Abstract

We have studied the influence of absorption, scattering, and refractive index of a phantom medium in conjunction with various beam diameters on the penetration depth of light at 633 nm. We used mixtures of Intralipid 10% (scattering medium) and Evans blue (absorbing medium). Measurements were performed in media with a scattering coefficient of 1 mm−1, an anisotropy factor of 0.71, absorption coefficients of 1.3 × 10−3, 0.01, and 0.05 mm−1, and a refractive index of 1.33. The experimental results were compared with an analytical solution of the fluence rate based on diffusion theory. We found good agreement (deviations of <10%) between theory and experiment for incident beam diameters between 10 and 60 mm.

© 1989 Optical Society of America

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References

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  1. S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1960).
  2. A. Ishimaru, Wave Propagation in Random Media, Vol. 1 (Academic, New York, 1978).
  3. L. O. Reynolds, C. Johnson, A. Ishimaru, “Diffuse Reflectance from a Finite Blood Medium: Applications to the Modeling of Fiber Optic Catheters,” Appl. Opt. 15, 2059–2067 (1976).
    [CrossRef] [PubMed]
  4. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and Absorption of Turbid Materials Determined from Reflection Measurements I and II,” Appl. Opt. 22, 2456–2467 (1983).
    [CrossRef] [PubMed]
  5. S. A. Prahl, “Light Transport in Tissue,” Ph.D. Dissertation, U. Texas at Austin (1988).
  6. W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
    [CrossRef] [PubMed]
  7. S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).
  8. W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
    [CrossRef] [PubMed]

1988 (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

1987 (2)

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).

1983 (1)

1976 (1)

Alter, C. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1960).

Ferwerda, H. A.

Groenhuis, R. A. J.

Ishimaru, A.

Jacques, S. L.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).

Jansen, H.

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Johnson, C.

Keijzer, M.

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Marijnissen, J. P. A.

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Prahl, S. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).

S. A. Prahl, “Light Transport in Tissue,” Ph.D. Dissertation, U. Texas at Austin (1988).

Reynolds, L. O.

Star, W. M.

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Ten Bosch, J. J.

Van Gemert, M. J. C.

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Appl. Opt. (2)

Lasers Life Sci. (1)

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular Dependence of He-Ne Laser Light Scattering by Human Dermis,” Lasers Life Sci. 4, 309–333 (1987).

Photochem. Photobiol. (1)

W. M. Star, J. P. A. Marijnissen, H. Jansen, M. Keijzer, M. J. C. Van Gemert, “Light Dosimetry for Photodynamic Therapy by Whole Bladder Irradiation,” Photochem. Photobiol. 46, 619–624 (1987).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “Light Dosimetry in Optical Phantoms and in Tissues. 1: Multiple Flux and Transport Theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

Other (3)

S. A. Prahl, “Light Transport in Tissue,” Ph.D. Dissertation, U. Texas at Austin (1988).

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1960).

A. Ishimaru, Wave Propagation in Random Media, Vol. 1 (Academic, New York, 1978).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for determination of μa and μs. I, II, and III are pinholes with diameters of 0.5, 1, and 1 mm, respectively; L is 2 m.

Fig. 2
Fig. 2

Transmitted light as a function of the concentration of Intralipid.

Fig. 3
Fig. 3

Experimental setup for determination of the asymmetry parameter.

Fig. 4
Fig. 4

(a) ln(ψ·r) vs the r diagram of the detected fluence rate for μs = 1 mm−1. (b) ln(ψx·r) vs the r diagram of the detected fluence rate for μs = 2 mm−1.

Fig. 5
Fig. 5

Experimental setup for the fluence rate measurements.

Fig. 6
Fig. 6

Calibration of the isotropic detector: (a) energy fluence rate measurement; (b) calibration measurement.

Fig. 7
Fig. 7

(a) Fluence rate as a function of depth in the case of index matching. (b) Fluence rate as a function of the depth in the case of index matching. (c) Fluence rate as a function of the depth in the case of a refractive index mismatch.

Fig. 8
Fig. 8

Fitted attenuation coefficient for curves from Fig. 7(a) as a function of beam diameter in the case of index matching.

Equations (10)

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E = E 0 exp ( μ s · c · d ) ,
μ s = 1 d ln ( E / E 0 ) c ,
μ s = ( 38 . 6 ± 0 . 4 ) × 10 3 mm 1 / ( mliter / liter ) ,
μ a = ( 7 . 60 ± 0 . 05 ) × 10 - 3 mm / ( mliter / liter ) ,
ψ ( r ) = c r exp ( r · μ eff ) ,
μ eff 2 = 3 μ a [ μ a + ( 1 g ) μ s ] .
μ eff = r ln ( ψ · r ) ,
g = 1 μ a μ s ( μ eff 2 3 μ a 2 1 ) .
g = 0 . 71 ± 0 . 03 ;
μ a 0 = ( 5 . 7 ± 1 . 5 ) × 10 5 mm 1 / ( mliter / liter ) .

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