Abstract

We use transmission and backscattering optical coherence tomography (OCT) to distinguish and quantify dependent and multiple scattering effects in turbid media. With transmission OCT the dependent scattering coefficients for a range of monodisperse silica particle suspensions are determined. An excellent agreement is observed between the measured dependent scattering coefficients and calculations based on Mie calculations, the Percus-Yevick radial distribution function, and coherent light scattering theory. Backscattering OCT measurements are fitted using the extended Huygens-Fresnel (EHF) model with the dependent scattering coefficients obtained from the transmission OCT measurements as input parameters. Good agreement between the EHF model and the backscattering OCT measurements is observed. For large particles, the rms scattering angle θrms obtained from the EHF fit is in fair agreement with θrms calculated from the transmission OCT data.

© 2013 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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2013 (1)

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities using optical coherence tomography,” Phys. Rev. E 88, 042312 (2013).
[Crossref]

2012 (2)

2011 (2)

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16, 030503 (2011).
[Crossref] [PubMed]

V. M. Kodach, D. J. Faber, J. van Marle, T. G. van Leeuwen, and J. Kalkman, “Determination of the scattering anisotropy with optical coherence tomography,” Opt. Express 19, 6131–6140 (2011).
[Crossref] [PubMed]

2010 (3)

J. Kalkman, R. Sprik, and T. G. van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[Crossref]

J. Kalkman, A. V. Bykov, D. J. Faber, and T. G. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express 18, 3883–3892 (2010).
[Crossref] [PubMed]

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

2009 (1)

2008 (1)

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

2006 (1)

G. Singh and L. Song, “Influence of sodium dodecyl sulfate on colloidal fouling potential during ultrafiltration,” Colloids Surf. A 218, 138–146 (2006).
[Crossref]

2004 (1)

2003 (2)

2002 (1)

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol. 47, 2281–2299 (2002).
[Crossref] [PubMed]

2001 (1)

2000 (1)

1997 (1)

1996 (1)

1995 (1)

G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Complex Medium 5, 413–426 (1995).
[Crossref]

1993 (2)

1986 (1)

J. D. Cartigny, Y. Yamada, and C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1 -theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

1974 (1)

1958 (1)

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Aalders, M. C. G.

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16, 030503 (2011).
[Crossref] [PubMed]

D. J. Faber, F. J. van der Meer, M. C. G. Aalders, and T. G van Leeuwen, “Quantitative measurement of attenuation coefficients of weakly scattering media using optical coherence tomography,” Opt. Express,  124353–4365 (2004).
[Crossref] [PubMed]

Anderson, P. E.

Ao, C. O.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).

Bass, M.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borghese, F.

Bosschaart, N.

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16, 030503 (2011).
[Crossref] [PubMed]

Bykov, A. V.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol. 57, 1907–1917 (2012).
[Crossref] [PubMed]

J. Kalkman, A. V. Bykov, D. J. Faber, and T. G. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express 18, 3883–3892 (2010).
[Crossref] [PubMed]

Carlier, S. G.

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

Cartigny, J. D.

J. D. Cartigny, Y. Yamada, and C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1 -theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Cauberg, E. C. C.

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

de Bruin, D. M.

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

De Cusatis, C.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

de La Rosette, J. M. C. H.

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

de Reijke, T. M.

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

Del Bianco, S.

Denti, P.

Ding, K. H.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).

Enoch, J. M.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Faber, D. J.

Fricke, J.

G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Complex Medium 5, 413–426 (1995).
[Crossref]

Fujimoto, J. G.

Giusto, A.

Göbel, G.

G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Complex Medium 5, 413–426 (1995).
[Crossref]

Greffet, J. J.

Hanson, S. G.

Hee, M. R.

Hespel, L.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Iatì, M. A.

Izatt, J. A.

Jacobson, J. M.

Jacques, S. L.

Kalkman, J.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities using optical coherence tomography,” Phys. Rev. E 88, 042312 (2013).
[Crossref]

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol. 57, 1907–1917 (2012).
[Crossref] [PubMed]

V. M. Kodach, D. J. Faber, J. van Marle, T. G. van Leeuwen, and J. Kalkman, “Determination of the scattering anisotropy with optical coherence tomography,” Opt. Express 19, 6131–6140 (2011).
[Crossref] [PubMed]

J. Kalkman, A. V. Bykov, D. J. Faber, and T. G. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express 18, 3883–3892 (2010).
[Crossref] [PubMed]

J. Kalkman, R. Sprik, and T. G. van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[Crossref]

Klyen, B. R.

Knüttel, A.

Kodach, V. M.

Kong, J. A.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).

Kuhn, J.

G. Göbel, J. Kuhn, and J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Complex Medium 5, 413–426 (1995).
[Crossref]

Lakshminarayanan, V.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Li, G.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

MacDonald, C.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Mahajan, V. N.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Mainguy, S.

Martelli, F.

McLaughlin, R. A.

Palmer, K. F.

Percus, J. K.

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Robbins, P. D.

Saija, R.

Sampson, D. D.

Saunders, C. M.

Schmitt, J. M.

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

J. M. Schmitt and A. Knüttel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A 14, 1231–1242 (1997).
[Crossref]

Scolaro, L.

Sindoni, O. I.

Singh, G.

G. Singh and L. Song, “Influence of sodium dodecyl sulfate on colloidal fouling potential during ultrafiltration,” Colloids Surf. A 218, 138–146 (2006).
[Crossref]

Song, L.

G. Singh and L. Song, “Influence of sodium dodecyl sulfate on colloidal fouling potential during ultrafiltration,” Colloids Surf. A 218, 138–146 (2006).
[Crossref]

Sprik, R.

J. Kalkman, R. Sprik, and T. G. van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[Crossref]

Streekstra, G. J.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol. 57, 1907–1917 (2012).
[Crossref] [PubMed]

Swanson, E. A.

ten Bosch, J. J.

J. R. Zijp and J. J. ten Bosch, “Pascal program to perform Mie calculations,” Opt. Eng. 32, 1691–1695 (1993).
[Crossref]

Thrane, L.

Tien, C. L.

J. D. Cartigny, Y. Yamada, and C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1 -theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Tsang, L.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).

van der Meer, F. J.

van Leeuwen, T. G

van Leeuwen, T. G.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities using optical coherence tomography,” Phys. Rev. E 88, 042312 (2013).
[Crossref]

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol. 57, 1907–1917 (2012).
[Crossref] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16, 030503 (2011).
[Crossref] [PubMed]

V. M. Kodach, D. J. Faber, J. van Marle, T. G. van Leeuwen, and J. Kalkman, “Determination of the scattering anisotropy with optical coherence tomography,” Opt. Express 19, 6131–6140 (2011).
[Crossref] [PubMed]

J. Kalkman, A. V. Bykov, D. J. Faber, and T. G. van Leeuwen, “Multiple and dependent scattering effects in Doppler optical coherence tomography,” Opt. Express 18, 3883–3892 (2010).
[Crossref] [PubMed]

J. Kalkman, R. Sprik, and T. G. van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[Crossref]

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

van Marle, J.

Van Stryland, E.

M. Bass, C. De Cusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4.

Virmani, R.

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

Visser, M.

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

Wang, R. K.

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol. 47, 2281–2299 (2002).
[Crossref] [PubMed]

Weiss, N.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities using optical coherence tomography,” Phys. Rev. E 88, 042312 (2013).
[Crossref]

Williams, D.

Wood, B. A.

Xu, C.

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

Yamada, Y.

J. D. Cartigny, Y. Yamada, and C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1 -theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Yevick, G. J.

J. K. Percus and G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Yura, H. T.

Zaccanti, G.

Zijp, J. R.

J. R. Zijp and J. J. ten Bosch, “Pascal program to perform Mie calculations,” Opt. Eng. 32, 1691–1695 (1993).
[Crossref]

Appl. Opt. (2)

Biomed. Opt. Express (1)

Colloids Surf. A (1)

G. Singh and L. Song, “Influence of sodium dodecyl sulfate on colloidal fouling potential during ultrafiltration,” Colloids Surf. A 218, 138–146 (2006).
[Crossref]

J. Biomed. Opt. (3)

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, and M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16, 030503 (2011).
[Crossref] [PubMed]

E. C. C. Cauberg, D. M. de Bruin, D. J. Faber, T. M. de Reijke, M. Visser, J. M. C. H. de La Rosette, and T. G. van Leeuwen, “Quantitative measurement of attenuation coefficients of bladder biopsies using optical coherence tomography for grading urothelial carcinoma of the bladder,” J. Biomed. Opt. 15, 066013 (2010).
[Crossref]

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt. 13, 034003 (2008).
[Crossref] [PubMed]

J. Heat Transfer (1)

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Figures (5)

Fig. 1
Fig. 1 Size distribution of Psi-0.5 silica particles measured with transmission electron microscopy (inset) and the corresponding Gaussian fit. The fit yields a mean diameter of ϕ =376 nm and a standard deviation of 20 nm.
Fig. 2
Fig. 2 Experimental setup for backscattering (a) and transmission (b) SD-OCT. SLD: super luminescent diode, BS1: 90:10 fiber splitter, BS2: 50:50 fiber splitter, PC: polarization control, C: achromatic lenses, NDF: neutral density filter, SM: spectrometer, M: mirror, S: sample.
Fig. 3
Fig. 3 Measured OCT signal versus optical path length in transmission OCT for ϕ = 1215 nm silica particles at varying volume concentrations (indicated). The dashed horizontal lines indicate |awater| and |asol|.
Fig. 4
Fig. 4 Measured scattering coefficients for (a) 376 nm (b) 759 nm (c) 906 nm and (d) 1215 nm diameter particles. Mie (dashed black lines) and dependent scattering (solid red line) calculations of the scattering coefficient and the scattering anisotropy gs are shown.
Fig. 5
Fig. 5 Measured OCT signal versus depth in backscattering geometry for ϕ = 1215 nm silica particles at varying volume fractions (indicated). The solid red line indicates the EHF model fit, the dashed blue line indicates the single scattering contribution to the OCT backscatter signal.

Tables (2)

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Table 1 Catalog number, mean diameter, standard deviation, and maximum volume concentration of silica beads. Scattering cross section and anisotropy factor gs are obtained from Mie theory.

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Table 2 Average scattering angle θrms for ϕ =1215 nm from the theory based on the transmission OCT data and from the EHF fits of the backscattering OCT data.

Equations (7)

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Q dep ( f v ) Q Mie = 2 π 0 π S ( f v , θ ) p Mie ( θ ) sin θ d θ ,
S ( f v , θ ) = 1 + 24 f v 0 R 2 ( g ( R ) 1 ) sin ( q ϕ R ) q ϕ R d R ,
2 x | n part n med 1 | 1 ,
p dep ( θ ) = Q Mie Q dep S ( f v , θ ) p Mie ( θ ) .
i ( z ) 2 exp ( 2 μ s z ) + 2 exp ( μ s z ) [ 1 exp ( μ s z ) ] 1 + w s 2 w h 2 + [ 1 exp ( μ s z ) ] 2 w h 2 w s 2 ,
θ rms = 0 π sin 2 θ p dep ( θ ) sin θ d θ 0 π p dep ( θ ) sin θ d θ .
μ s = ln | a water | 2 | a sol | 2

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