Abstract

Diffuse photon density waves are proposed for use in characterizing diffuse media, similar to the use of electro-magnetic waves to characterize reflection from materials. To this end basic expressions for the reflection and transmission coefficients at interfaces are put forward. Effects such as the existence of modes analogous with Brewster modes are shown. Also, we illustrate through numerical simulations how the diffusion optical parameters are estimated both with and without noise in the data.

© 1999 Optical Society of America

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References

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  1. See related studies in J. G. Fujimoto and M. S. Patterson, eds., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998).
  2. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
    [CrossRef] [PubMed]
  3. J. B. Frishkin and E. Gratton, J. Opt. Soc. Am. A 10, 127 (1993).
    [CrossRef]
  4. E. M. Sevik-Muraca, D. L. Heintzelman, J. Lee, T. L. Troy, and D. Y. Paithankar, Appl. Opt. 36, 9058 (1997).
    [CrossRef]
  5. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), Chap.??3.
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.??Press, Cambridge, 1995), Chap.??3.
    [CrossRef]
  8. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley-Interscience, New York, 1991), Chap.??2.
  9. J. Ripoll, M. Nieto-Vesperinas, and R. Carminati, J. Opt. Soc. Am. A 16, 1466 (1999).
    [CrossRef]
  10. R. Aronson, J. Opt. Soc. Am. A 12, 2532 (1995).
    [CrossRef]
  11. J. Ripoll and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 16, 1453 (1999).
    [CrossRef]

1999 (2)

1997 (1)

1995 (1)

1993 (1)

1992 (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Aronson, R.

Boas, D. A.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), Chap.??3.

Carminati, R.

Chance, B.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Frishkin, J. B.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gratton, E.

Heintzelman, D. L.

Lee, J.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.??Press, Cambridge, 1995), Chap.??3.
[CrossRef]

Nieto-Vesperinas, M.

O’Leary, M. A.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Paithankar, D. Y.

Ripoll, J.

Sevik-Muraca, E. M.

Troy, T. L.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.??Press, Cambridge, 1995), Chap.??3.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), Chap.??3.

Yodh, A. G.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

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

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Other (5)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), Chap.??3.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.??Press, Cambridge, 1995), Chap.??3.
[CrossRef]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley-Interscience, New York, 1991), Chap.??2.

See related studies in J. G. Fujimoto and M. S. Patterson, eds., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998).

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Figures (2)

Fig. 1
Fig. 1

RK, near zero reflection, with ω=0, D0=0.041666 cm, D1=4/5D0=0.033333 cm, and μa1=0.025 cm-1, for the following cases: solid curve, μa0=μa1=0.025 cm-1; dotted curve, μa0=4/5μa1=0.020 cm-1, which gives Kzero=0.0; dotted–dashed curve, μa0=0.0175 cm-1, which gives Kzero=0.408 cm-1; filled circles, μa0=0.015 cm-1, which gives Kzero=0.577 cm-1; open circles, μa0=0.0125 cm-1, which gives Kzero=0.707 cm-1; open squares, μa0=0.010 cm-1, which gives Kzero=0.816 cm-1. In all cases n0=n1.

Fig. 2
Fig. 2

Reflected amplitude at z0=1 cm, with ω=0, n0=n1, D0=0.041666 cm, D1=4/5D0=0.033333 cm, μa1=0.025 cm-1, and μa0=0.0175 cm-1, which gives Kzero=0.408 cm-1.

Tables (1)

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Table 1 Values of the Lower Medium Retrieved With Eqs.  (4) and (6) a

Equations (6)

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UR,z=-+AKexpiK·R+iqKzdK,
n12n02U0R,z|z=0-CnD0U0R,zzz=0=U1R,zz=0,
D0U0R,zzz=0=D1U1R,zzz=0,
RK=n02D0qiK1-iCnD1qtK-n12D1qtKn02D0qiK1-iCnD1qtK+n12D1qtK,
TK=2n12D0qiKn02D0qiK1-iCnD1qtK+n12D1qtK,
RK=U˜rK,z0U˜incK,0×expiκ02-K21/2z0-1.

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