OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 8 — Aug. 10, 2007
« Show journal navigation

Quantification of optical Doppler broadening and optical path lengths of multiply scattered light by phase modulated low coherence interferometry

B. Varghese, V. Rajan, T. G. van Leeuwen, and W. Steenbergen  »View Author Affiliations


Optics Express, Vol. 15, Issue 15, pp. 9157-9165 (2007)
http://dx.doi.org/10.1364/OE.15.009157


View Full Text Article

Acrobat PDF (143 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show experimental validation of a novel technique to measure optical path length distributions and path length resolved Doppler broadening in turbid media for different reduced scattering coefficients and anisotropies. The technique involves a phase modulated low coherence Mach-Zehnder interferometer, with separate fibers for illumination and detection. Water suspensions of Polystyrene microspheres with high scattering and low absorption levels are used as calibrated scattering phantoms. The path length dependent diffusion broadening or Doppler broadening of scattered light is shown to agree with Diffusive Wave Spectroscopy within 5%. The optical path lengths are determined experimentally from the zero order moment of the phase modulation peak around the modulation frequency in the power spectrum and the results are validated with Monte Carlo simulations.

© 2007 Optical Society of America

1. Introduction

In turbid media, photons follow different trajectories and reach different depths. This complicates the noninvasive diagnosis of tissue with light. For example, in laser Doppler blood perfusion monitors (LDPM), the coherent light delivered into the tissue interacts with static as well as moving scatterers, e.g. red blood cells and it records values averaged over different and basically unknown path lengths. This creates an uncertainty in the relation between the measured perfusion signal and the real perfusion [1

1. A. P. Shepherd and P.Å Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, 1990).

]. A longer path length will increase the probability that a Doppler shift will occur, thus yielding an overestimation of the blood perfusion, compared to the short path length situation. The distance between illumination and detection fibers also influences the perfusion signal and for large distances the average path length followed by the detected photons through the tissue increases and therefore a larger Doppler shift will be detected [2

2. A. Liebert, M. Leahy, and R. Maniewski, “Multichannel laser-Doppler probe for blood perfusion measurements with depth discrimination,” Med. Bio. Eng. Comp 36, 740–747 (1998). [CrossRef]

, 3

3. F. Morales, R. Graaff, A. J. Smit, R. Gush, and G. Rakhorst, “The influence of probe fibre distance on laser Doppler perfusion monitoring measurements,” Microcirculation 10, 433–441 (2003). [PubMed]

, 4

4. M. Larsson, W. Steenbergen, and T. Strömberg, “Influence of optical properties and fibre separation on laser Doppler flowmetry,” J.Biomed. Opt 7, 236–243 (2001). [CrossRef]

]. Thus detection of multiple scattered light as function of path length in the scattering medium would result in more quantitative and more reliable tissue perfusion information. Another step in more quantified LDPM would be to develop a calibration procedure. For the calibration of LDPM, different calibration models such as mixed static and dynamic media [5

5. A. Liebert, M. Leahy, and R. Maniewski, “A calibration standard for laser-Doppler perfusion measurements,” Rev. Sci. Inst. 66, 5169–5173 (1995). [CrossRef]

], optoelectronic calibration [6

6. A. Liebert, P. Lukasiewicz, D. Boggett, and R. Maniewski, “Optoelectronic standardization of laser Doppler perfusion monitors,” 70, 1352–1354 (1999).

], layered scattering phantom [7

7. W. Steenbergen and F. F. M. de Mul, “New optical tissue phantom and its use for studying laser Doppler blood flowmetry,” Proc. SPIE 3196, 12 (1997). [CrossRef]

] were developed. The present calibration procedure based on motility standard utilizes the Doppler shift imparted by the Brownian motion of polystyrene microspheres in a water suspension. These efforts have been important for the quality assurance of the technique, however the physiological and anatomical complexity of the microcirculation prevents calibration from leading to a more quantified assessment of perfusion. In this study, we pursue quantitative optical Doppler flowmetry by means of path length selectivity.

Path length resolved temporal fluctuations of photon intensity can be measured using amplitude modulation of the light intensity [8

8. E. Gratton and M. Limkerman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J 44, 315–324 (1983). [CrossRef] [PubMed]

], time resolved measurements [9

9. B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, and R. Boretsky, “Comparison of time-resolved and -unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. 85, 4971–4975 (1988). [CrossRef] [PubMed]

] or recently developed low coherence interferometry [10

10. K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998). [CrossRef]

-11

11. A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, “Path-length-resolved dynamic light scattering: modeling the transition from single to diffusive scattering,” Appl. Opt. 40, 4222–4227 (2001). [CrossRef]

]. However, for a spatial resolution of 50 micrometers, time resolved and amplitude modulation techniques require either a temporal resolution of 150 fs or electronics working in the GHz range. For this reason, for optical path lengths of only a few millimeters a low coherence interferometric approach is much more suitable. In low coherence interferometry, a user-positioned coherence gate selects the light that has traveled a known optical path length in the medium to interfere with reference light.

In this manuscript, we show the optical path length distributions and spectral diffusion broadening of multiple scattered light measured for calibrated scattering samples with high scattering and low absorption levels. While in ref.[14

14. B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, “Path length resolved measurements of multiple scattered photons in static and dynamic turbid media using phase modulated low coherence interferometry,” J. Biomed. Opt. 12, 024020 (2007). [CrossRef] [PubMed]

] we validated the measured optical path length distributions using Lambert-Beer’s law on samples with different absorption levels, in this letter we validate with Monte Carlo simulations for optical path length distributions. In addition the path length dependent diffusion broadening or Doppler broadening is validated with Diffusive Wave Spectroscopy.

2. Materials and method

In that preliminary study, we showed that the path length distribution can be measured from the area (the zero order moment M0) of the Doppler broadened interference peak appearing at the modulation frequency in the photodetector signal power spectrum [14

14. B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, “Path length resolved measurements of multiple scattered photons in static and dynamic turbid media using phase modulated low coherence interferometry,” J. Biomed. Opt. 12, 024020 (2007). [CrossRef] [PubMed]

]. Noise correction is performed by subtraction of M0 of the reference arm noise and of the sample arm Doppler signal from M0 of the corresponding total spectra in the frequency range of 20 kHz to 24 kHz around the phase modulation frequency of 22 kHz. The zeroth moment M0 of the noise corrected heterodyne spectrum is proportional to the intensity of photons with a certain optical path length. The average Doppler shift is measured from the full width at half maximum (FWHM) of a Lorentzian fit of the Doppler broadened phase modulation interference peak appearing in the photodetector signal power spectrum, exhibiting diffusion broadening obeying Einstein-Stokes relation.

Diffusive Wave spectroscopy (DWS), which is an extension of conventional dynamic light scattering (DLS) to the limit of multiply scattering media, relies on the diffusion approximation (DA), to describe the diffusive light transport from the intensity autocorrelation of scattered light [15

15. G. Maret and P. E. Wolf, “Multiple light-scattering from disordered media - the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987). [CrossRef]

-19

19. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, Piscataway, 1997).

]. DA has been extensively used in characterizing the dynamical properties of physical and biological media [16

16. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988). [CrossRef] [PubMed]

, 21

21. P. D. Kaplan, M. H. Kap, A.G. Yodh, and D. J. Pine, “Geometric constraints for the design of diffusingwave spectroscopy experiments,” Appl. Opt. 32, 3828 (1993). [PubMed]

, 25

25. K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990). [CrossRef] [PubMed]

]. The accuracy and domain validity of the diffusion approximation [20

20. D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350 (1995). [CrossRef]

-22

22. P. A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498 (1998). [CrossRef]

] has been studied as regards experimental geometries [21

21. P. D. Kaplan, M. H. Kap, A.G. Yodh, and D. J. Pine, “Geometric constraints for the design of diffusingwave spectroscopy experiments,” Appl. Opt. 32, 3828 (1993). [PubMed]

, 23

23. B. B. Das, F. Liu, and R. R. Alfano, Vol. 2 of Trends in optics and photonics, 41–44 (1996).

] and fundamental limits [24

24. I. Freund, M. Kaveh, and M. Rosenbluh, “Dynamic multiple scattering: Ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988). [CrossRef] [PubMed]

-25

25. K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990). [CrossRef] [PubMed]

] and the theory has been extended to describe the crossover between the single scattering and the diffusive regimes [26

26. R. Carminati, R. Elaloufi, and J.J . Greffet, “Beyond the diffusing-wave spectroscopy model for the temporal fluctuations of scattered light,” Phys. Rev. Lett. 92, 213903 (2004). [CrossRef] [PubMed]

].

According to the fluctuation-dissipation theorem, the power spectrum of light that is scattered by a monodisperse suspension of particles undergoing Brownian motion and is heterodyne detected is a Lorentzian distribution,

P(f)=1f0A1+(ff0)2

where A is the amplitude of the power spectrum and f 0 is the linewidth [17

17. P. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

-18

18. R. Pecora, Dynamic light scattering: Applications of photon correlation spectroscopy (Plenum, New York, 1985).

]. According to DWS theory, in the case of diffusive scattering, the power spectrum of diffusive light that is heterodyne detected is Lorentzian and the linewidth, πf 0=k 2 DB L(1−g)/l depends on the on the self-diffusion coefficient, (DB=KBT/3πηa) of the particles in Brownian motion [10

10. K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998). [CrossRef]

]. Here k is the wave number in the scattering medium, l is the photon mean free scattering path, g=<cosθ> is the scattering anisotropy of the medium, L is the geometrical photon path length (Optical path length/refractive index of water), KB is the Boltzmann constant, T is the temperature (293 K), η is the viscosity of the suspending liquid [η=1.0 cps for water] and a is the hydrodynamic diameter (∅0.20 and ∅0.77 µm) of the scattering particles [11

11. A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, “Path-length-resolved dynamic light scattering: modeling the transition from single to diffusive scattering,” Appl. Opt. 40, 4222–4227 (2001). [CrossRef]

,28

28. A. G. Yodh, P. D, Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,“Phys. Rev. B 42, 4744 (1990). [CrossRef]

]. Water suspensions of Polystyrene microspheres (Polysciences Inc) with diameters of ∅0.20 µm (anisotropy factor, g=0.18) and ∅0.77 µm (g=0.85) are used to make calibrated scattering phantoms. Samples with reduced scattering coefficients (µs′) of 7.00 (g=0.85), 4.95 and 3.25 mm-1 (g=0.18) and absorption coefficient (µa) of 0.001 mm-1, are made from each particle suspension, based on scattering cross sections following from Mie theory calculations, taking into account the wavelength of the laser light of 832 nm and the refractive index of water. This corresponds to photon mean free scattering path of 22, 166 and 252 µm respectively. A cubic glass cuvette (20*20*20 mm) is used as a sample holder. We have used samples with high scattering and low absorption levels so that the medium’s absorption is negligible compared to its scattering level and the propagation of the multiply scattered photons can be described as a diffusion process. This gives DWS maximum possible validity, even for short optical path lengths in our measurements. In DWS measurements, a thick slab of a random medium with sample thickness much greater than the transport mean free path l* is used so that the number of scattering events is large and the diffusive transport criteria is satisfied. For smaller thickness, the failure of diffusion theory predictions has been observed experimentally [21

21. P. D. Kaplan, M. H. Kap, A.G. Yodh, and D. J. Pine, “Geometric constraints for the design of diffusingwave spectroscopy experiments,” Appl. Opt. 32, 3828 (1993). [PubMed]

, 22

22. P. A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498 (1998). [CrossRef]

, 25

25. K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990). [CrossRef] [PubMed]

].

To verify our path length resolved measurements, we have performed Monte Carlo simulations to predict the optical path length distributions [27

27. F. F. M. de Mul, M. H. Koelink, M. L. Kok, P. J. Harmsma, J. Greve, R. Graaff, and J. G. Aarnoudse, “Laser Doppler velocimetry and Monte Carlo simulations on models for blood perfusion in tissue,” Appl. Opt. 34, 6595–6611 (1995). [CrossRef] [PubMed]

]. A two-layer system is defined in which light (λ=832nm) from a fiber with a diameter of 100 µm is randomly scattered in a layer of water suspension of polystyrene micro spheres (µa=0.001 mm-1) with a thickness equal to that of the cuvette (20 mm). Since the scattering properties and the particle number density of calibrated polystyrene sphere suspensions as used in this study are well known, it is possible to exactly mimic these properties in simulations. The parameters used for the scattering samples are refractive index, 1.33; absorption coefficient, 0.001 mm-1; Henyey–Greenstein scattering function, g=0.18 (∅0.20 µm) and g=0.85 (∅0.77), reduced scattering coefficients (µs) of 7.00 (g=0.85), 4.95 and 3.25 mm-1 (g=0.18). The second layer is defined with a high absorption (µa=10 mm-1) in order to avoid the possible long path length photons that may penetrate beyond the first layer. But we estimated from the statistics of the maximum scattering depth of Monte Carlo simulated detected photons that there are no photons reaching a depth beyond 10 mm in a scattering sample with lowest scattering level. So in this case there is no influence of highly absorbing second layer on the detected photons. Both the fibers are defined inside the scattering sample. In all simulations, 100000 photons are injected into the sample, and each photon returning to the detection fiber (fiber diameter=100 µm, fiber separation=300 µm, NA=0.29) is assumed to be detected, and its optical path length is recorded.

3. Results and discussion

Typical phase modulation peaks appearing in the power spectra measured in our experiments for ∅0.20 µm and ∅0.77 µm microspheres for different reduced scattering coefficients (7.00, 4.95 and 3.25 mm-1) and at two geometrical photon path lengths (1 and 2 mm) are shown in Fig. 1. The interference peak appearing at the modulation frequency is fitted with a Lorentzian function. The line shape is Lorentzian in all cases and it can be characterized by its amplitude and line width.

The experimental optical path length distributions and simulation results for isotropic and anisotropic scatterers are shown in Figs. 2 and 3, respectively. The results are normalized to the maximum value obtained in the sample with higher scattering coefficient. There is a good agreement between the experimental data (squares and triangles) and the simulation results (solid curve).

Fig. 1. Phase modulation peaks appearing in the photodetector signal power spectrum fitted with Lorentzian functions.
Fig. 2. Measured (points) and Monte Carlo simulated (lines) optical path length distributions for a particle suspension of ∅0.20 µm (g=0.18) for two scattering levels.
Fig. 3. Measured (points) and Monte Carlo simulated (line) optical path length distributions for a particle suspension of ∅0.77 µm (g=0.85).
Fig. 4. Experimental (points) and DWS-predicted (lines) average Doppler shift (FWHM of the Lorentzian fit to the phase modulation peak), vs. optical path length, for a particle suspension of ∅0.20 µm (g=0.18). Inset and lower line in main graph: prediction for single scattering.

Figures 4 and 5 show the measured FWHM of the fitted Lorentzian spectra vs. the optical path length of the multiple scattered light, compared with the predicted linewidth based on Diffusive Wave Spectroscopy. The data points are the experimentally measured Doppler shift and the lines indicate the path length dependent Doppler broadening predicted by Diffusive Wave Spectroscopy. As depicted in Figs. 4 and 5, the average Doppler shift increases with the optical path length and for the suspension with g=0.18 (Fig. 4), the average Doppler shift decreases with a decrease in reduced scattering coefficient. This can be attributed to the decrease in the number of scattering events per unit optical path length. The experimental results are in good agreement with the predictions of DWS for optical path lengths up to 4.5mm. For large optical path lengths, the amplitude of the interference signal is low and an estimation of the line width based on the Lorentzian fit to the spectra results in significant errors. In Figs. 4 and 5, theoretical predictions are given of the linewidth broadening for single scattering as a function of the optical path length, where we used the expression f 0=q 2 DB, with photon momentum transfer q=2k sinθ/2 a function of the scattering angle θ.

Fig. 5. Experimental (points) and DWS-predicted (line) average Doppler shift (FWHM of the Lorentzian fit to the phase modulation peak) vs. optical path length for a particle suspension of ∅0.77 µm (g=0.85).. Inset and lower line in main graph: prediction for single scattering.

4. Conclusion

To summarize, in this manuscript we present path length distributions and path length dependent diffusion broadening of multiple scattered light from turbid media for different reduced scattering coefficients and anisotropies, where the particle dynamics are governed by Brownian motion. The path length dependent diffusion broadening of scattered light showed good agreement with the predictions of Diffusive Wave Spectroscopy. Good agreement between experimental path-length distributions and Monte Carlo simulations were found. Hence, we can use this method to measure optical path lengths and path length resolved Doppler information from general turbid media. The experimental approach presented here is not restricted to the study of Brownian motion or to completely dynamic samples. In an earlier study, we demonstrated that the path length distributions could be obtained from mixed static and dynamic turbid media [14

14. B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, “Path length resolved measurements of multiple scattered photons in static and dynamic turbid media using phase modulated low coherence interferometry,” J. Biomed. Opt. 12, 024020 (2007). [CrossRef] [PubMed]

] and path length resolved Doppler information obtained from the width of the modulation peak can be used to determine the Brownian and translational movement of moving particles within static matrices, such as microcirculatory blood flow in tissue.

Acknowledgments

References and links

1.

A. P. Shepherd and P.Å Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, 1990).

2.

A. Liebert, M. Leahy, and R. Maniewski, “Multichannel laser-Doppler probe for blood perfusion measurements with depth discrimination,” Med. Bio. Eng. Comp 36, 740–747 (1998). [CrossRef]

3.

F. Morales, R. Graaff, A. J. Smit, R. Gush, and G. Rakhorst, “The influence of probe fibre distance on laser Doppler perfusion monitoring measurements,” Microcirculation 10, 433–441 (2003). [PubMed]

4.

M. Larsson, W. Steenbergen, and T. Strömberg, “Influence of optical properties and fibre separation on laser Doppler flowmetry,” J.Biomed. Opt 7, 236–243 (2001). [CrossRef]

5.

A. Liebert, M. Leahy, and R. Maniewski, “A calibration standard for laser-Doppler perfusion measurements,” Rev. Sci. Inst. 66, 5169–5173 (1995). [CrossRef]

6.

A. Liebert, P. Lukasiewicz, D. Boggett, and R. Maniewski, “Optoelectronic standardization of laser Doppler perfusion monitors,” 70, 1352–1354 (1999).

7.

W. Steenbergen and F. F. M. de Mul, “New optical tissue phantom and its use for studying laser Doppler blood flowmetry,” Proc. SPIE 3196, 12 (1997). [CrossRef]

8.

E. Gratton and M. Limkerman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J 44, 315–324 (1983). [CrossRef] [PubMed]

9.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, and R. Boretsky, “Comparison of time-resolved and -unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. 85, 4971–4975 (1988). [CrossRef] [PubMed]

10.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998). [CrossRef]

11.

A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, “Path-length-resolved dynamic light scattering: modeling the transition from single to diffusive scattering,” Appl. Opt. 40, 4222–4227 (2001). [CrossRef]

12.

A. L. Petoukhova, W. Steenbergen, and F F. M. de Mul, “Path-length distribution and path-length resolved Doppler measurements of multiply scattered photons by use of low-coherence interferometer,” Opt. Lett. 26, 1492–1494 (2001). [CrossRef]

13.

A. L. Petoukhova, W. Steenbergen, T. G. van Leeuwen, and F. F. M. de Mul, “Effects of absorption on coherence domain path length resolved dynamic light scattering in the diffuse regime,” Appl. Phys. Lett. 81, 595–597 (2002). [CrossRef]

14.

B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, “Path length resolved measurements of multiple scattered photons in static and dynamic turbid media using phase modulated low coherence interferometry,” J. Biomed. Opt. 12, 024020 (2007). [CrossRef] [PubMed]

15.

G. Maret and P. E. Wolf, “Multiple light-scattering from disordered media - the effect of Brownian motion of scatterers,” Z. Phys. B 65, 409 (1987). [CrossRef]

16.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988). [CrossRef] [PubMed]

17.

P. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

18.

R. Pecora, Dynamic light scattering: Applications of photon correlation spectroscopy (Plenum, New York, 1985).

19.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, Piscataway, 1997).

20.

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350 (1995). [CrossRef]

21.

P. D. Kaplan, M. H. Kap, A.G. Yodh, and D. J. Pine, “Geometric constraints for the design of diffusingwave spectroscopy experiments,” Appl. Opt. 32, 3828 (1993). [PubMed]

22.

P. A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498 (1998). [CrossRef]

23.

B. B. Das, F. Liu, and R. R. Alfano, Vol. 2 of Trends in optics and photonics, 41–44 (1996).

24.

I. Freund, M. Kaveh, and M. Rosenbluh, “Dynamic multiple scattering: Ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988). [CrossRef] [PubMed]

25.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990). [CrossRef] [PubMed]

26.

R. Carminati, R. Elaloufi, and J.J . Greffet, “Beyond the diffusing-wave spectroscopy model for the temporal fluctuations of scattered light,” Phys. Rev. Lett. 92, 213903 (2004). [CrossRef] [PubMed]

27.

F. F. M. de Mul, M. H. Koelink, M. L. Kok, P. J. Harmsma, J. Greve, R. Graaff, and J. G. Aarnoudse, “Laser Doppler velocimetry and Monte Carlo simulations on models for blood perfusion in tissue,” Appl. Opt. 34, 6595–6611 (1995). [CrossRef] [PubMed]

28.

A. G. Yodh, P. D, Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,“Phys. Rev. B 42, 4744 (1990). [CrossRef]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(170.3340) Medical optics and biotechnology : Laser Doppler velocimetry
(170.3890) Medical optics and biotechnology : Medical optics instrumentation
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: March 22, 2007
Revised Manuscript: July 5, 2007
Manuscript Accepted: July 9, 2007
Published: July 11, 2007

Virtual Issues
Vol. 2, Iss. 8 Virtual Journal for Biomedical Optics

Citation
B. Varghese, V. Rajan, T. G. van Leeuwen, and W. Steenbergen, "Quantification of optical Doppler broadening and optical path lengths of multiply scattered light by phase modulated low coherence interferometry," Opt. Express 15, 9157-9165 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-15-9157


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. P. Shepherd and P. Å. Öberg, Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, 1990).
  2. A. Liebert, M. Leahy and R. Maniewski, "Multichannel laser-Doppler probe for blood perfusion measurements with depth discrimination," Med. Bio. Eng. Comp 36, 740-747 (1998). [CrossRef]
  3. F. Morales, R. Graaff, A. J. Smit, R. Gush, and G. Rakhorst, "The influence of probe fibre distance on laser Doppler perfusion monitoring measurements," Microcirculation 10, 433-441 (2003). [PubMed]
  4. M. Larsson, W. Steenbergen, and T. Strömberg, "Influence of optical properties and fibre separation on laser doppler flowmetry," J.Biomed. Opt. 7, 236-243 (2001). [CrossRef]
  5. A. Liebert, M. Leahy and R. Maniewski, "A calibration standard for laser-Doppler perfusion measurements," Rev. Sci. Inst. 66, 5169-5173 (1995). [CrossRef]
  6. A. Liebert, P. Lukasiewicz, D. Boggett and R. Maniewski, "Optoelectronic standardization of laser doppler perfusion monitors," 70, 1352-1354 (1999).
  7. W. Steenbergen and F. F. M. de Mul, "New optical tissue phantom and its use for studying laser Doppler blood flowmetry," Proc. SPIE 3196, 12 (1997). [CrossRef]
  8. E. Gratton and M. Limkerman, "A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution," Biophys. J 44, 315-324 (1983). [CrossRef] [PubMed]
  9. B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, and R. Boretsky, "Comparison of time-resolved and -unresolved measurements of deoxyhemoglobin in brain," Proc. Natl. Acad. Sci. 85, 4971-4975 (1988). [CrossRef] [PubMed]
  10. K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998). [CrossRef]
  11. A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, "Path-length-resolved dynamic light scattering: modeling the transition from single to diffusive scattering," Appl. Opt. 40, 4222-4227 (2001). [CrossRef]
  12. A. L. Petoukhova, W. Steenbergen, and F. F. M. de Mul, "Path-length distribution and path-length resolved Doppler measurements of multiply scattered photons by use of low-coherence interferometer," Opt. Lett. 26, 1492-1494 (2001). [CrossRef]
  13. A. L. Petoukhova, W. Steenbergen, T. G. van Leeuwen and F. F. M. de Mul, "Effects of absorption on coherence domain path length resolved dynamic light scattering in the diffuse regime," Appl. Phys. Lett. 81, 595-597 (2002). [CrossRef]
  14. B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, "Path length resolved measurements of multiple scattered photons in static and dynamic turbid media using phase modulated low coherence interferometry," J. Biomed. Opt. 12, 024020 (2007). [CrossRef] [PubMed]
  15. G. Maret and P. E. Wolf, 'Multiple light-scattering from disordered media - the effect of Brownian motion of scatterers," Z. Phys. B 65, 409 (1987). [CrossRef]
  16. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Diffusing-wave spectroscopy Phys. Rev. Lett. 60, 1134-1137 (1988). [CrossRef] [PubMed]
  17. P. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  18. R. Pecora, Dynamic light scattering: Applications of photon correlation spectroscopy (Plenum, New York, 1985).
  19. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, Piscataway, 1997).
  20. D. J. Durian, "Accuracy of diffusing-wave spectroscopy theories," Phys. Rev. E 51, 3350 (1995). [CrossRef]
  21. P. D. Kaplan, M. H. Kap, A.G. Yodh, and D. J. Pine, "Geometric constraints for the design of diffusing-wave spectroscopy experiments," Appl. Opt. 32, 3828 (1993). [PubMed]
  22. P. A. Lemieux, M. U. Vera, and D. J. Durian, "Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering," Phys. Rev. E 57, 4498 (1998). [CrossRef]
  23. B. B. Das, F. Liu, and R. R. Alfano, Vol. 2 of Trends in Optics and Photonics, 41-44 (1996).
  24. I. Freund, M. Kaveh, and M. Rosenbluh, 'Dynamic multiple scattering: Ballistic photons and the breakdown of the photon-diffusion approximation,' Phys. Rev. Lett. 60, 1130-1133 (1988). [CrossRef] [PubMed]
  25. K. M. Yoo, F. Liu, and R. R. Alfano, "When does the diffusion approximation fail to describe photon transport in random media," Phys. Rev. Lett. 64, 2647-2650 (1990). [CrossRef] [PubMed]
  26. R. Carminati, R. Elaloufi, and J. J. Greffet, "Beyond the diffusing-wave spectroscopy model for the temporal fluctuations of scattered light," Phys. Rev. Lett. 92, 213903 (2004). [CrossRef] [PubMed]
  27. F. F. M. de Mul, M. H. Koelink, M. L. Kok, P. J. Harmsma, J. Greve, R. Graaff, and J. G. Aarnoudse, "Laser doppler velocimetry and Monte Carlo simulations on models for blood perfusion in tissue," Appl. Opt. 34, 6595-6611 (1995). [CrossRef] [PubMed]
  28. A. G. Yodh, P. D, Kaplan, and D. J.Pine, "Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating," Phys. Rev. B 42, 4744 (1990). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited