Abstract

The transfer function of a turbid medium such as biological tissue provides a method of analyzing the spatial resolution of a time-resolved tissue imaging system. A method is presented of calculating the transfer function with the use of a Monte Carlo simulation. The model allows the computation of the time-resolved line-spread function of a sample of thickness d from a simulation of thickness d/2 by use of reciprocity under certain conditions, and the transfer function can then be computed from the line-spread function. Results with this method agree with previously published theoretical and experimental results.

© 1996 Optical Society of America

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  1. J. Hebden, R. Kruger, “Transillumination imaging performance: spatial resolution simulation studies,” Med. Phys. 17, 41–47 (1990).
    [CrossRef] [PubMed]
  2. L. Wang, X. Liang, P. Ho, R. Alfano, “Time and Fourier-space gated optical imaging and thick turbid media,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 2–5 (1993).
    [CrossRef]
  3. K. Yoo, B. Das, R. Alfano, “Imaging of a translucent object hidden in a highly scattering medium from the early portion of the diffuse component of a transmitted laser pulse,” Opt. Lett. 17, 958–960 (1992).
    [CrossRef] [PubMed]
  4. Y. Chen, “Characterization of the image resolution for the first-arriving-light method,” Appl. Opt. 33, 2544–2552 (1994).
    [CrossRef] [PubMed]
  5. J. Hebden, “A time-of-flight breast imaging system: spatial resolution performance,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 225–231 (1991).
    [CrossRef]
  6. K. Carson, Y. Wickramasinghe, P. Rolfe, “Experimental study of the spatial resolution for time resolved near infrared imaging,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 10–19 (1993).
    [CrossRef]
  7. A. Gandjbakhche, R. Nossal, R. Bonner, “Theoretical study of resolution limits for time resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
    [CrossRef]
  8. L. Wang, S. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in StandardC, (M. D. Andersen Cancer Center, University of Texas, Houston, Tex., 1992).
  9. W. Cheong, S. Prahl, A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  10. V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
    [CrossRef] [PubMed]
  11. H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
    [CrossRef] [PubMed]
  12. J. Hebden, “Evaluating the spatial resolution performance of a time-resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
    [CrossRef] [PubMed]
  13. F. Liu, K. Yoo, R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissue,” Appl. Opt. 32, 554–558 (1993).
    [CrossRef] [PubMed]
  14. E. DeHaller, C. Depeursinge, “Time resolved breast transillumination: Monte Carlo simulation and comparison with experimental results,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc Soc. Photo-Opt. Instrum. Eng.1888, 191–200 (1993).
    [CrossRef]
  15. E. DeHaller, C. Depeursinge, “Time-resolved breast transillumination: comparison of theoretical and experimental image resolution,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 2–9 (1993).
    [CrossRef]

1994 (1)

1993 (1)

1992 (2)

1991 (1)

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

1990 (3)

J. Hebden, R. Kruger, “Transillumination imaging performance: spatial resolution simulation studies,” Med. Phys. 17, 41–47 (1990).
[CrossRef] [PubMed]

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

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Alfano, R.

Bonner, R.

A. Gandjbakhche, R. Nossal, R. Bonner, “Theoretical study of resolution limits for time resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
[CrossRef]

Carson, K.

K. Carson, Y. Wickramasinghe, P. Rolfe, “Experimental study of the spatial resolution for time resolved near infrared imaging,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 10–19 (1993).
[CrossRef]

Chen, Y.

Cheong, W.

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

Das, B.

Davies, E.

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

DeHaller, E.

E. DeHaller, C. Depeursinge, “Time resolved breast transillumination: Monte Carlo simulation and comparison with experimental results,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc Soc. Photo-Opt. Instrum. Eng.1888, 191–200 (1993).
[CrossRef]

E. DeHaller, C. Depeursinge, “Time-resolved breast transillumination: comparison of theoretical and experimental image resolution,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 2–9 (1993).
[CrossRef]

Depeursinge, C.

E. DeHaller, C. Depeursinge, “Time-resolved breast transillumination: comparison of theoretical and experimental image resolution,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 2–9 (1993).
[CrossRef]

E. DeHaller, C. Depeursinge, “Time resolved breast transillumination: Monte Carlo simulation and comparison with experimental results,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc Soc. Photo-Opt. Instrum. Eng.1888, 191–200 (1993).
[CrossRef]

Frank, G.

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Gandjbakhche, A.

A. Gandjbakhche, R. Nossal, R. Bonner, “Theoretical study of resolution limits for time resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
[CrossRef]

Hebden, J.

J. Hebden, “Evaluating the spatial resolution performance of a time-resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

J. Hebden, R. Kruger, “Transillumination imaging performance: spatial resolution simulation studies,” Med. Phys. 17, 41–47 (1990).
[CrossRef] [PubMed]

J. Hebden, “A time-of-flight breast imaging system: spatial resolution performance,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 225–231 (1991).
[CrossRef]

Ho, P.

L. Wang, X. Liang, P. Ho, R. Alfano, “Time and Fourier-space gated optical imaging and thick turbid media,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 2–5 (1993).
[CrossRef]

Jackson, P.

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

Jacques, S.

L. Wang, S. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in StandardC, (M. D. Andersen Cancer Center, University of Texas, Houston, Tex., 1992).

Key, H.

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

Kruger, R.

J. Hebden, R. Kruger, “Transillumination imaging performance: spatial resolution simulation studies,” Med. Phys. 17, 41–47 (1990).
[CrossRef] [PubMed]

Liang, X.

L. Wang, X. Liang, P. Ho, R. Alfano, “Time and Fourier-space gated optical imaging and thick turbid media,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 2–5 (1993).
[CrossRef]

Liu, F.

Nossal, R.

A. Gandjbakhche, R. Nossal, R. Bonner, “Theoretical study of resolution limits for time resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
[CrossRef]

Patterson, M.

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Peters, V.

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Prahl, S.

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

Rolfe, P.

K. Carson, Y. Wickramasinghe, P. Rolfe, “Experimental study of the spatial resolution for time resolved near infrared imaging,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 10–19 (1993).
[CrossRef]

Wang, L.

L. Wang, S. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in StandardC, (M. D. Andersen Cancer Center, University of Texas, Houston, Tex., 1992).

L. Wang, X. Liang, P. Ho, R. Alfano, “Time and Fourier-space gated optical imaging and thick turbid media,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 2–5 (1993).
[CrossRef]

Welch, A.

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

Wells, P.

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

Wickramasinghe, Y.

K. Carson, Y. Wickramasinghe, P. Rolfe, “Experimental study of the spatial resolution for time resolved near infrared imaging,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 10–19 (1993).
[CrossRef]

Wyman, D.

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Yoo, K.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

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

Med. Phys. (2)

J. Hebden, R. Kruger, “Transillumination imaging performance: spatial resolution simulation studies,” Med. Phys. 17, 41–47 (1990).
[CrossRef] [PubMed]

J. Hebden, “Evaluating the spatial resolution performance of a time-resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (2)

V. Peters, D. Wyman, M. Patterson, G. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

H. Key, E. Davies, P. Jackson, P. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol. 36, 579–590 (1991).
[CrossRef] [PubMed]

Other (7)

L. Wang, X. Liang, P. Ho, R. Alfano, “Time and Fourier-space gated optical imaging and thick turbid media,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888, 2–5 (1993).
[CrossRef]

J. Hebden, “A time-of-flight breast imaging system: spatial resolution performance,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 225–231 (1991).
[CrossRef]

K. Carson, Y. Wickramasinghe, P. Rolfe, “Experimental study of the spatial resolution for time resolved near infrared imaging,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 10–19 (1993).
[CrossRef]

A. Gandjbakhche, R. Nossal, R. Bonner, “Theoretical study of resolution limits for time resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2135, 176–185 (1994).
[CrossRef]

L. Wang, S. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in StandardC, (M. D. Andersen Cancer Center, University of Texas, Houston, Tex., 1992).

E. DeHaller, C. Depeursinge, “Time resolved breast transillumination: Monte Carlo simulation and comparison with experimental results,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc Soc. Photo-Opt. Instrum. Eng.1888, 191–200 (1993).
[CrossRef]

E. DeHaller, C. Depeursinge, “Time-resolved breast transillumination: comparison of theoretical and experimental image resolution,” in Quantification and Localization Using Diffuse Photons in a Highly Scattering Medium, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2082, 2–9 (1993).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Geometry for the product-of-probabilities method. The vectors q1A, q1B, and q2 each represent a point and a direction of a photon. The tissue is split along the plane z = d/2.

Fig. 2
Fig. 2

Graphical representation of the characterization of the photon exit direction. (a) Bottom view. The arrows represent different directions s, and the corresponding values for β are indicated for a particular rxy. (b) Three-dimensional view. The values for β are distributed into strips ranging from −1 to 1.

Fig. 3
Fig. 3

Time-resolved LSF for a thickness of 1 cm. The optical properties used in the simulation are (σs = 100 cm−1, (σa = 0.5 cm−1, and g = 0.97.

Fig. 4
Fig. 4

Time-resolved LSF for a thickness of 2 cm. The optical properties are the same as those in Fig. 3.

Fig. 5
Fig. 5

Time-resolved MTF for the 1-cm case.

Fig. 6
Fig. 6

Time-resolved MTF for the 2-cm case.

Fig. 7
Fig. 7

Spatial frequency versus detector time gate for the 1-cm case.

Fig. 8
Fig. 8

Spatial frequency versus detector time gate for the 2-cm case.

Tables (1)

Tables Icon

Table 1 Percentages of Photons Crossing the Midplane More Than Oncea

Equations (14)

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q 0 = ( 0 , 0 , 0 , 0 , 0 , 1 ) , q 1 A = ( x , y , d / 2 , μ x , μ y , μ z ) , q 1 B = ( x , y , d / 2 , - μ x , - μ y , μ z ) , q 2 = ( 0 , 0 , d , 0 , 0 , 1 ) .
P ( q 2 q 0 ) = P ( q 1 A q 0 ) P ( q 2 q 1 A ) d q 1 A .
P ( q 2 q 1 A ) = P ( q 1 B q 2 ) .
P ( q 1 B q 2 ) = P ( q 1 B q 0 )
P ( q 2 q 0 ) = P ( q 1 A q 0 ) P ( q 1 B q 0 ) d q ,
P ( q 2 q 0 ) = - 1 1 - 1 1 P ( q 1 A q 0 ) P ( q 1 B q 0 ) d μ x d μ y .
t 2 + t 1 τ ,
P ( q 2 , τ q 0 , 0 ) = - 1 1 - 1 1 0 τ 0 τ - t 1 P ( q 1 A , t 1 q 0 , 0 ) × P ( q 1 B , t 2 q 0 , 0 ) d t 2 d t 1 d μ x d μ y .
P ( q 1 A q 0 ) = P ( q 1 A q 0 ) ,
R θ = [ cos θ sin θ 0 0 0 0 - sin θ cos θ 0 0 0 0 0 0 1 0 0 0 0 0 0 cos θ sin θ 0 0 0 0 - sin θ cos θ 0 0 0 0 0 0 1 ] .
r x y = x x ^ + y y ^ ,             s = μ x x ^ + μ y y ^ + μ z z ^ .
β = r x y · s r x y · s = ( x x ^ + y y ^ x 2 + y 2 ) · ( μ x x ^ + μ y y ^ + μ z z ^ ) = x μ x + y μ y x 2 + y 2 .
β = - 1 β = + 1 , β = - 1 + Δ β β = + 1 - Δ β , β = 0 β = 0 , β = + 1 - Δ β β = - 1 + Δ β , β = + 1 β = - 1.
P ( q 2 , τ q 0 , 0 ) = β i = 1 N β t n = 1 N t t m = 1 N t - t n T ( r i , β i , t n ) T ( r i , N β - β i , t m ) ,

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