Abstract

A simple and quick approach is used to measure the reduced scattering coefficient (μs′) of a semi-infinite turbid medium having a much smaller absorption coefficient than μs′. A laser beam with an oblique angle of incidence to the medium causes the center of the diffuse reflectance that is several transport mean-free paths away from the incident point to shift away from the point of incidence by an amount Δx. This amount is used to compute μs′ by μs′ = sin(αi)/(nΔx), where n is the refractive index of the turbid medium divided by that of the incident medium and αi is the angle of incidence measured from the surface normal. For a turbid medium having an absorption coefficient comparable with μs′, a revision to the above formula is made. This method is tested theoretically by Monte Carlo simulations and experimentally by a video reflectometer.

© 1995 Optical Society of America

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  1. J. W. Pickering, S. A. Prahl, N. Vanwieringen, J. F. Beek, H. J. C. M. Sterenborg, M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
    [CrossRef] [PubMed]
  2. B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for noninvasive investigation of photodynamic sensitizers n vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Goner, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–232.
  3. S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.
  4. M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  5. T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  6. L.-H. Wang, S. L. Jacques, “Analysis of diffusion theory and similarity relations,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1888, 107–116 (1993).
  7. L.-H. Wang, S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10, 1746–1752 (1993).
    [CrossRef]
  8. L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser-Tissue Interaction 5, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2134A, 247–254 (1994).
  9. S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
    [CrossRef] [PubMed]
  10. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  11. S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

1993 (2)

1992 (2)

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

1990 (1)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989 (1)

Beek, J. F.

Chance, B.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for noninvasive investigation of photodynamic sensitizers n vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Goner, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–232.

Flock, S. T.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Gutsche, A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Jacques, S. L.

L.-H. Wang, S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10, 1746–1752 (1993).
[CrossRef]

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser-Tissue Interaction 5, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2134A, 247–254 (1994).

L.-H. Wang, S. L. Jacques, “Analysis of diffusion theory and similarity relations,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1888, 107–116 (1993).

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

Patterson, M. S.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for noninvasive investigation of photodynamic sensitizers n vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Goner, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–232.

Pickering, J. W.

Prahl, S. A.

J. W. Pickering, S. A. Prahl, N. Vanwieringen, J. F. Beek, H. J. C. M. Sterenborg, M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

Schwartz, J. A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Star, W. M.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

Tittel, F. K.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

van Gemert, M. J.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

van Gemert, M. J. C.

Vanwieringen, N.

Wang, L.-H.

L.-H. Wang, S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10, 1746–1752 (1993).
[CrossRef]

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser-Tissue Interaction 5, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2134A, 247–254 (1994).

L.-H. Wang, S. L. Jacques, “Analysis of diffusion theory and similarity relations,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1888, 107–116 (1993).

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

Wilson, B. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for noninvasive investigation of photodynamic sensitizers n vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Goner, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–232.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Lasers Surg. Med. (1)

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Other (5)

L.-H. Wang, S. L. Jacques, “Analysis of diffusion theory and similarity relations,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1888, 107–116 (1993).

L.-H. Wang, S. L. Jacques, “Animated simulation of light transport in tissues,” in Laser-Tissue Interaction 5, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2134A, 247–254 (1994).

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for noninvasive investigation of photodynamic sensitizers n vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Goner, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–232.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L.-H. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989), pp. 102–111.

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Figures (5)

Fig. 1
Fig. 1

Lumped isotropic point sources for a laser beam of (a) normal incidence (α i = 0), (b) oblique incidence (α i > 0°). A coordinate system was set up in which the y axis pointed outward from the paper.

Fig. 2
Fig. 2

Schematic of the video reflectometer.

Fig. 3
Fig. 3

Curve M is the Monte Carlo simulated diffuse reflectance of a 1-W laser beam incident to a turbid medium with α i = 45°, and curve C is the center line of curve M, i.e., the midpoint of the left and right sides of curve M for specific reflectance values. The optical properties of the turbid medium were n = 1.33, μ a = 0.25 cm−1, μ s = 20 cm−1, and g = 0.853.

Fig. 4
Fig. 4

Symbols with error bars are Monte Carlo simulated Δx for different (a) μ s , (b) μ a , (c) angles of incidence α i . The dashed and solid curves were computed by use of Eqs. (1) and (2), respectively. The parameters for (a)–(c) are listed in the text.

Fig. 5
Fig. 5

(a), (b) CCD video images of a diffuse reflectance pattern from a turbid medium with the same optical properties as those in Fig. 3; (c) diffuse reflectance along the x axis. The resolution of the images was 8.5 × 10−3 cm/pixel; (a) is the video image without laser beam attenuation (the center of the image was saturated on the CCD camera) and (b) is the video image with a 3.3-fold attenuation by a filter to measure the saturated center portion of (a).

Equations (5)

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Δ x = sin ( α t ) / μ s = sin ( α i ) / ( n μ s ) ,
Δ x = sin ( α i ) / [ n ( μ s + 0.35 μ a ) ] ,
μ s = sin ( α i ) / ( n Δ x ) .
R ( x , y ) = - + - + S ( x , y ) G ( x - x , y - y ) d x d y ,
R ( Δ x - x , y ) = - + - + S ( x , y ) × G ( Δ x - x - x , y - y ) d x d y , = - + - + S ( x , y ) × G ( Δ x + x + x , y - y ) d x d y , = + - - + S ( - x , y ) × G ( Δ x + x - x , y - y ) d ( - x ) d y , = - + - + S ( x , y ) × G ( Δ x + x - x , y - y ) d x d y , = R ( Δ x + x , y ) ,

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