Abstract

Low-coherence interferometry is used to measure changes in signal intensity that are dependent on the phase of the light backscattered from particles distributed in dielectric matrices. The measurements provide the unique opportunity to follow the dynamics of the small fraction of scattered light, to 10-10 of the initial intensity, that retains phase characteristics of the incident wave packet. The wave phase effects are manifested in the observed reshaping of backscattered wave packets, the optical-length-dependent degree of phase randomization, and the fluctuation patterns. The experimental results indicate the presence of photon trapping effects. The corresponding data analysis not only allows for an estimation of particle concentration but also provides information on Brownian motion of particles in a liquid and characteristics of particle distribution in size and space.

© 1997 Optical Society of America

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References

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  1. Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.
  2. F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
    [CrossRef]
  3. S. John, “The localization of light,” in Photonic Band Gaps and Localization, C. Soukoulis, ed. (Plenum, New York, 1993), pp. 1–22.
  4. Ping Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).
  5. M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
    [CrossRef]
  6. There are a number of publications in the astrophysical and geophysical literature concerned with the related problem of the phase effects in imaging after double passage through turbulence (random disorder) when the object studied is coherently illuminated. See a review by C. Solomon, “Double passing imaging through turbulence,” in Wave Propagation in Random Media, V. Tatarsky, A. Ishimaru, V. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 200–215.
  7. B. Danielson, C. Whittenberg, “Guided-wave reflectometry with micrometer resolution,” Appl. Opt. 26, 2836–2842 (1987).
    [CrossRef] [PubMed]
  8. H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
    [CrossRef]
  9. K. Takada, A. Himeno, K. Yukimatsu, “Jagged appearance of rayleigh-backscatter signal in ultrahigh-resolution optical time-domain reflectometry based on low-coherence interference,” Opt. Lett. 16, 1433–1438 (1991).
    [CrossRef] [PubMed]
  10. K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
    [CrossRef]
  11. P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in distorted media,” Phys. Rev. Lett. 55, 2696–2699 (1985). This is one of the first experiments in which coherent backscattering was observed in a water suspension of polystyrene microspheres.
    [CrossRef] [PubMed]
  12. P. Shelley, K. Booksh, L. Burgess, B. Kowalski, “Polymer film thickness determination with a high-precision scanning reflectometer,” Appl. Spectrosc. 50, 119–125 (1996).
    [CrossRef]
  13. H. Chou, W. V. Sorin, “High-resolution and high-sensitivity optical reflection measurements using white light interferometry,” Hewlett-Packard J.52–59 (February1993).
  14. It is possible that IDUT(t) in some intervals of t is not a self-averaging quantity and obeys the log-normal or even a log–log-normal distribution law as in the case of electron reflectance in disordered media. See I. Lifshits, S. Gredeskul, L. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), pp. 447–455.
  15. B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
    [CrossRef]
  16. S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [CrossRef] [PubMed]

1996 (3)

M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

P. Shelley, K. Booksh, L. Burgess, B. Kowalski, “Polymer film thickness determination with a high-precision scanning reflectometer,” Appl. Spectrosc. 50, 119–125 (1996).
[CrossRef]

B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
[CrossRef]

1993 (1)

H. Chou, W. V. Sorin, “High-resolution and high-sensitivity optical reflection measurements using white light interferometry,” Hewlett-Packard J.52–59 (February1993).

1992 (2)

K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
[CrossRef]

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

1991 (1)

1988 (2)

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

1987 (1)

1985 (1)

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in distorted media,” Phys. Rev. Lett. 55, 2696–2699 (1985). This is one of the first experiments in which coherent backscattering was observed in a water suspension of polystyrene microspheres.
[CrossRef] [PubMed]

Anderson, B.

B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
[CrossRef]

Barabanenkov, Y. N.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.

Booksh, K.

Brodsky, A.

B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
[CrossRef]

Burgess, L.

B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
[CrossRef]

P. Shelley, K. Booksh, L. Burgess, B. Kowalski, “Polymer film thickness determination with a high-precision scanning reflectometer,” Appl. Spectrosc. 50, 119–125 (1996).
[CrossRef]

Chou, H.

H. Chou, W. V. Sorin, “High-resolution and high-sensitivity optical reflection measurements using white light interferometry,” Hewlett-Packard J.52–59 (February1993).

Danielson, B.

Feng, S.

F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Freud, F.

F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

Furukawa, S.

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

Gredeskul, S.

It is possible that IDUT(t) in some intervals of t is not a self-averaging quantity and obeys the log-normal or even a log–log-normal distribution law as in the case of electron reflectance in disordered media. See I. Lifshits, S. Gredeskul, L. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), pp. 447–455.

Himeno, A.

Horiguchi, T.

K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
[CrossRef]

Izumita, H.

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

John, S.

S. John, “The localization of light,” in Photonic Band Gaps and Localization, C. Soukoulis, ed. (Plenum, New York, 1993), pp. 1–22.

Kame, C.

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Kowalski, B.

Koyamada, Y.

K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
[CrossRef]

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

Kravtsov, Y. A.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.

Lee, R.

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Lifshits, I.

It is possible that IDUT(t) in some intervals of t is not a self-averaging quantity and obeys the log-normal or even a log–log-normal distribution law as in the case of electron reflectance in disordered media. See I. Lifshits, S. Gredeskul, L. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), pp. 447–455.

Maret, G.

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in distorted media,” Phys. Rev. Lett. 55, 2696–2699 (1985). This is one of the first experiments in which coherent backscattering was observed in a water suspension of polystyrene microspheres.
[CrossRef] [PubMed]

Mostowski, J.

M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Orlowski, A.

M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Ozrin, V. D.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.

Pastur, L.

It is possible that IDUT(t) in some intervals of t is not a self-averaging quantity and obeys the log-normal or even a log–log-normal distribution law as in the case of electron reflectance in disordered media. See I. Lifshits, S. Gredeskul, L. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), pp. 447–455.

Rosenbluh, M.

F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

Ruzek, M.

M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

Saichev, A. I.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.

Sankawa, I.

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

Shelley, P.

Sheng, Ping

Ping Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).

Shimizu, K.

K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
[CrossRef]

Solomon, C.

There are a number of publications in the astrophysical and geophysical literature concerned with the related problem of the phase effects in imaging after double passage through turbulence (random disorder) when the object studied is coherently illuminated. See a review by C. Solomon, “Double passing imaging through turbulence,” in Wave Propagation in Random Media, V. Tatarsky, A. Ishimaru, V. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 200–215.

Sorin, W. V.

H. Chou, W. V. Sorin, “High-resolution and high-sensitivity optical reflection measurements using white light interferometry,” Hewlett-Packard J.52–59 (February1993).

Stone, A.

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Takada, K.

Whittenberg, C.

Wolf, P. E.

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in distorted media,” Phys. Rev. Lett. 55, 2696–2699 (1985). This is one of the first experiments in which coherent backscattering was observed in a water suspension of polystyrene microspheres.
[CrossRef] [PubMed]

Yukimatsu, K.

Appl. Opt. (1)

Appl. Spectrosc. (1)

Hewlett-Packard J. (1)

H. Chou, W. V. Sorin, “High-resolution and high-sensitivity optical reflection measurements using white light interferometry,” Hewlett-Packard J.52–59 (February1993).

IEEE Photon. Technol. Lett. (1)

H. Izumita, S. Furukawa, Y. Koyamada, I. Sankawa, “Fading noise reduction in coherent OTDR,” IEEE Photon. Technol. Lett. 4, 201–203 (1992).
[CrossRef]

J. Lightwave Technol. (1)

K. Shimizu, T. Horiguchi, Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurements for optical fibers and components,” J. Lightwave Technol. 10, 982–989 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (2)

M. Ruzek, A. Orlowski, J. Mostowski, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122–4130 (1996).
[CrossRef]

B. Anderson, A. Brodsky, L. Burgess, “Threshold effects in light scattering from a binary diffraction grating,” Phys. Rev. E 54, 912–923 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

S. Feng, C. Kame, R. Lee, A. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

F. Freud, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988);M. Tomita, K. Ikouri, “Influence of finite coherence length of incoming light on enhanced backscattering,” Phys. Rev. B 43, 3716–3719 (1991);A. McGuan, A. Muradudin, “Intensity correlation function for light elastically scattered from a randomly rough metallic grating,” Phys. Rev. B 39, 13160–13169 (1989);W. Sorin, D. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in distorted media,” Phys. Rev. Lett. 55, 2696–2699 (1985). This is one of the first experiments in which coherent backscattering was observed in a water suspension of polystyrene microspheres.
[CrossRef] [PubMed]

Other (5)

S. John, “The localization of light,” in Photonic Band Gaps and Localization, C. Soukoulis, ed. (Plenum, New York, 1993), pp. 1–22.

Ping Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).

There are a number of publications in the astrophysical and geophysical literature concerned with the related problem of the phase effects in imaging after double passage through turbulence (random disorder) when the object studied is coherently illuminated. See a review by C. Solomon, “Double passing imaging through turbulence,” in Wave Propagation in Random Media, V. Tatarsky, A. Ishimaru, V. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 200–215.

It is possible that IDUT(t) in some intervals of t is not a self-averaging quantity and obeys the log-normal or even a log–log-normal distribution law as in the case of electron reflectance in disordered media. See I. Lifshits, S. Gredeskul, L. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), pp. 447–455.

Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 67–190.

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Figures (5)

Fig. 1
Fig. 1

Block diagram of the Hewlett-Packard 8504A optical low-coherence reflectometer.  

Fig. 2
Fig. 2

Particle size distributions in the 3% FS-in-PDMS solutions as measured by the Coulter method with the percent of each particle size normalized to 100% in each graph: a, low-attrition mixing; b, medium-attrition mixing; c, high-attrition mixing.

Fig. 3
Fig. 3

Three different positions in the sample with 3% FS in PDMS with high-attrition mixing. In this and the following figures the y axis is the log of the ratio of measured intensity to incident intensity. The zero time t=0 corresponds to the reflection from the probe–media interface.

Fig. 4
Fig. 4

(i) Dependence of signal on attrition mixing. All profiles are of 3% FS in PDMS. The bold curves represent the empirical fit given by Eq. (5): a, low-attrition mixing; b, medium-attrition mixing. (ii) Dependence of signal on attrition mixing. The profile is of 3% FS in PDMS. The bold curve represents the empirical fit given by Eq. (5): c, high-attrition mixing. (iii) Dependence of signal on FS concentration in PDMS. All three profiles are with medium-attrition mixing. The bold curves represent the empirical fit given by Eq. (5): d, 1% FS in PDMS; b, 3% FS in PDMS; e, 10% FS in PDMS.

Fig. 5
Fig. 5

2.5% by weight polystyrene microspheres in deionized water.

Tables (3)

Tables Icon

Table 1 Dependence of 1/τ2 and 1/τ3 [Given in Eq. (5)] on Concentration of FS in PDMS for a Medium Degree of Mixing

Tables Icon

Table 2 Dependence of 1/τ2 and 1/τ3 [Given in Eq. (5)] on the PMS Particle Size for 2.5% Solids in Deionized Water

Tables Icon

Table 3 Dependence of 1/τ2 and 1/τ3 [Given in Eq. (5)] on the Degree of Mixing of FS in PDMS for a 3% FS Concentration

Equations (8)

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

ID=Rd(Iref+IDUT+2IrefIDUT cos Δϕ),
P[IDUT(t)-IDUT¯(t)]
=12πS(t) exp-{[IDUT(t)-IDUT¯(t)]2/S(t)2},
IDUT=Idev+I0[(1-a)exp(-t/τ2)+a exp(-t/τ3)]fort>t1,
τ2τ3,a<1.
log IDUT=log Idev+log[A2 exp(-t/τ2)+A3 exp(-t/τ3+1)],
A2=I0(1-a)/Idev,A3=I0a/Idev.
qn2=(ω) ω2c2-q2<˜0,

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