Abstract

In many measurements used for the determination of optical properties of biological tissues, a detector with a small cone of acceptance is used. Therefore a small part of the anisotropically distributed backscattered light is detected. We present the results of Monte Carlo calculations and study the anisotropy of the direction distribution of volume-backscattered photons. Close to the source it is impossible to give a general correction factor to relate the measurements to theoretical results. Far from the source, the measured radiation divided by the square of the sine of the accepting angle of the detector is a relatively good approximation of the radiant exitance at the surface of the sample under investigation. We recommend the use of a detector with a large angle of acceptance for these kinds of measurements.

© 1997 Optical Society of America

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References

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  1. R. A. J. Groenhuis, J. J. ten Bosch, H. A. Ferwerda, “Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
    [CrossRef] [PubMed]
  2. M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE1065, 115–122 (1989).
    [CrossRef]
  3. R. A. Bolt, J. J. ten Bosch, “Method for measuring position-dependent volume reflection,” Appl. Opt. 32, 4641–4645 (1993).
    [CrossRef] [PubMed]
  4. A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.
  5. R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
    [CrossRef]
  6. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
    [CrossRef] [PubMed]
  7. Commission Internationale de ’l Eclairage, International Lighting Vocabulary (Bureau Central de la Commission Electrotechnique Internationale, Geneva, Switzerland, 1987).
  8. J. R. Zijp, J. J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 22, 533–534 (1994).
    [CrossRef]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9.
  10. J. R. Zijp, J. J. ten Bosch, “Pascal program to perform Mie calculations,” Opt. Eng. 32, 1691–1695 (1993).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics, 6th Ed. (Pergamon, Oxford, 1980), p. 42.
  12. J. R. Zijp, J. J. ten Bosch, R. A. J. Groenhuis, “HeNe-laser light scattering by human dental enamel,” J. Dent. Res. 22, 1891–1898 (1995).
    [CrossRef]
  13. A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
    [CrossRef] [PubMed]

1996 (2)

1995 (1)

J. R. Zijp, J. J. ten Bosch, R. A. J. Groenhuis, “HeNe-laser light scattering by human dental enamel,” J. Dent. Res. 22, 1891–1898 (1995).
[CrossRef]

1994 (1)

J. R. Zijp, J. J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 22, 533–534 (1994).
[CrossRef]

1993 (3)

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

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

R. A. Bolt, J. J. ten Bosch, “Method for measuring position-dependent volume reflection,” Appl. Opt. 32, 4641–4645 (1993).
[CrossRef] [PubMed]

1983 (1)

Barilli, M.

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

Bolt, R. A.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th Ed. (Pergamon, Oxford, 1980), p. 42.

Chuang, C. H.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Ferrari, M.

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

Ferwerda, H. A.

Groenhuis, R. A. J.

Hibst, R.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

Kienle, A.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

Lilge, L.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

Littmann, L.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Martelli, F.

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

Nanney, G.A.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Patterson, M. S.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE1065, 115–122 (1989).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

Schwartz, E.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE1065, 115–122 (1989).
[CrossRef]

Splinter, R.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Steiner, R.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

Svenson, R. H.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Taddeucci, A.

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

Tatsis, G. P.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

ten Bosch, J. J.

J. R. Zijp, J. J. ten Bosch, R. A. J. Groenhuis, “HeNe-laser light scattering by human dental enamel,” J. Dent. Res. 22, 1891–1898 (1995).
[CrossRef]

J. R. Zijp, J. J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 22, 533–534 (1994).
[CrossRef]

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

R. A. Bolt, J. J. ten Bosch, “Method for measuring position-dependent volume reflection,” Appl. Opt. 32, 4641–4645 (1993).
[CrossRef] [PubMed]

R. A. J. Groenhuis, J. J. ten Bosch, H. A. Ferwerda, “Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
[CrossRef] [PubMed]

Tuntelder, J.R.

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9.

Wilson, B. C.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2313 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE1065, 115–122 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th Ed. (Pergamon, Oxford, 1980), p. 42.

Zaccanti, G.

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

Zijp, J. R.

J. R. Zijp, J. J. ten Bosch, R. A. J. Groenhuis, “HeNe-laser light scattering by human dental enamel,” J. Dent. Res. 22, 1891–1898 (1995).
[CrossRef]

J. R. Zijp, J. J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 22, 533–534 (1994).
[CrossRef]

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

Appl. Opt. (4)

J. Biomed. Opt. (1)

A. Taddeucci, F. Martelli, M. Barilli, M. Ferrari, G. Zaccanti, “Optical properties of brain tissue,” J. Biomed. Opt. 1, 117–123 (1996).
[CrossRef] [PubMed]

J. Dent. Res. (1)

J. R. Zijp, J. J. ten Bosch, R. A. J. Groenhuis, “HeNe-laser light scattering by human dental enamel,” J. Dent. Res. 22, 1891–1898 (1995).
[CrossRef]

Lasers Life Sci. (1)

R. Splinter, G.A. Nanney, L. Littmann, C. H. Chuang, R. H. Svenson, J.R. Tuntelder, G. P. Tatsis, “Monitoring tissue optical characteristics in-situ using a CCD camera,” Lasers Life Sci. 6, 15–25 (1993).
[CrossRef]

Opt. Eng. (1)

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

Other (5)

M. Born, E. Wolf, Principles of Optics, 6th Ed. (Pergamon, Oxford, 1980), p. 42.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9.

Commission Internationale de ’l Eclairage, International Lighting Vocabulary (Bureau Central de la Commission Electrotechnique Internationale, Geneva, Switzerland, 1987).

A. Kienle, L. Lilge, M. S. Patterson, B. C. Wilson, R. Hibst, R. Steiner, “Investigation of multi-layered tissue with in-vivo reflectance measurements,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 212–221.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE1065, 115–122 (1989).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Experimental setups used by several authors: (a) Groenhuis et al.,1 (b) Patterson et al.,2 (c) Bolt and ten Bosch,3 (d) Kienle et al.,4 (e) Splinter et al. 5

Fig. 2
Fig. 2

Lambertian direction distribution of reemitted radiation.

Fig. 3
Fig. 3

Geometry of the single-scattered light calculation.

Fig. 4
Fig. 4

Distribution ϕ(θ) of single-scattered light as calculated by Eq. (8).

Fig. 5
Fig. 5

Geometry used for the Monte Carlo calculations, which defines the vectors ρ and E and the angles θ and ϕ.

Fig. 6
Fig. 6

Radiant existence M e (in arbitrary units) as a function of the distance ρ (expressed in inverse scattering mean free paths).

Fig. 7
Fig. 7

Distribution of the photons escaping within 5° from the N ρ plane at ρ = 0–0.1, ρ = 1, ρ= 10, and ρ = 100 for the case of g = 0.00 and n = 1.00.

Fig. 8
Fig. 8

Distributions of the photons escaping within 5° from the N ρ plane at ρ = 0–0.1, ρ = 1, ρ = 10 and ρ = 100 for all six simulations. The distributions have been smoothed.

Fig. 9
Fig. 9

Fraction of the number of photons measured by a detector with a CA of 2θ as a function of θ. The curves from the simulation with g = 0.00 and n =1.00 are shown for values of ρ = 0–0.1, ρ = 1, ρ = 1, ρ 10, and ρ = 100. The corresponding curve for the Lambertian distribution is shown.

Fig. 10
Fig. 10

Error function G (θ), which expresses the error made when the radiant exitance M e is measured with a detector with a CA of 2θ and assuming that the reemitted radiation obeys a Lambertian distribution.

Fig. 11
Fig. 11

Ratio of the number of counted photons simulated and predicted by Patterson et al.2 (Sim/Theor) and first moments of cos θ, both as functions of the distance ρ (expressed in inverse scattering mean free paths). The long-dashed lines indicate the expected value 1.0. The short-dashed lines indicate the value of M 1,cos θ for a Lambertian distribution.

Fig. 12
Fig. 12

First and second moments of cos ϕ as functions of the distance ρ (expressed in inverse scattering mean free paths). The dashed lines indicate the values of M 1,cos ϕ and M 2,cos ϕ for a Lambertian distribution.

Tables (2)

Tables Icon

Table 1 Ranges of the Radius ρ at which Photons were Detecteda

Tables Icon

Table 2 Fraction of the Reemitted Light that is detected by the Setup Used by Groenhuis et al.1 as a function of the Distance ρ for the Cases of g = 0.90 and n = 1.33a

Equations (14)

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

Meρ=M0z02πz02+ρ2μeff+1z02+ρ21/2×exp-μeffz02+ρ21/2,
z0=s1-g-1, μeff=3aa+s1-g1/2,
Meρ=M0z02πz02+ρ23/2.
Φz=Φ0 exp-sz.
Φzdz s Qθscatt dθ.
Qθ=sin θ2.
exp-ρs/sin θ.
Φdρθ=Φ0scos θ2exp-ρs1+cos θ/sinθ dρ dθ.
Φρ=0-0.1θ=Φ0scos θ sin θ dθ2 1+cos θ×1-exp-0.1s1+cos θ/sin θ.
Mi,cos ϕ=0πdϕ 0π/2dθ sin θ ϕθ, ϕcosi ϕ0πdϕ 0π/2dθ sin θ Φθ, ϕ,
Mi,cos θ=0πdϕ 0π/2dθ sin θ ϕθ, ϕcosi θ0πdϕ 0π/2dθ sin θ Φθ, ϕ,
Fθ=θ=0°θdθϕθθ=0°90°dθϕθ.
Gθ=FsimulatedθFLambertianθ.
Fθ  0.5-0.5n=05 anPncos 2θ,

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