Abstract

The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers’ sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.

© 2010 Optical Society of America

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2006 (1)

2005 (2)

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
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D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

2004 (1)

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

2003 (2)

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

2002 (2)

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

O. V. Angelsky, D. N. Burkovets, A. V. Kovalchuk, and S. G. Hanson, "Fractal description of rough surfaces," Appl. Opt. 41, 4620-4629 (2002).
[CrossRef] [PubMed]

2001 (2)

E. Hull, and T. Foster, "Steady-state reflectance spectroscopy in the p3 approximation," J. Opt. Soc. Am. A 18, 584-599 (2001).
[CrossRef]

P. Waliszewski, and J. Konarski, "Tissue as a self-organizing system with fractal dynamics," Adv. Space Res. 28, 545-548 (2001).
[CrossRef]

1999 (2)

1998 (2)

J. Mourant, J. Freyer, A. Hielscher, A. Eick, D. Shen, and T. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
[CrossRef]

V. Venugopalan, J. You, and B. Tromberg, "Radiative transport in the diffusion approximation: An extension for highly absorbing media and small source-detector separations," Phys. Rev. E 58, 2395-2407 (1998).
[CrossRef]

1997 (1)

1996 (5)

1995 (1)

1994 (2)

1993 (2)

P. van der Zee, M. Essenpreis, and D. Delpy, "Optical properties of brain tissue," Proc. SPIE 1888, 454-465 (1993).
[CrossRef]

R. Bolt, and J. Ten Bosch, "Method for measuring position dependent volume reflection," Appl. Opt. 32, 4641-4645 (1993).
[CrossRef] [PubMed]

1990 (1)

W.-F. Cheong, S. Prahl, and A. Welsh, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

1989 (3)

G. Weiss, R. Nossal, and R. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

D. Wyman, M. Patterson, and B. Wilson, "Similarity relations for anisotropic scattering in monte carlo simulations of deeply penetrating neutral particles," J. Comput. Phys. 81, 137-150 (1989).
[CrossRef]

R. Marchesini, A. Bertoni, S. Andreola, E. Melloni, and A. Sichirollo, "Extinction and absorption coefficients and scattering phase functions of human tissues in vitro," Appl. Opt. 28, 2318-2324 (1989).
[CrossRef] [PubMed]

1983 (2)

1974 (1)

A. Brunsting, and P. F. Mullaney, "Differential light-scattering from spherical mammalian-cells," Biophys. J. 14, 439-453 (1974).
[CrossRef] [PubMed]

1908 (1)

G. Mie, "Articles on the optical characteristics of turbid tubes, especially colloidal metal solutions," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Anderson, R. R.

I. A. Vitkin, J. Woolsey, B. C. Wilson, and R. R. Anderson, "Optical and thermal characterization of natural (sepia officinalis) melanin," Photochem. Photobiol. 59, 455-462 (1994).
[CrossRef] [PubMed]

Andersson-Engels, S.

Andreola, S.

Angelsky, O. V.

Avrillier, S.

B. Gélébart, T. Tinet, J.-M. Tualle, and S. Avrillier, "Phase function simulation in tissue phantoms: a fractal approach," J. Opt. A, Pure Appl. Opt. 5, 377-388 (1996).

Azarpey, N.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

Beauvoit, B.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1, 200-211 (1996).
[CrossRef]

Bertoni, A.

Bevilacqua, F.

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

F. Bevilacqua, and C. Depeursinge, "Monte carlo study of diffuse reflectance at source-detector separations close to one transport mean free path," J. Opt. Soc. Am. A 16, 2935-2945 (1999).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, J. Gross, B. Tromberg, and C. Depeursinge, "In vivo local determination of tissue optical properties: application to human brain," Appl. Opt. 38, 4939-4950 (1999).
[CrossRef]

Bigio, I.

Biton, C.

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Bolt, R.

Bonner, R.

G. Weiss, R. Nossal, and R. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

Boyer, J.

Brock, R.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Brundler, M. A.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

Brunsting, A.

A. Brunsting, and P. F. Mullaney, "Differential light-scattering from spherical mammalian-cells," Biophys. J. 14, 439-453 (1974).
[CrossRef] [PubMed]

Burkovets, D. N.

Chance, B.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1, 200-211 (1996).
[CrossRef]

Charvet, I.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Cheong, W.-F.

W.-F. Cheong, S. Prahl, and A. Welsh, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Cheung, R.-T.

Cuche, E.

Delpy, D.

P. van der Zee, M. Essenpreis, and D. Delpy, "Optical properties of brain tissue," Proc. SPIE 1888, 454-465 (1993).
[CrossRef]

Depeursinge, C.

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
[CrossRef] [PubMed]

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

F. Bevilacqua, and C. Depeursinge, "Monte carlo study of diffuse reflectance at source-detector separations close to one transport mean free path," J. Opt. Soc. Am. A 16, 2935-2945 (1999).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, J. Gross, B. Tromberg, and C. Depeursinge, "In vivo local determination of tissue optical properties: application to human brain," Appl. Opt. 38, 4939-4950 (1999).
[CrossRef]

Dimou, A.

Durian, D.

Eick, A.

Emery, Y.

Essenpreis, M.

P. van der Zee, M. Essenpreis, and D. Delpy, "Optical properties of brain tissue," Proc. SPIE 1888, 454-465 (1993).
[CrossRef]

Fantini, S.

Ferwerda, H.

Foster, T.

Franceschini, M. A.

Freyer, J.

Gélébart, B.

B. Gélébart, T. Tinet, J.-M. Tualle, and S. Avrillier, "Phase function simulation in tissue phantoms: a fractal approach," J. Opt. A, Pure Appl. Opt. 5, 377-388 (1996).

Ghislain, M.

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

Gratton, E.

Grohenhuis, R.

Gross, J.

Guerra, R.

D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Hadengue, A.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

Hanson, S. G.

Hebden, J.

D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Hibst, R.

Hielscher, A.

Hu, X.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Hull, E.

Ishimaru, A.

Jacobs, K.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Jacquet, J.

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Johnson, T.

Kienle, A.

Kimura, M.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1, 200-211 (1996).
[CrossRef]

Konarski, J.

P. Waliszewski, and J. Konarski, "Tissue as a self-organizing system with fractal dynamics," Adv. Space Res. 28, 545-548 (2001).
[CrossRef]

Kovalchuk, A. V.

Kuga, Y.

Kumar, G.

Lilge, L.

Liu, H.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1, 200-211 (1996).
[CrossRef]

Lu, J.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Magistretti, P.

Maier, J. S.

Marchesini, R.

Marquet, P.

Meda, P.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Melloni, E.

Mie, G.

G. Mie, "Articles on the optical characteristics of turbid tubes, especially colloidal metal solutions," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Mourant, J.

Mullaney, P. F.

A. Brunsting, and P. F. Mullaney, "Differential light-scattering from spherical mammalian-cells," Biophys. J. 14, 439-453 (1974).
[CrossRef] [PubMed]

Nossal, R.

G. Weiss, R. Nossal, and R. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

Ory, G.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

Osei, E.

Passos, D.

D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Patterson, M.

Piguet, D.

Pinto, P.

D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Prahl, S.

W.-F. Cheong, S. Prahl, and A. Welsh, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Rappaz, B.

Rudnick, J.

Saint-Ghislain, M.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Schmitt, J.

Shen, D.

Sichirollo, A.

Steiner, R.

Ten Bosch, J.

Thueler, P.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Tinet, T.

B. Gélébart, T. Tinet, J.-M. Tualle, and S. Avrillier, "Phase function simulation in tissue phantoms: a fractal approach," J. Opt. A, Pure Appl. Opt. 5, 377-388 (1996).

Tromberg, B.

F. Bevilacqua, D. Piguet, P. Marquet, J. Gross, B. Tromberg, and C. Depeursinge, "In vivo local determination of tissue optical properties: application to human brain," Appl. Opt. 38, 4939-4950 (1999).
[CrossRef]

V. Venugopalan, J. You, and B. Tromberg, "Radiative transport in the diffusion approximation: An extension for highly absorbing media and small source-detector separations," Phys. Rev. E 58, 2395-2407 (1998).
[CrossRef]

Tualle, J.-M.

B. Gélébart, T. Tinet, J.-M. Tualle, and S. Avrillier, "Phase function simulation in tissue phantoms: a fractal approach," J. Opt. A, Pure Appl. Opt. 5, 377-388 (1996).

van der Zee, P.

P. van der Zee, M. Essenpreis, and D. Delpy, "Optical properties of brain tissue," Proc. SPIE 1888, 454-465 (1993).
[CrossRef]

Venugopalan, V.

V. Venugopalan, J. You, and B. Tromberg, "Radiative transport in the diffusion approximation: An extension for highly absorbing media and small source-detector separations," Phys. Rev. E 58, 2395-2407 (1998).
[CrossRef]

Vermeulen, B.

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Vitkin, I. A.

I. A. Vitkin, J. Woolsey, B. C. Wilson, and R. R. Anderson, "Optical and thermal characterization of natural (sepia officinalis) melanin," Photochem. Photobiol. 59, 455-462 (1994).
[CrossRef] [PubMed]

Waliszewski, P.

P. Waliszewski, and J. Konarski, "Tissue as a self-organizing system with fractal dynamics," Adv. Space Res. 28, 545-548 (2001).
[CrossRef]

Walker, S. A.

Weiss, G.

G. Weiss, R. Nossal, and R. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

Welsh, A.

W.-F. Cheong, S. Prahl, and A. Welsh, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Wilson, B.

Wilson, B. C.

I. A. Vitkin, J. Woolsey, B. C. Wilson, and R. R. Anderson, "Optical and thermal characterization of natural (sepia officinalis) melanin," Photochem. Photobiol. 59, 455-462 (1994).
[CrossRef] [PubMed]

Woolsey, J.

I. A. Vitkin, J. Woolsey, B. C. Wilson, and R. R. Anderson, "Optical and thermal characterization of natural (sepia officinalis) melanin," Photochem. Photobiol. 59, 455-462 (1994).
[CrossRef] [PubMed]

Wyman, D.

D. Wyman, M. Patterson, and B. Wilson, "Similarity relations for anisotropic scattering in monte carlo simulations of deeply penetrating neutral particles," J. Comput. Phys. 81, 137-150 (1989).
[CrossRef]

Yang, P.

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

You, J.

V. Venugopalan, J. You, and B. Tromberg, "Radiative transport in the diffusion approximation: An extension for highly absorbing media and small source-detector separations," Phys. Rev. E 58, 2395-2407 (1998).
[CrossRef]

Zonios, G.

Adv. Space Res. (1)

P. Waliszewski, and J. Konarski, "Tissue as a self-organizing system with fractal dynamics," Adv. Space Res. 28, 545-548 (2001).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Articles on the optical characteristics of turbid tubes, especially colloidal metal solutions," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Appl. Opt. (8)

R. Marchesini, A. Bertoni, S. Andreola, E. Melloni, and A. Sichirollo, "Extinction and absorption coefficients and scattering phase functions of human tissues in vitro," Appl. Opt. 28, 2318-2324 (1989).
[CrossRef] [PubMed]

M. Patterson, S. Andersson-Engels, B. Wilson, and E. Osei, "Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon path," Appl. Opt. 34, 22-29 (1995).
[CrossRef] [PubMed]

J. Mourant, J. Freyer, A. Hielscher, A. Eick, D. Shen, and T. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
[CrossRef]

R. Bolt, and J. Ten Bosch, "Method for measuring position dependent volume reflection," Appl. Opt. 32, 4641-4645 (1993).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. Patterson, R. Hibst, R. Steiner, and B. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[CrossRef] [PubMed]

R. Grohenhuis, H. Ferwerda, and J. Ten Bosch, "Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory," Appl. Opt. 22, 2456-2462 (1983).
[CrossRef]

F. Bevilacqua, D. Piguet, P. Marquet, J. Gross, B. Tromberg, and C. Depeursinge, "In vivo local determination of tissue optical properties: application to human brain," Appl. Opt. 38, 4939-4950 (1999).
[CrossRef]

O. V. Angelsky, D. N. Burkovets, A. V. Kovalchuk, and S. G. Hanson, "Fractal description of rough surfaces," Appl. Opt. 41, 4620-4629 (2002).
[CrossRef] [PubMed]

Biophys. J. (1)

A. Brunsting, and P. F. Mullaney, "Differential light-scattering from spherical mammalian-cells," Biophys. J. 14, 439-453 (1974).
[CrossRef] [PubMed]

Eur. J. Gastroenterol. Hepatol. (1)

I. Charvet, G. Ory, P. Thueler, M. A. Brundler, M. Saint-Ghislain, N. Azarpey, A. Hadengue, C. Depeursinge, B. Vermeulen, and P. Meda, "Diagnosis and grading of gastritis by non-invasive optical analysis," Eur. J. Gastroenterol. Hepatol. 16, 1189-1198 (2004).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W.-F. Cheong, S. Prahl, and A. Welsh, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

J. Biomed. Opt. (3)

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1, 200-211 (1996).
[CrossRef]

D. Passos, J. Hebden, P. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

P. Thueler, I. Charvet, F. Bevilacqua, M. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, "In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties," J. Biomed. Opt. 8, 495-503 (2003).
[CrossRef] [PubMed]

J. Comput. Phys. (1)

D. Wyman, M. Patterson, and B. Wilson, "Similarity relations for anisotropic scattering in monte carlo simulations of deeply penetrating neutral particles," J. Comput. Phys. 81, 137-150 (1989).
[CrossRef]

J. Mod. Opt. (1)

G. Weiss, R. Nossal, and R. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

B. Gélébart, T. Tinet, J.-M. Tualle, and S. Avrillier, "Phase function simulation in tissue phantoms: a fractal approach," J. Opt. A, Pure Appl. Opt. 5, 377-388 (1996).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Express (2)

Opt. Lett. (3)

Photochem. Photobiol. (1)

I. A. Vitkin, J. Woolsey, B. C. Wilson, and R. R. Anderson, "Optical and thermal characterization of natural (sepia officinalis) melanin," Photochem. Photobiol. 59, 455-462 (1994).
[CrossRef] [PubMed]

Phys. Med. Biol. (2)

X. Ma, J. Lu, R. Brock, K. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

I. Charvet, P. Thueler, B. Vermeulen, M. Saint-Ghislain, C. Biton, J. Jacquet, F. Bevilacqua, C. Depeursinge, and P. Meda, "A new optical method for the non-invasive detection of minimal tissue alterations," Phys. Med. Biol. 47, 2095-2108 (2002).
[CrossRef] [PubMed]

Phys. Rev. E (1)

V. Venugopalan, J. You, and B. Tromberg, "Radiative transport in the diffusion approximation: An extension for highly absorbing media and small source-detector separations," Phys. Rev. E 58, 2395-2407 (1998).
[CrossRef]

Proc. SPIE (1)

P. van der Zee, M. Essenpreis, and D. Delpy, "Optical properties of brain tissue," Proc. SPIE 1888, 454-465 (1993).
[CrossRef]

Other (4)

S. Prahl, "Mie scattering calculator," (2007). http://omlc.ogi.edu/calc/mie calc.html.

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).

H. van de Hulst, Light scattering by small particles (Dover Publications, Inc, New York, 1981).

D. Segelstein, "The complex refractive index of water," Master’s thesis, University of Missouri-Kansas City (1981). http://www.philiplaven.com/Segelstein.txt.

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Figures (8)

Fig. 1
Fig. 1

Scattering cross section according to Mie’s formalism [19] plotted here in a normalized form σs,sph/πd2 (right) as a function of the normalized sphere diameter d/λ

Fig. 2
Fig. 2

Expression of g1,sph (left) and g2,sph (right) as a function of the normalized sphere diameter d/λ derived from psph as expressed in Eq. (3)

Fig. 3
Fig. 3

Numerical expression of g1,eff (left) and γeff (right) as a function of the fractal dimension α as defined in Eq. (11) and (12). The dashed lines indicate the α and γeff values corresponding to experimental g1 values measured on brain and liver [24, 25], thus defining an experiment-based physiological range for these coefficients.

Fig. 4
Fig. 4

Numerical expression of g1,eff (left) and γeff (right) as a function of the fractal dimension α as defined in Eq. (11) and (12). The dashed lines indicate the α and γeff values corresponding to experimental g1 values measured on brain and liver [24, 25], thus defining an experiment-based physiological range for these coefficients.

Fig. 5
Fig. 5

Optical coefficients μ′s,eff and μ′s,exp as numerically simulated (right) and measured with spatially-resolved reflectance spectrometry (left). Data are plotted as a function of λ for α ∈ [2.5, 4]. Relative errors (standard deviation/mean) on μ′s,exp amount to approximately 4%.

Fig. 6
Fig. 6

Optical coefficients γeff and γexp (lower row) as numerically simulated (right) and measured with spatially-resolved reflectance spectrometry (left). Data are plotted as a function of λ for α ∈ [2.5, 4]. Relative errors (standard deviation/mean) on γexp amount to approximately 6%.

Fig. 8
Fig. 8

Optical coefficients μs,eff computed as a function of λ for a range of α values indicated in the embedded legend. A trend line indicates the λ−4 behavior expected from Rayleigh’s theory.

Fig. 7
Fig. 7

Measured optical coefficients γeff and γexp as a function of α for a discrete set of λ ∈ [500, 800]. Relative errors (standard deviation/mean) on γexp amount to approximately 6%.

Tables (1)

Tables Icon

Table 1 Refractive index of cell components reported in literature

Equations (12)

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

γ = 1 g 2 1 g 1
p ( cos θ ) = Σ m 0 ( 2 m + 1 ) g m P m ( cos θ )
g m = 2 π 0 π P m ( cos θ ) p ( θ ) d θ
μ s , sph ( d , λ ) = ρ sph ( d ) σ s , sph ( x )
μ s , eff ( λ ) = i = 1 M μ s , sph ( d i , λ )
g m , eff ( λ ) = Σ i = 1 M μ s , sph ( d i , λ ) g m , sph ( x i ) Σ i = 1 M μ s , sph ( d i , λ )
γ eff ( λ ) = Σ i = 1 M μ s , sph ( d i , λ ) ( 1 g 2 , sph ( x i ) ) Σ i = 1 M μ s , sph ( d i , λ ) ( 1 g 1 , sph ( x i ) )
μ s , eff ( λ ) = μ s , eff ( λ ) ( 1 g 1 , eff ( λ ) )
ρ ( d ) = Ad α
μ s , eff ( λ ) = A i = 1 M d i α σ s , sph ( x i )
g m , eff ( λ ) = Σ i = 1 M d i α σ s , sph ( x i ) g m , sph ( x i ) Σ i = 1 M d i α σ s , sph ( x i )
γ eff ( λ ) = Σ i = 1 M d i α σ s , sph ( x i ) ( 1 g 2 , sph x i ) ) Σ i = 1 M d i α σ s , sph ( x i ) ( 1 g 1 , sph ( x i ) )

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