Abstract

The position dependence of volume reflection caused by the illumination of a turbid material by a pencil beam of light yields information about the optical parameters of that material. Existing methods to measure the position dependence of the volume-reflection profile usually require scanning the sample surface and are hardly applicable to the area near the illuminating pencil beam. This paper describes an experimental set up based on a two-dimensional CCD camera with 14-bit dynamic range and a spatial resolution down to 20 μm. As a demonstration of its use, measurements are compared with theoretical results from the random-walk and diffusion theories. The conclusions are made that the equipment is suitable for measuring close to the illuminating beam without the need for scanning and that it gives an indication in terms of the product of radial distance toward the center of the beam and reduced scattering coefficient (rμs) for the area where the theoretical results presented are valid.

© 1993 Optical Society of America

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References

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  1. A. Consortini, R. A. Elliott, feature eds., Propagation and Scattering in the Atmosphere, Part 2, Appl. Opt.27, 2375–2546 (1988).
  2. S. G. Jennings, “Backscatter and extinction measurements in cloud and drizzle at CO2 laser wavelengths,” Appl. Opt. 15, 2499–2505 (1986).
    [Crossref]
  3. T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
    [Crossref]
  4. M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
    [Crossref]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  6. M. Kerker, ed., Selected Papers on Light Scattering, Proc. Spc. Photo-Opt. Instrum. Eng.951 (1988).
  7. J. C. Garland, D. B. Tanner, eds., Electrical Transport and Optical Properties of Inhomogeneous Media (American Institute of Physics, New York, 1978).
  8. R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
    [Crossref]
  9. 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. 16, 2463–2467 (1983).
    [Crossref]
  10. R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
    [Crossref] [PubMed]
  11. 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. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).
  12. M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 31, 4474–4476 (1991).
    [Crossref]
  13. H. J. Trodahl, R. G. Buckley, S. Brown, “Diffusive transport of light in sea ice,” Appl. Opt. 26, 3005–3011 (1987).
    [Crossref] [PubMed]
  14. H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
    [Crossref]
  15. R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. Greve, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport. Part I: theory,” Appl. Opt. 32, 426–434 (1993).
    [Crossref] [PubMed]
  16. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), formula 8.486.14, p. 970.

1993 (1)

1991 (3)

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[Crossref]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 31, 4474–4476 (1991).
[Crossref]

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

1990 (1)

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

1987 (2)

1986 (1)

S. G. Jennings, “Backscatter and extinction measurements in cloud and drizzle at CO2 laser wavelengths,” Appl. Opt. 15, 2499–2505 (1986).
[Crossref]

1983 (2)

R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
[Crossref]

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. 16, 2463–2467 (1983).
[Crossref]

Aarnoudse, J. G.

Berndt, K. W.

Bonner, R. F.

Borsboom, P. C. F.

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

Brown, S.

Buckley, R. G.

Dassel, A. C. M.

de Mul, F. F. M.

Ferwerda, H. A.

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. 16, 2463–2467 (1983).
[Crossref]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
[Crossref]

Graaff, R.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), formula 8.486.14, p. 970.

Greve, J.

Groenhuis, R. A. J.

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. 16, 2463–2467 (1983).
[Crossref]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
[Crossref]

Havlin, S.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jennings, S. G.

S. G. Jennings, “Backscatter and extinction measurements in cloud and drizzle at CO2 laser wavelengths,” Appl. Opt. 15, 2499–2505 (1986).
[Crossref]

Koelink, M. H.

Kortsmit, W. J. P. M.

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

Lakowicz, J. R.

Moes, C. J.

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

Moulton, J. D.

Nossal, R.

Patterson, M. S.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[Crossref]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 31, 4474–4476 (1991).
[Crossref]

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. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

Prahl, S. A.

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), formula 8.486.14, p. 970.

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. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

ten Bosch, J. J.

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

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. 16, 2463–2467 (1983).
[Crossref]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
[Crossref]

Trodahl, H. J.

van der Burgt, T. P.

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

van Gemert, M. J. C.

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

van Marie, J.

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

van Staveren, H. J.

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

Weiss, G. H.

Wilson, B. C.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 31, 4474–4476 (1991).
[Crossref]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[Crossref]

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. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

Wyman, D. R.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[Crossref]

Zijlstra, W. G.

Appl. Opt. (7)

S. G. Jennings, “Backscatter and extinction measurements in cloud and drizzle at CO2 laser wavelengths,” Appl. Opt. 15, 2499–2505 (1986).
[Crossref]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 16, 2456–2462 (1983).
[Crossref]

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. 16, 2463–2467 (1983).
[Crossref]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 31, 4474–4476 (1991).
[Crossref]

H. J. Trodahl, R. G. Buckley, S. Brown, “Diffusive transport of light in sea ice,” Appl. Opt. 26, 3005–3011 (1987).
[Crossref] [PubMed]

H. J. van Staveren, C. J. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 31, 4507–4514 (1991).
[Crossref]

R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. Greve, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport. Part I: theory,” Appl. Opt. 32, 426–434 (1993).
[Crossref] [PubMed]

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

J. Prosthet. Dent. (1)

T. P. van der Burgt, J. J. ten Bosch, P. C. F. Borsboom, W. J. P. M. Kortsmit, “A comparison of new and conventional methods for quantification of tooth colour,” J. Prosthet. Dent. 8, 155–162 (1990).
[Crossref]

Lasers Med. Sci. (1)

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue II. Optical properties of tissue and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[Crossref]

Other (6)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

M. Kerker, ed., Selected Papers on Light Scattering, Proc. Spc. Photo-Opt. Instrum. Eng.951 (1988).

J. C. Garland, D. B. Tanner, eds., Electrical Transport and Optical Properties of Inhomogeneous Media (American Institute of Physics, New York, 1978).

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. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), formula 8.486.14, p. 970.

A. Consortini, R. A. Elliott, feature eds., Propagation and Scattering in the Atmosphere, Part 2, Appl. Opt.27, 2375–2546 (1988).

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Figures (4)

Fig. 1
Fig. 1

Experiment setup. The radiance factor is measured as a function of r, the distance from the incident beam.

Fig. 2
Fig. 2

Radiance profile L(r) and L(r)r2: (a) samples I10. and L08, r < 1.6 mm; (b) samples I10 and 1I25, r < 6 mm. Ordinate units are the same in both figures. Optical characteristics of the samples are given in Table 1.

Fig. 3
Fig. 3

L ( r ) r for the same two samples as shown in Fig. 2(a).

Fig. 4
Fig. 4

Scaling of radiance profiles with μs according to Graaff et al.,15 i.e., L(rs2 versus rμs for six samples. Lxx, the group of latex samples; Ixx, the group of intralipid samples.

Tables (3)

Tables Icon

Table 1 Optical Properties of Samples Used to Measure Position-Dependent Volume Reflection

Tables Icon

Table 2 Slope and Offset of the Linear Part of ln[L(r)r2] versus r, as Determined for Large r From Theorya (and Sample Characteristics) and Experiments

Tables Icon

Table 3 Slope and Offset for the Area Where ln [ L ( r ) r ] versus r Shows a Linear Behaviora

Equations (9)

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

L ( r ) = i = 1 C i 1 r r K 1 ( λ i r ) ,
L ( r ) = z 0 2 π exp [ μ eff ( z 0 2 + r 2 ) 1 / 2 ] z 0 2 + r 2 [ μ eff + 1 ( r 2 + z 0 2 ) 1 / 2 ] ,
L ( r ) = z 0 exp ( μ eff r ) 2 π r 2 ( μ eff + 1 r ) .
L ( ρ ) 1 4 π ρ [ exp ( ρ 6 μ ) ρ ( ρ 2 + 4 ) 1 / 2 × exp { [ 6 μ ( ρ 2 + 4 ) ] 1 / 2 } ] exp ( 2 μ ) .
L ( ρ ) 6 μ 4 π ρ 2 exp ( 2 μ ) exp ( ρ 6 μ ) .
L ( r ) C 1 r 1 / 2 exp ( C 2 r ) .
L ( r ) = i = 1 C i 1 r r K 1 ( λ i r ) ,
( z z ) m [ z ν K ν ( z ) ] = ( 1 ) m z υ m K ν m ( z )
L ( r ) = i = 1 C i 1 λ i K 0 ( λ i r ) .

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