## Dynamic light scattering optical coherence tomography |

Optics Express, Vol. 20, Issue 20, pp. 22262-22277 (2012)

http://dx.doi.org/10.1364/OE.20.022262

Acrobat PDF (1289 KB)

### Abstract

We introduce an integration of dynamic light scattering (DLS) and optical coherence tomography (OCT) for high-resolution 3D imaging of heterogeneous diffusion and flow. DLS analyzes fluctuations in light scattered by particles to measure diffusion or flow of the particles, and OCT uses coherence gating to collect light only scattered from a small volume for high-resolution structural imaging. Therefore, the integration of DLS and OCT enables high-resolution 3D imaging of diffusion and flow. We derived a theory under the assumption that static and moving particles are mixed within the OCT resolution volume and the moving particles can exhibit either diffusive or translational motion. Based on this theory, we developed a fitting algorithm to estimate dynamic parameters including the axial and transverse velocities and the diffusion coefficient. We validated DLS-OCT measurements of diffusion and flow through numerical simulations and phantom experiments. As an example application, we performed DLS-OCT imaging of the living animal brain, resulting in 3D maps of the absolute and axial velocities, the diffusion coefficient, and the coefficient of determination.

© 2012 OSA

## 1. Introduction

1. N. A. Clark, J. H. Lunacek, and G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. **38**(5), 575–585 (1970). [CrossRef]

3. D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A **14**(1), 192–215 (1997). [CrossRef]

4. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science **254**(5035), 1178–1181 (1991). [CrossRef] [PubMed]

6. Y. Chen, L. N. Vuong, J. Liu, J. Ho, V. J. Srinivasan, I. Gorczynska, A. J. Witkin, J. S. Duker, J. Schuman, and J. G. Fujimoto, “Three-dimensional ultrahigh resolution optical coherence tomography imaging of age-related macular degeneration,” Opt. Express **17**(5), 4046–4060 (2009). [CrossRef] [PubMed]

## 2. Materials and methods

### 2.1 Spectral-domain optical coherence tomography system

13. J. Lee, V. Srinivasan, H. Radhakrishnan, and D. A. Boas, “Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex,” Opt. Express **19**(22), 21258–21270 (2011). [CrossRef] [PubMed]

14. J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. **28**(21), 2067–2069 (2003). [CrossRef] [PubMed]

15. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express **11**(8), 889–894 (2003). [CrossRef] [PubMed]

### 2.2 Animal preparation

13. J. Lee, V. Srinivasan, H. Radhakrishnan, and D. A. Boas, “Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex,” Opt. Express **19**(22), 21258–21270 (2011). [CrossRef] [PubMed]

## 3. Results

### 3.1 DLS-OCT theory

*z*

_{1}(

*t*) along the z axis with respect to the center of the voxel:where the amplitude

*R*

_{01}is proportional to the field reflectivity of the particle. The other quantities are defined in Table 1 . The spectral width of the light source Δ

*q*determines the axial length of the coherence gating of SD-OCT (i.e. the Gaussian function in the magnitude of Eq. (1)). The transverse resolution is generally determined by the objective lens used in the focusing optics. Therefore, the signal from a particle moving in the three-dimensional space is

*h*=

_{t}*h*) for simplicity. The OCT signal from the voxel iswhere

*N*

_{Ω}is the number of Ω-type particles in the voxel (Ω = S, F, or E). Here, the

*r*(

_{Ej}*t*) and

*z*(

_{Ej}*t*) will randomly vary by the definition of the E-particles. Again, we assumed

*w*(

*t*) is complex-valued white noise. In practice, the third term may include stochastic fluctuations in the OCT signal due to imperfections of the OCT system.

*M*) is the center of rotation, and

_{S}*M*is the initial amplitude of rotation. The speed of rotation is determined by the axial velocity-dependent phase term (

_{F}7. R. V. Edwards, J. C. Angus, and M. J. French, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. **42**(2), 837–850 (1971). [CrossRef]

9. T. W. Taylor and C. M. Sorensen, “Gaussian beam effects on the photon correlation spectrum from a flowing Brownian motion system,” Appl. Opt. **25**(14), 2421–2426 (1986). [CrossRef] [PubMed]

12. A. B. Leung, K. I. Suh, and R. R. Ansari, “Particle-size and velocity measurements in flowing conditions using dynamic light scattering,” Appl. Opt. **45**(10), 2186–2190 (2006). [CrossRef] [PubMed]

*M*and

_{S}*M*) do not vary during a short correlation time (e.g., 0.5 ms in this study).

_{F}### 3.2 Fitting algorithm

*M*,

_{S}*M*,

_{F}*v*,

_{t}*v*, and

_{z}*D*) such that they minimize the sum of squared residuals (i.e., maximizing the coefficient of determination,

*R*

^{2}):

17. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” Siam J Optimiz **9**(1), 112–147 (1998). [CrossRef]

*D*,

*v*and

_{z}*v*directly in the least square manner given

_{t}*M*and

_{S}*M*:

_{F}*M*-

_{S}*M*)

_{F}*δ*(

*τ*). The radius of rotation |

*g*(

*τ*)-

*M*| was weighted in calculating

_{S}*v*to reduce the contribution of noisy movements of small-radius data points. Also,

_{z}*g*

_{1}(

*τ*) was weighted in calculating

*v*and

_{t}*D*to minimize distortion of the residuals that is caused by applying the logarithm.

*D*was forced to have a positive value.

*M*and

_{S}*M*), searching for the minimum was very sensitive to the initial guess (i.e., there was more than one local minimum). Therefore, our algorithm guesses and tests three different initial guess of

_{F}*M*and

_{S}*M*.

_{F}*M*and

_{S}*M*, an initial estimation of 1-

_{F}*M*-

_{S}*M*=

_{F}*M*was helpful.

_{E}*M*was simply estimated from the first three non-zero timelag data under the assumption that the first four data points can be approximated to a second-order polynomial. That is,where

_{E}*τ*=

_{k}*k*Δ

*τ*is the k-th timelag.

*M*was forced to have a value between zero and one.

_{E}*M*, the center of rotation was used. We derived an equation to find the center of rotation (

_{S}*A*+

*iB*) in the complex plane for a given set of autocorrelation data points

*g*(

*τ*) =

_{k}*a*+

_{k}*ib*such that the center minimizes the variation in the radius of rotation (i.e., the distance from the center). This equation (Eq. (18)) was used to choose an initial guess of

_{k}*M*as the center of rotation of the latter half of the autocorrelation function. We used only the latter half because the radius of rotation varied largely during the first half of the timelag when flow and/or diffusion were large. The real part of the center of rotation was chosen as the initial guess for

_{S}*M*.

_{S}*k*>

*N*/2 and

_{τ}*N*is the number of autocorrelation data points (i.e., the number of timelag points).

_{τ}*M*was determined by

_{F}*M*= 1-

_{F}*M*-

_{S}*M*. Both

_{E}*M*and

_{S}*M*were forced to have a value between zero and one.

_{F}*M*and

_{S}*M*, a mesh of

_{F}*M*and

_{S}*M*was tested. For each pair of

_{F}*M*and

_{S}*M*in the mesh grid,

_{F}*D*,

*v*and

_{z}*v*were determined (Eq. (16)) and then

_{t}*R*

^{2}was calculated (Eq. (15)). One pair of

*M*and

_{S}*M*was chosen as the second initial guess where it maximizes

_{F}*R*

^{2}. As the third initial guess, we chose a set of typical values that empirically turned out to result in good fitting,

*M*=

_{S}*M*= (1-

_{F}*M*)/2.

_{E}*M*and

_{S}*M*minimizing the sum of squared residuals, where

_{F}*D*,

*v*and

_{z}*v*were directly determined from

_{t}*M*and

_{S}*M*during each iteration (Eq. (16)). This process resulted in three sets of

_{F}*M*,

_{S}*M*,

_{F}*D*,

*v*and

_{z}*v*. We chose the one with the maximum

_{t}*R*

^{2}. A diagram summarizing our fitting algorithm is presented in Fig. 3 .

### 3.3 Validation through numerical simulation

*t*= 20 μs) for various parameter values (Table 2 ). Position data were used to generate SD-OCT signals, and autocorrelation data were obtained from the signals. The autocorrelation data were fit using the algorithm described in the above section, leading to the estimation of the dynamic parameters.

*D*,

*v*, and

*v*) multiplied by

_{z}*M*, because a small

_{F}*M*in practice can make the estimation result in unreasonably large diffusion coefficient or velocities. Since

_{F}*M*is dimensionless,

_{F}*M*and

_{F}D*M*have the units of μm

_{F}v^{2}/s and mm/s, respectively. As a result, the absolute velocity and the axial velocity were estimated close to the true values (Fig. 6(b)). In addition, the diffusion coefficient was estimated negligible (0.20 ± 0.27 μm

^{2}/s). These results verify that the field autocorrelation function of the OCT signal numerically obtained from the position data of flowing particles exhibits the behavior that our theory predicts and thus the flow velocity can be accurately estimated by fitting the model of Eq. (14) to data.

18. P. Abry and F. Sellan, “The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: remarks and fast implementation,” Appl. Comput. Harmon. Anal. **3**(4), 377–383 (1996). [CrossRef]

*M*-weighted diffusion coefficient was estimated close to the true values (Fig. 7(b)). In this simulation, the absolute velocity was estimated negligible (0.24 ± 0.47 mm/s).

_{F}*M*-term (Fig. 7(c)) as predicted in Eq. (14).

_{F}### 3.4 Validation through phantom experiment

*g*(

*x*,

*z*,

*τ*). The autocorrelation function was averaged over neighboring 3 × 3 voxels and then was used to estimate the dynamic parameters, leading to 2D maps of

*M*(

_{S}*x*,

*z*),

*M*(

_{F}*x*,

*z*),

*D*(

*x*,

*z*),

*v*(

_{z}*x*,

*z*),

*v*(

_{t}*x*,

*z*), and

*R*

^{2}(

*x*,

*z*), where

*R*

^{2}is the coefficient of determination (Eq. (15)). The values of a bad-fitting voxel (

*R*

^{2}<0.5) were replaced with the mean value of the neighboring good-fitting voxels. As noise can result in a small

*M*and large

_{F}*v*or

*D*, the velocity and diffusion maps were weighted by

*M*while

_{F}*M*smaller than 0.1 was forced to zero. Then, each map of the dynamic parameters was convolved with a 2D Gaussian kernel (10 μm in diameter). As a result, the absolute and axial velocities were reliably measured across various true velocities and flow angles (Fig. 8(a) ). Microsphere samples of 0.1 and 1 μm in diameter were used for validation of the diffusion measurement, where the measured diffusion coefficient agreed with the theoretical values given by the Einstein-Stokes equation (Fig. 8(b)). For this phantom experiment, monodisperse polystyrene microspheres in 2.5% solids (w/v) aqueous suspension (Polysciences, Inc.) were used.

_{F}### 3.5 DLS-OCT imaging of the rodent brain

*x*×

*y*×

*z*) of the cortical surface. This FOV consisted of 400 × 400 positions, leading to the scanning step size of 1.5 μm and a total scanning time of ~10 min. We chose 100 A-scans per position because our fitting algorithm worked well when the autocorrelation function data had ≥25 time points, and the measurement time of ~2 ms corresponding to 100 A-scans was sufficiently shorter than the characteristic time constants of the primary sources of motion artifacts (i.e., cardiac and respiratory motions) as revealed in our previous study [13

13. J. Lee, V. Srinivasan, H. Radhakrishnan, and D. A. Boas, “Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex,” Opt. Express **19**(22), 21258–21270 (2011). [CrossRef] [PubMed]

*R*

^{2}). This processing took ~3 hours with our 200-core parallel processing cluster system.

*R*

^{2}. At the circular cross-sections of the vessels (Fig. 9(c), blue arrows), high-velocity and high-

*R*

^{2}blood flow are surrounded by the high-diffusion, low-velocity, and low-

*R*

^{2}dynamics of the vessel boundaries. In particular, the low

*R*

^{2}means that the motion was neither translational nor diffusive; we hypothesize that it might be oscillatory due to the interaction between blood flow and the tension of vessel walls. As can be seen in the examples of the autocorrelation functions (Fig. 9(d)), the composition ratio of static particles (

*M*; the center of rotation in the complex plane) increased as the voxel is located far from the center of the vessel. When the voxel is located at the vessel boundary, it exhibited the characteristic dynamics with a low

_{S}*R*

^{2}(i.e., bad fitting). As the present paper focuses on describing this new technique, a detailed interpretation of the brain imaging data will be described elsewhere.

## 4. Discussion

19. M. D. Stern, “In vivo evaluation of microcirculation by coherent light scattering,” Nature **254**(5495), 56–58 (1975). [CrossRef] [PubMed]

20. U. Dirnagl, B. Kaplan, M. Jacewicz, and W. Pulsinelli, “Continuous measurement of cerebral cortical blood flow by laser-Doppler flowmetry in a rat stroke model,” J. Cereb. Blood Flow Metab. **9**(5), 589–596 (1989). [CrossRef] [PubMed]

21. B. M. Ances, J. H. Greenberg, and J. A. Detre, “Laser Doppler imaging of activation-flow coupling in the rat somatosensory cortex,” Neuroimage **10**(6), 716–723 (1999). [CrossRef] [PubMed]

22. J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, “In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. **22**(18), 1439–1441 (1997). [CrossRef] [PubMed]

*R*

^{2}and

*M*). The

_{F}*R*

^{2}map quantitatively images the degree of how much the motion is close to translational or diffusive ones; and for example it clearly revealed characteristic dynamics of the vessel boundaries. The

*M*map will quantify the fraction of moving particles in each voxel, which is similar to the mobile fraction suggested in non-ergodic DLS studies [10

_{F}10. P. N. Pusey and W. Van Megen, “Dynamic light scattering by non-ergodic media,” Physica A **157**(2), 705–741 (1989). [CrossRef]

11. J. G. H. Joosten, E. T. F. Geladé, and P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A **42**(4), 2161–2175 (1990). [CrossRef] [PubMed]

7. R. V. Edwards, J. C. Angus, and M. J. French, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. **42**(2), 837–850 (1971). [CrossRef]

9. T. W. Taylor and C. M. Sorensen, “Gaussian beam effects on the photon correlation spectrum from a flowing Brownian motion system,” Appl. Opt. **25**(14), 2421–2426 (1986). [CrossRef] [PubMed]

10. P. N. Pusey and W. Van Megen, “Dynamic light scattering by non-ergodic media,” Physica A **157**(2), 705–741 (1989). [CrossRef]

11. J. G. H. Joosten, E. T. F. Geladé, and P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A **42**(4), 2161–2175 (1990). [CrossRef] [PubMed]

12. A. B. Leung, K. I. Suh, and R. R. Ansari, “Particle-size and velocity measurements in flowing conditions using dynamic light scattering,” Appl. Opt. **45**(10), 2186–2190 (2006). [CrossRef] [PubMed]

*M*and

_{S}*M*) do not vary during the measurement time. The validity of this assumption will depend on the measurement time and the magnitude of dynamics within a sample. For example, the assumption was reasonable when imaging blood flow of the brain with the measurement time of ~2 ms, because the blood flow velocity is typically 1-5 mm/s and thus leads to 2-10 μm displacement during the measurement time, smaller than or approximately comparable to the resolution volume. When we used a longer measurement time (200 ms), the autocorrelation function deviated from our model. In contrast, the fitting result was not reliable if only very short correlation times were used. Therefore, the correlation and measurement times for DLS-OCT imaging should be chosen carefully, taking into account both the scale of target dynamics and the fitting performance.

_{F}12. A. B. Leung, K. I. Suh, and R. R. Ansari, “Particle-size and velocity measurements in flowing conditions using dynamic light scattering,” Appl. Opt. **45**(10), 2186–2190 (2006). [CrossRef] [PubMed]

*v*= 0.1 and 1 mm/s approximately correspond to

*D*= 0.004 and 0.4 μm

^{2}/s, respectively. The coupling between diffusion and large flow will not be a critical problem in the studies investigating a sample where diffusion and flow are spatially separated. Meanwhile, considerable caution would be required if one wants to apply the present technique to the measurement of diffusion that is mixed with large flow within the resolution volume. On the other hand, the voxels with large blood flow in vessels often exhibited high diffusion, which can be either a real diffusive motion or decorrelation of the OCT signal that can be quantified by the exponential decay with the diffusion coefficient. This high diffusion in vessels might be attributed to the mixture of non-translational motion of red blood cells including rotation, turbulence in blood flow, and the variance in the velocity distribution within the resolution volume. Since this interpretation has not been yet validated, and since the present study used the DLS-OCT theory for determining whether the motion is translational or not, we overlaid the diffusion map with the velocity map as in Figs. 9(B) and 9(C). This overlay means that our analysis gave priority to flow over diffusion so that diffusion is of interest only at the voxels with low flow. Therefore, the coupling between diffusion and large flow was not an important concern at those vessel boundaries.

23. B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, and P. Lambelet, “Multiple scattering in optical coherence tomography. I. Investigation and modeling,” J. Opt. Soc. Am. A **22**(7), 1369–1379 (2005). [CrossRef] [PubMed]

**19**(22), 21258–21270 (2011). [CrossRef] [PubMed]

*en face*image by including surface vessels as in Fig. 9(b), in the future it will be interesting to derive a DLS-OCT model that considers the effect of multiple scattering.

## 5. Conclusion

*in vivo*imaging of translational blood flow and non-translational motion of the vessel boundary in the living animal brain cortex.

## Acknowledgments

## References and links

1. | N. A. Clark, J. H. Lunacek, and G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. |

2. | D. J. Durian, D. A. Weitz, and D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science |

3. | D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A |

4. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science |

5. | G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science |

6. | Y. Chen, L. N. Vuong, J. Liu, J. Ho, V. J. Srinivasan, I. Gorczynska, A. J. Witkin, J. S. Duker, J. Schuman, and J. G. Fujimoto, “Three-dimensional ultrahigh resolution optical coherence tomography imaging of age-related macular degeneration,” Opt. Express |

7. | R. V. Edwards, J. C. Angus, and M. J. French, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. |

8. | D. P. Chowdhury, C. M. Sorensen, T. W. Taylor, J. F. Merklin, and T. W. Lester, “Application of photon correlation spectroscopy to flowing Brownian motion systems,” Appl. Opt. |

9. | T. W. Taylor and C. M. Sorensen, “Gaussian beam effects on the photon correlation spectrum from a flowing Brownian motion system,” Appl. Opt. |

10. | P. N. Pusey and W. Van Megen, “Dynamic light scattering by non-ergodic media,” Physica A |

11. | J. G. H. Joosten, E. T. F. Geladé, and P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A |

12. | A. B. Leung, K. I. Suh, and R. R. Ansari, “Particle-size and velocity measurements in flowing conditions using dynamic light scattering,” Appl. Opt. |

13. | J. Lee, V. Srinivasan, H. Radhakrishnan, and D. A. Boas, “Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex,” Opt. Express |

14. | J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. |

15. | R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express |

16. | L. Van Hove, “Correlations in space and time and Born approximation scattering in systems of interacting particles,” Phys. Rev. |

17. | J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” Siam J Optimiz |

18. | P. Abry and F. Sellan, “The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: remarks and fast implementation,” Appl. Comput. Harmon. Anal. |

19. | M. D. Stern, “In vivo evaluation of microcirculation by coherent light scattering,” Nature |

20. | U. Dirnagl, B. Kaplan, M. Jacewicz, and W. Pulsinelli, “Continuous measurement of cerebral cortical blood flow by laser-Doppler flowmetry in a rat stroke model,” J. Cereb. Blood Flow Metab. |

21. | B. M. Ances, J. H. Greenberg, and J. A. Detre, “Laser Doppler imaging of activation-flow coupling in the rat somatosensory cortex,” Neuroimage |

22. | J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, “In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. |

23. | B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, and P. Lambelet, “Multiple scattering in optical coherence tomography. I. Investigation and modeling,” J. Opt. Soc. Am. A |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(180.6900) Microscopy : Three-dimensional microscopy

(110.4153) Imaging systems : Motion estimation and optical flow

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: June 15, 2012

Revised Manuscript: August 18, 2012

Manuscript Accepted: August 24, 2012

Published: September 13, 2012

**Virtual Issues**

Vol. 7, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Jonghwan Lee, Weicheng Wu, James Y. Jiang, Bo Zhu, and David A. Boas, "Dynamic light scattering optical coherence tomography," Opt. Express **20**, 22262-22277 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-20-22262

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### References

- N. A. Clark, J. H. Lunacek, and G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys.38(5), 575–585 (1970). [CrossRef]
- D. J. Durian, D. A. Weitz, and D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science252(5006), 686–688 (1991). [CrossRef] [PubMed]
- D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A14(1), 192–215 (1997). [CrossRef]
- D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
- G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science276(5321), 2037–2039 (1997). [CrossRef] [PubMed]
- Y. Chen, L. N. Vuong, J. Liu, J. Ho, V. J. Srinivasan, I. Gorczynska, A. J. Witkin, J. S. Duker, J. Schuman, and J. G. Fujimoto, “Three-dimensional ultrahigh resolution optical coherence tomography imaging of age-related macular degeneration,” Opt. Express17(5), 4046–4060 (2009). [CrossRef] [PubMed]
- R. V. Edwards, J. C. Angus, and M. J. French, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys.42(2), 837–850 (1971). [CrossRef]
- D. P. Chowdhury, C. M. Sorensen, T. W. Taylor, J. F. Merklin, and T. W. Lester, “Application of photon correlation spectroscopy to flowing Brownian motion systems,” Appl. Opt.23(22), 4149–4154 (1984). [CrossRef] [PubMed]
- T. W. Taylor and C. M. Sorensen, “Gaussian beam effects on the photon correlation spectrum from a flowing Brownian motion system,” Appl. Opt.25(14), 2421–2426 (1986). [CrossRef] [PubMed]
- P. N. Pusey and W. Van Megen, “Dynamic light scattering by non-ergodic media,” Physica A157(2), 705–741 (1989). [CrossRef]
- J. G. H. Joosten, E. T. F. Geladé, and P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A42(4), 2161–2175 (1990). [CrossRef] [PubMed]
- A. B. Leung, K. I. Suh, and R. R. Ansari, “Particle-size and velocity measurements in flowing conditions using dynamic light scattering,” Appl. Opt.45(10), 2186–2190 (2006). [CrossRef] [PubMed]
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