Abstract

Laser Speckle Imaging (LSI) is a simple, noninvasive technique for rapid imaging of particle motion in scattering media such as biological tissue. LSI is generally used to derive a qualitative index of relative blood flow due to unknown impact from several variables that affect speckle contrast. These variables may include optical absorption and scattering coefficients, multi-layer dynamics including static, non-ergodic regions, and systematic effects such as laser coherence length. In order to account for these effects and move toward quantitative, depth-resolved LSI, we have developed a method that combines Monte Carlo modeling, multi-exposure speckle imaging (MESI), spatial frequency domain imaging (SFDI), and careful instrument calibration. Monte Carlo models were used to generate total and layer-specific fractional momentum transfer distributions. This information was used to predict speckle contrast as a function of exposure time, spatial frequency, layer thickness, and layer dynamics. To verify with experimental data, controlled phantom experiments with characteristic tissue optical properties were performed using a structured light speckle imaging system. Three main geometries were explored: 1) diffusive dynamic layer beneath a static layer, 2) static layer beneath a diffuse dynamic layer, and 3) directed flow (tube) submerged in a dynamic scattering layer. Data fits were performed using the Monte Carlo model, which accurately reconstructed the type of particle flow (diffusive or directed) in each layer, the layer thickness, and absolute flow speeds to within 15% or better.

© 2013 Optical Society of America

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2012 (1)

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

2011 (5)

T. B. Rice, S. D. Konecky, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. Choi, and B. J. Tromberg, “Quantitative determination of dynamical properties using coherent spatial frequency domain imaging,” J. Opt. Soc. Am. A28(10), 2108–2114 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, T. B. Rice, S. A. Carp, A. J. Durkin, D. A. Boas, B. Choi, and B. J. Tromberg, “Laser speckle imaging in the spatial frequency domain,” Biomed. Opt. Express2(6), 1553–1563 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

M. S. Singh, K. Rajan, and R. M. Vasu, “Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis,” J. Appl. Phys.109, 104704 (2011).

2010 (2)

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt.15(1), 011109 (2010).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

2009 (4)

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

P. Zakharov, A. C. Völker, M. T. Wyss, F. Haiss, N. Calcinaghi, C. Zunzunegui, A. Buck, F. Scheffold, and B. Weber, “Dynamic laser speckle imaging of cerebral blood flow,” Opt. Express17(16), 13904–13917 (2009).
[CrossRef] [PubMed]

S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express17(17), 14780–14790 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

2008 (3)

2006 (3)

J. C. Hebden, B. D. Price, A. P. Gibson, and G. Royle, “A soft deformable tissue-equivalent phantom for diffuse optical tomography,” Phys. Med. Biol.51(21), 5581–5590 (2006).
[CrossRef] [PubMed]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.11(4), 041102 (2006).
[CrossRef] [PubMed]

P. Zakharov, A. Völker, A. Buck, B. Weber, and F. Scheffold, “Quantitative modeling of laser speckle imaging,” Opt. Lett.31(23), 3465–3467 (2006).
[CrossRef] [PubMed]

2005 (2)

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett.30(11), 1354–1356 (2005).
[CrossRef] [PubMed]

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

2004 (1)

B. Choi, N. M. Kang, and J. S. Nelson, “Laser speckle imaging for monitoring blood flow dynamics in the in vivo rodent dorsal skin fold model,” Microvasc. Res.68(2), 143–146 (2004).
[CrossRef] [PubMed]

1999 (2)

J. D. Briers, G. Richards, and X. W. He, “Capillary Blood Flow Monitoring Using Laser Speckle Contrast Analysis (LASCA),” J. Biomed. Opt.4(1), 164–175 (1999).
[CrossRef] [PubMed]

P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A16(7), 1651–1664 (1999).
[CrossRef]

1998 (1)

N. Dögnitz and G. Wagnières, “Determination of tissue optical properties by steady-state spatial frequency-domain reflectometry,” Lasers Med. Sci.13, 55–65 (1998).
[CrossRef]

1997 (1)

1995 (2)

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics51(4), 3350–3358 (1995).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio.47(2), 131–146 (1995).
[CrossRef]

1994 (2)

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, and J. G. Aarnoudse, “Laser Doppler blood flowmetry using two wavelengths: Monte Carlo simulations and measurements,” Appl. Opt.33(16), 3549–3558 (1994).
[CrossRef] [PubMed]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

1991 (1)

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter43(7), 5934–5938 (1991).
[CrossRef] [PubMed]

1990 (2)

P. A. Oberg, “Laser-Doppler flowmetry,” Crit. Rev. Biomed. Eng.18(2), 125–163 (1990).
[PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
[CrossRef]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

1987 (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Z. Phys. B Condens. Matter65(4), 409–413 (1987).
[CrossRef]

1981 (1)

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981).
[CrossRef]

1980 (1)

G. E. Nilsson, T. Tenland, and P. A. Oberg, “Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow,” IEEE Trans. Biomed. Eng.27(10), 597–604 (1980).
[CrossRef] [PubMed]

Aarnoudse, J. G.

Ackerson, B. J.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

Ayers, F.

F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical properties in the visible and near infrared domain,” Proc. SPIE 687007 (2008).

Ayers, F. R.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

Bandyopadhyay, R.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

Bearman, G. H.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Bevilacqua, F.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett.30(11), 1354–1356 (2005).
[CrossRef] [PubMed]

Binder, D. K.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Boas, D. A.

Briers, J. D.

J. D. Briers, G. Richards, and X. W. He, “Capillary Blood Flow Monitoring Using Laser Speckle Contrast Analysis (LASCA),” J. Biomed. Opt.4(1), 164–175 (1999).
[CrossRef] [PubMed]

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981).
[CrossRef]

Buck, A.

Calcinaghi, N.

Carp, S. A.

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Choi, B.

Cuccia, D.

Cuccia, D. J.

T. B. Rice, S. D. Konecky, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. Choi, and B. J. Tromberg, “Quantitative determination of dynamical properties using coherent spatial frequency domain imaging,” J. Opt. Soc. Am. A28(10), 2108–2114 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, T. B. Rice, S. A. Carp, A. J. Durkin, D. A. Boas, B. Choi, and B. J. Tromberg, “Laser speckle imaging in the spatial frequency domain,” Biomed. Opt. Express2(6), 1553–1563 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett.30(11), 1354–1356 (2005).
[CrossRef] [PubMed]

F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical properties in the visible and near infrared domain,” Proc. SPIE 687007 (2008).

Dassel, A. C. M.

de Mul, F. F. M.

Dixon, P. K.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

Dögnitz, N.

N. Dögnitz and G. Wagnières, “Determination of tissue optical properties by steady-state spatial frequency-domain reflectometry,” Lasers Med. Sci.13, 55–65 (1998).
[CrossRef]

Dorri-Nowkoorani, F.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

Dougherty, R. L.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

Duncan, D. D.

Dunn, A. K.

Durian, D. J.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A16(7), 1651–1664 (1999).
[CrossRef]

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics51(4), 3350–3358 (1995).
[CrossRef] [PubMed]

Durkin, A. J.

A. Mazhar, D. J. Cuccia, T. B. Rice, S. A. Carp, A. J. Durkin, D. A. Boas, B. Choi, and B. J. Tromberg, “Laser speckle imaging in the spatial frequency domain,” Biomed. Opt. Express2(6), 1553–1563 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

T. B. Rice, S. D. Konecky, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. Choi, and B. J. Tromberg, “Quantitative determination of dynamical properties using coherent spatial frequency domain imaging,” J. Opt. Soc. Am. A28(10), 2108–2114 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express17(17), 14780–14790 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett.30(11), 1354–1356 (2005).
[CrossRef] [PubMed]

F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical properties in the visible and near infrared domain,” Proc. SPIE 687007 (2008).

Fercher, A. F.

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981).
[CrossRef]

Fisher, D. S.

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter43(7), 5934–5938 (1991).
[CrossRef] [PubMed]

Frangioni, J. V.

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

Gibson, A. P.

J. C. Hebden, B. D. Price, A. P. Gibson, and G. Royle, “A soft deformable tissue-equivalent phantom for diffuse optical tomography,” Phys. Med. Biol.51(21), 5581–5590 (2006).
[CrossRef] [PubMed]

Gioux, S.

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

Gittings, A. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

Gopal, A.

Graaff, R.

Grant, A.

F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical properties in the visible and near infrared domain,” Proc. SPIE 687007 (2008).

Greve, J.

Haiss, F.

He, X. W.

J. D. Briers, G. Richards, and X. W. He, “Capillary Blood Flow Monitoring Using Laser Speckle Contrast Analysis (LASCA),” J. Biomed. Opt.4(1), 164–175 (1999).
[CrossRef] [PubMed]

Hebden, J. C.

J. C. Hebden, B. D. Price, A. P. Gibson, and G. Royle, “A soft deformable tissue-equivalent phantom for diffuse optical tomography,” Phys. Med. Biol.51(21), 5581–5590 (2006).
[CrossRef] [PubMed]

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Hsu, M.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio.47(2), 131–146 (1995).
[CrossRef]

Johnson, W. R.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Kang, N. M.

B. Choi, N. M. Kang, and J. S. Nelson, “Laser speckle imaging for monitoring blood flow dynamics in the in vivo rodent dorsal skin fold model,” Microvasc. Res.68(2), 143–146 (2004).
[CrossRef] [PubMed]

Kirkpatrick, S. J.

Koelink, M. H.

Kolste, K.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Konecky, S. D.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

T. B. Rice, S. D. Konecky, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. Choi, and B. J. Tromberg, “Quantitative determination of dynamical properties using coherent spatial frequency domain imaging,” J. Opt. Soc. Am. A28(10), 2108–2114 (2011).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express17(17), 14780–14790 (2009).
[CrossRef] [PubMed]

Kuo, D.

F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical properties in the visible and near infrared domain,” Proc. SPIE 687007 (2008).

Leblond, F.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Lemieux, P. A.

Lin, A.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Maret, G.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Z. Phys. B Condens. Matter65(4), 409–413 (1987).
[CrossRef]

Mazhar, A.

Middleton, A. A.

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B Condens. Matter43(7), 5934–5938 (1991).
[CrossRef] [PubMed]

Nelson, J. S.

B. Choi, N. M. Kang, and J. S. Nelson, “Laser speckle imaging for monitoring blood flow dynamics in the in vivo rodent dorsal skin fold model,” Microvasc. Res.68(2), 143–146 (2004).
[CrossRef] [PubMed]

Nilsson, G. E.

G. E. Nilsson, T. Tenland, and P. A. Oberg, “Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow,” IEEE Trans. Biomed. Eng.27(10), 597–604 (1980).
[CrossRef] [PubMed]

Nobbmann, U.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

Oberg, P. A.

P. A. Oberg, “Laser-Doppler flowmetry,” Crit. Rev. Biomed. Eng.18(2), 125–163 (1990).
[PubMed]

G. E. Nilsson, T. Tenland, and P. A. Oberg, “Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow,” IEEE Trans. Biomed. Eng.27(10), 597–604 (1980).
[CrossRef] [PubMed]

Owen, C. M.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Parthasarathy, A. B.

Patterson, M. S.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.11(4), 041102 (2006).
[CrossRef] [PubMed]

Paulsen, K. D.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Pine, D. J.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Pogue, B. W.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.11(4), 041102 (2006).
[CrossRef] [PubMed]

Price, B. D.

J. C. Hebden, B. D. Price, A. P. Gibson, and G. Royle, “A soft deformable tissue-equivalent phantom for diffuse optical tomography,” Phys. Med. Biol.51(21), 5581–5590 (2006).
[CrossRef] [PubMed]

Rajan, K.

M. S. Singh, K. Rajan, and R. M. Vasu, “Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis,” J. Appl. Phys.109, 104704 (2011).

Reguigui, N. M.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbmann, “Correlation transfer: Development and application,” J. Quantum Spectrosc. Radiative Transf.52(6), 713–727 (1994).
[CrossRef]

Rice, T.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

Rice, T. B.

Richards, G.

J. D. Briers, G. Richards, and X. W. He, “Capillary Blood Flow Monitoring Using Laser Speckle Contrast Analysis (LASCA),” J. Biomed. Opt.4(1), 164–175 (1999).
[CrossRef] [PubMed]

Roberts, D. W.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Royle, G.

J. C. Hebden, B. D. Price, A. P. Gibson, and G. Royle, “A soft deformable tissue-equivalent phantom for diffuse optical tomography,” Phys. Med. Biol.51(21), 5581–5590 (2006).
[CrossRef] [PubMed]

Scheffold, F.

Schotland, J. C.

Singh, M. S.

M. S. Singh, K. Rajan, and R. M. Vasu, “Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis,” J. Appl. Phys.109, 104704 (2011).

Suh, S. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005).
[CrossRef]

Tenland, T.

G. E. Nilsson, T. Tenland, and P. A. Oberg, “Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow,” IEEE Trans. Biomed. Eng.27(10), 597–604 (1980).
[CrossRef] [PubMed]

Tom, W. J.

Tromberg, B. J.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

T. B. Rice, S. D. Konecky, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. Choi, and B. J. Tromberg, “Quantitative determination of dynamical properties using coherent spatial frequency domain imaging,” J. Opt. Soc. Am. A28(10), 2108–2114 (2011).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, T. B. Rice, S. A. Carp, A. J. Durkin, D. A. Boas, B. Choi, and B. J. Tromberg, “Laser speckle imaging in the spatial frequency domain,” Biomed. Opt. Express2(6), 1553–1563 (2011).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express17(17), 14780–14790 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett.30(11), 1354–1356 (2005).
[CrossRef] [PubMed]

Valdés, P. A.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Vasu, R. M.

M. S. Singh, K. Rajan, and R. M. Vasu, “Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis,” J. Appl. Phys.109, 104704 (2011).

Völker, A.

Völker, A. C.

Wagnières, G.

N. Dögnitz and G. Wagnières, “Determination of tissue optical properties by steady-state spatial frequency-domain reflectometry,” Lasers Med. Sci.13, 55–65 (1998).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio.47(2), 131–146 (1995).
[CrossRef]

Wang, R. K.

Weber, B.

Weber, J. R.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

Weitz, D. A.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988).
[CrossRef] [PubMed]

Wells-Gray, E. M.

Wilson, B. C.

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

Wilson, D.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Wolf, P. E.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of brownian motion of scatterers,” Z. Phys. B Condens. Matter65(4), 409–413 (1987).
[CrossRef]

Wyss, M. T.

Yodh, A. G.

Zakharov, P.

Zhang, X.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio.47(2), 131–146 (1995).
[CrossRef]

Zhu, J. X.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
[CrossRef]

Zunzunegui, C.

Appl. Opt. (1)

Biomed. Opt. Express (1)

Comput. Meth. Prog. Bio. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio.47(2), 131–146 (1995).
[CrossRef]

Crit. Rev. Biomed. Eng. (1)

P. A. Oberg, “Laser-Doppler flowmetry,” Crit. Rev. Biomed. Eng.18(2), 125–163 (1990).
[PubMed]

IEEE Trans. Biomed. Eng. (1)

G. E. Nilsson, T. Tenland, and P. A. Oberg, “Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow,” IEEE Trans. Biomed. Eng.27(10), 597–604 (1980).
[CrossRef] [PubMed]

J. Appl. Phys. (2)

M. S. Singh, K. Rajan, and R. M. Vasu, “Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis,” J. Appl. Phys.109, 104704 (2011).

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys.105(10), 102028 (2009).
[CrossRef]

J. Biomed. Opt. (8)

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

S. D. Konecky, T. Rice, A. J. Durkin, and B. J. Tromberg, “Imaging scattering orientation with spatial frequency domain imaging,” J. Biomed. Opt.16(12), 126001 (2011).
[CrossRef] [PubMed]

S. D. Konecky, C. M. Owen, T. Rice, P. A. Valdés, K. Kolste, B. C. Wilson, F. Leblond, D. W. Roberts, K. D. Paulsen, and B. J. Tromberg, “Spatial frequency domain tomography of protoporphyrin IX fluorescence in preclinical glioma models,” J. Biomed. Opt.17(5), 056008 (2012).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt.14(2), 024012 (2009).
[CrossRef] [PubMed]

A. Mazhar, D. J. Cuccia, S. Gioux, A. J. Durkin, J. V. Frangioni, and B. J. Tromberg, “Structured illumination enhances resolution and contrast in thick tissue fluorescence imaging,” J. Biomed. Opt.15(1), 010506 (2010).
[CrossRef] [PubMed]

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt.15(1), 011109 (2010).
[CrossRef] [PubMed]

J. D. Briers, G. Richards, and X. W. He, “Capillary Blood Flow Monitoring Using Laser Speckle Contrast Analysis (LASCA),” J. Biomed. Opt.4(1), 164–175 (1999).
[CrossRef] [PubMed]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.11(4), 041102 (2006).
[CrossRef] [PubMed]

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

J. Phys. (Paris) (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris)51(18), 2101–2127 (1990).
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J. Quantum Spectrosc. Radiative Transf. (1)

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Figures (6)

Fig. 1
Fig. 1

(Left) Experimental setup for laser speckle imaging with structured light. Spatial frequencies are set by the (vertical) distance between the sinusoidal film and divergent laser diode. The film is moved horizontally to change the phase. (Right) Three phantom validation setups to test our models: (1) static layer above dynamic layer, (2) dynamic layer above static layer, and (3) diffusing dynamic layer above flowing dynamic layer.

Fig. 2
Fig. 2

(a) Photon weight probability distribution for total momentum transfer P(Y,f). Dotted lines represent the mean momentum transfer for each spatial frequency. Note the increase in mean momentum transfer with low spatial frequency. Some noise is visible at high spatial frequencies and momentum transfers due to insufficient Monte Carlo sampling, but due to small weights here was found to have insignificant effect on calculated speckle contrast values. (b) Layer-specific fractional momentum transfer P(y|f). Here we see a relatively constant probability among all fractions, up to the abrupt discontinuity highlighted by the dotted rectangle, which represents photons that do not reach the bottom layer. These photons create large non-ergodic effects, which are naturally accounted for using the Monte Carlo method.

Fig. 3
Fig. 3

Validation phantom speckle contrast fits for configurations 1 and 2. Experimental speckle contrast measurements (circles) and subsequent fits (solid line) for five values of thickness d, linearly spaced between 0.7mm (lightest) and 3.0mm (darkest). Notice the drastic difference between the shape of the speckle contrast curve, as low frequencies tend to average both layers, and high frequencies tend toward the dynamics of the top layer.

Fig. 4
Fig. 4

Fitted values V1, V2, d for phantom configurations one (top) and two (bottom). Recovered n values were found to be one in both cases, and thus we define the flow coefficient as six times the Brownian Diffusion Coefficient Db. Multi-layer fits for dynamic phantom Db (circles) and static phantom (squares) are shown alongside blind single layer fits (x’s) and expected values (solid and dashed lines). Blind fits can be seen to vary significantly, over two orders of magnitude in some cases, from expected values. Notice the effective zero line (dashed) depends on layer thickness and depends heavily on the phantom geometry. Depth fits generally underestimate true values by a small margin.

Fig. 5
Fig. 5

Experimental speckle contrast image for DC spatial frequency (0 mm−1), and representative ROI for “homogenous” regions (left). The region appears uniform but is actually highly dependent on tube velocity for low spatial frequencies, as shown in the plot (right). Here, the DC frequency (x’s) varies by as much as 13% from a truly homogenous sample. The AC (circles) spatial frequency (0.12 mm−1), in contrast, is not heavily influenced by tube velocity due to lower average path lengths.

Fig. 6
Fig. 6

Validation phantom results for configuration 3. Raw speckle contrast is shown in (a), with an ROI chosen to highlight the high flowing tube region. Fitted contrast values for both ROI’s are shown at one exposure (0.5 ms) in (b). Averaged fits for n2 (c), V2 (d), and d (e), show good agreement with expected values based on syringe pump settings and caliper measurements of flow and thickness. Because n2 is restricted to integer values, the fit shows perfect agreement with the expected power of two for directional flow. Therefore, V2 is defined as the flow velocity.

Equations (6)

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K= σ <I> ,
K 2 = 2 β 2 T 0 T (1 τ T ) | G 1 ( τ ) G 1 ( 0 ) | 2 dτ.
G 1 ( τ, ρ i )= 0 P( Y, ρ i )exp[ k 0 2 Y Δ r 2 ( τ ) 3 ]dY.
G 1 ( τ,d, ρ i )= 0 P( Y,d, ρ i ) 0 1 P( y|d, ρ i ) exp{ k 0 2 Y[ V 1 t n 1 ( y )+ V 2 t n 2 ( 1y ) ] 3 }dydY.
G 1 ( τ,d,f )=2π 0 G 1 ( τ,d,ρ ) J 0 ( 2πfρ )ρdρ.
I i = I DC + I AC cos( 2πfx+ φ i )=> I AC = 2 3 [ ( I 1 I 2 ) 2 + ( I 2 I 3 ) 2 + ( I 1 I 3 ) 2 ] 1/2

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