Abstract

Measurements of the phase and modulation of amplitude-modulated light diffusely reflected by turbid media can be used to deduce absorption and scattering coefficients.

© 1991 Optical Society of America

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References

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  1. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  2. J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
    [CrossRef]
  3. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 340.
  4. J. D. Moulton, “Diffusion modelling of picosecond laser pulse propagation in turbid media,” M. Eng. thesis (McMaster University, Hamilton, Canada, 1990).
  5. C. J. M. Moes, M. J. C. van Gemert, W. M. Star, J. P. A. Marijnissen, S. A. Prahl, “Measurements and calculations of the energy fluence rate in a scattering and absorbing phantom at 633 nm,” Appl. Opt. 28, 2292–2296 (1989).
    [CrossRef] [PubMed]
  6. K. W. Brendt, H. Duerr, D. Palme, “Picosecond laser spectroscopy with avalanche photodiodes,” in Time Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 209–215 (1988).
  7. B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).
  8. B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed. (SPIE Institutes, Bellingham, Wash., 1990), Vol. IS6, pp. 219–232.

1989 (2)

1988 (1)

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Brendt, K. W.

K. W. Brendt, H. Duerr, D. Palme, “Picosecond laser spectroscopy with avalanche photodiodes,” in Time Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 209–215 (1988).

Chance, B.

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

B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).

Duerr, H.

K. W. Brendt, H. Duerr, D. Palme, “Picosecond laser spectroscopy with avalanche photodiodes,” in Time Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 209–215 (1988).

Farrell, T. J.

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed. (SPIE Institutes, Bellingham, Wash., 1990), Vol. IS6, pp. 219–232.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 340.

Gryczynski, I.

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Laczko, G.

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Lakowicz, J. R.

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Marijnissen, J. P. A.

Maris, M.

B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).

Moes, C. J. M.

Moulton, J. D.

J. D. Moulton, “Diffusion modelling of picosecond laser pulse propagation in turbid media,” M. Eng. thesis (McMaster University, Hamilton, Canada, 1990).

Palme, D.

K. W. Brendt, H. Duerr, D. Palme, “Picosecond laser spectroscopy with avalanche photodiodes,” in Time Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 209–215 (1988).

Patterson, M. S.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive 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 non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed. (SPIE Institutes, Bellingham, Wash., 1990), Vol. IS6, pp. 219–232.

Prahl, S. A.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 340.

Sorge, J.

B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).

Star, W. M.

Szmacinki, H.

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

van Gemert, M. J. C.

Wiczk, W.

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Wilson, B. C.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive 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 non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed. (SPIE Institutes, Bellingham, Wash., 1990), Vol. IS6, pp. 219–232.

Zhang, M. Z.

B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).

Appl. Opt. (2)

J. Photochem. Photobiol. B: Biol. (1)

J. R. Lakowicz, G. Laczko, I. Gryczynski, H. Szmacinki, W. Wiczk, “Gigahertz frequency-domain fluorometry: resolution of complex decays, picosecond processes and future developments,” J. Photochem. Photobiol. B: Biol. 2, 295–311 (1988).
[CrossRef]

Other (5)

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980), p. 340.

J. D. Moulton, “Diffusion modelling of picosecond laser pulse propagation in turbid media,” M. Eng. thesis (McMaster University, Hamilton, Canada, 1990).

K. W. Brendt, H. Duerr, D. Palme, “Picosecond laser spectroscopy with avalanche photodiodes,” in Time Resolved Laser Spectroscopy in Biochemistry, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.909, 209–215 (1988).

B. Chance, M. Maris, J. Sorge, M. Z. Zhang, “A phase modulation system for dual wavelength difference spectroscopy of hemoglobin deoxygenation in tissues,” in Time Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, 481–491 (1990).

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Applications in Photodynamic Therapy, C. J. Gomer, ed. (SPIE Institutes, Bellingham, Wash., 1990), Vol. IS6, pp. 219–232.

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Figures (4)

Fig. 1
Fig. 1

Diffusion-based calculations of lines of constant modulation (solid) and phase (dashed) for optical properties typical of soft tissues in the red and near infrared. The modulation frequency has been fixed at 400 MHz and the source–detector separation at 50 mm.

Fig. 2
Fig. 2

Plots of phase angle and modulation obtained for a scattering emulsion to which increasing amounts of India ink were added. The smooth curves were generated from solutions to Eqs. (4) and (5) and represent best estimates of the absorption and transport-scattering coefficients.

Fig. 3
Fig. 3

Plot of the best estimates of absorption and transport-scattering coefficients versus the relative amount of added ink. As expected the estimated values of μs are independent of the amount of added ink while the estimate of μa increases linearly.

Fig. 4
Fig. 4

Calculated lines of constant phase angle (solid) and effective steady-state attenuation coefficient (dashed) in the space defined by the tissue absorption and transport-scattering coefficients. The modulation frequency was fixed at 200 MHz and the source–detector separation (for the frequency domain) at 30 mm.

Equations (10)

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R ( ρ , t ) = z o ( 4 π D c ) 3 / 2 t 5 / 2 exp ( ρ 2 + z o 2 4 Dc t ) exp ( μ a c t ) ,
z o = [ ( 1 g ) μ s ] 1 ,
D [ 3 ( 1 g ) μ s ] 1
M ( ρ , f ) = ( 1 + ψ o 2 + 2 ψ i ) ( 1 / 2 ) ( 1 + ψ ) exp ( ψ ψ i ) ,
ϕ ( ρ , f ) = ψ r tan 1 ( ψ r 1 + ψ i ) ,
ψ o = { 3 [ μ a + ( 1 g ) μ s ] ( ρ 2 + z o 2 ) ( [ μ a c ] 2 + [ 2 π f ] 2 ) 1 / 2 c 1 } 1 / 2 ,
ψ r = ψ o sin ( θ 2 ) ,
ψ i = ψ o cos ( θ 2 ) ,
θ = tan 1 ( 2 π f μ a c ) ,
ψ = ψ o ( f = 0 ) = ψ i ( f = 0 ) = { 3 μ a [ μ a + ( 1 g ) μ s ] ( ρ 2 + z o 2 ) ] 1 / 2 .

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