (y-axis). For example, to calculate M22 four measurements are necessary: (HH), (VV), (HV) and (VH).

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Fig. 4.
Fig. 4.

Calculation of the Matrix element M22 from images obtained for the same polystyrene-sphere suspensions as shown in Fig. 2. Note that the color codes are different for the two sides of the equation, to allow for negative values of the matrix elementt.

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Fig. 5.
Fig. 5.

Diffuse backscattering Mueller matrix elements of polystyrene-sphere suspension withmonodisperse particle diameter of d = 2040nm (μs' = 1.9 cm-1). The upper left corner is M11, the lower right corner is M44 (see Eq. 2 and Fig. 3). The color scale is normalized so that the maximum intensity of the M11 element equals 1. All images displayed are 3.5cm x 3.5cm.

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Fig. 6.
Fig. 6.

Diffuse backscattering Mueller matrix elements of a polystyrene-sphere suspension with monodisperse particle diameter of d = 2040nm (with μs' = 1.9 cm-1). All images displayed are 3.5cm x 3.5cm.

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Fig. 7.
Fig. 7.

Radial dependence of M44 obtained from 4 different polystyrene-sphere suspensions. The numbers indicate the diameter, d, of the spheres in the suspension. The radial distance is given in units of transport mean free path (mfp').

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Fig.8.
Fig.8.

Diffuse-backscattering Mueller matrix of M1 cell suspension with 108 cells/cm-3.

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Fig.9.
Fig.9.

Diffuse-backscattering Mueller matrix of cancerous MR1 cell suspension with 108 cells/cm3.

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Fig. 10.
Fig. 10.

Radial dependence of M44 obtained from cell suspensions . As a reference the result for a 497-nm-polystyrene-sphere suspension is also shown (see Fig.7).

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Equations (4)

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

S = [ I Q U V ] = [ 〈 E h E h * + E v E v * 〉 〈 E h E h * − E v E v * 〉 〈 E h E v * + E v E h * 〉 〈 i ( E h E v * − E v E h * ) 〉 ]
M = [ M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ]
[ I Q U V ] = [ 1 − 1 0 0 − 1 1 0 0 0 0 0 0 0 0 0 0 ] • [ M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ] • [ 1 1 0 0 ]
[ I Q U V ] = [ M 11 + M 12 − M 21 − M 22 − M 11 − M 12 + M 21 + M 22 0 0 ]

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