Abstract

We have developed a methodology that can be used in reconstruction algorithms to quantify the optical coefficients and the geometrical cross section of a weakly abnormal optical target embedded in an otherwise homogeneous medium. This novel procedure uses different time-dependent point-spread functions to analyze the diffusive and absorptive contrasts obtained from time-of-flight measurements. Data obtained from time-resolved transillumination of a tissuelike phantom are used to test the accuracy of this new deconvolution methodology.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Chance, R. R. Alfano, eds., Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389 (1995).
  2. R. R. Alfano, ed., Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, Proc. SPIE2387 (1995).
  3. J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
    [CrossRef]
  4. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Biol. Med. 42, 841–853 (1997).
    [CrossRef]
  5. T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical tomography,” J. Biomed. Opt. 1, 342–355 (1996).
    [CrossRef] [PubMed]
  6. S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997).
    [CrossRef] [PubMed]
  7. H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
    [CrossRef]
  8. M. A. O’Leary, D. A. Boas, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing photon tomography,” Opt. Lett. 20, 426–428 (1995).
    [CrossRef]
  9. J. C. Hebden, R. A. Kruger, K. S. Wong, “Time-resolved imaging through a highly scattering medium,” Appl. Opt. 30, 788–794 (1991).
    [CrossRef] [PubMed]
  10. J. A. Moon, J. Reintjes, “Image resolution by use of multiply scattered light,” Opt. Lett. 19, 521–523 (1994).
    [CrossRef] [PubMed]
  11. A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).
  12. J. C. Hebden, D. J. Hall, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Med. Phys. 22, 201–208 (1995).
    [CrossRef] [PubMed]
  13. S. R. Arridge, “Photon measurement density functions: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
    [CrossRef] [PubMed]
  14. J. C. Hebden, S. R. Arridge, “Imaging through scattering media using an analytical model of perturbation amplitudes in the time-domain,” Appl. Opt. 35, 6788–6796 (1996).
    [CrossRef] [PubMed]
  15. A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
    [CrossRef] [PubMed]
  16. V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling argument,” Med. Phys. 23, 1857–1861 (1996).
    [CrossRef] [PubMed]
  17. A. H. Gandjbakhche, G. H. Weiss, “Random walk and diffusion-like model of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1995), Vol. 34, pp. 333–402.
    [CrossRef]
  18. A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
    [CrossRef]
  19. A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
    [CrossRef]

1997 (3)

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Biol. Med. 42, 841–853 (1997).
[CrossRef]

S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997).
[CrossRef] [PubMed]

1996 (5)

1995 (3)

1994 (2)

J. A. Moon, J. Reintjes, “Image resolution by use of multiply scattered light,” Opt. Lett. 19, 521–523 (1994).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).

1993 (1)

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

1992 (1)

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
[CrossRef]

1991 (1)

Arridge, S. R.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Biol. Med. 42, 841–853 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, “Imaging through scattering media using an analytical model of perturbation amplitudes in the time-domain,” Appl. Opt. 35, 6788–6796 (1996).
[CrossRef] [PubMed]

S. R. Arridge, “Photon measurement density functions: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

Boas, D. A.

Bonner, R. F.

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
[CrossRef]

Chernomordik, V.

V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling argument,” Med. Phys. 23, 1857–1861 (1996).
[CrossRef] [PubMed]

Delpy, D. T.

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
[CrossRef]

J. C. Hebden, D. J. Hall, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

Fantini, S.

Gandjbakhche, A. H.

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling argument,” Med. Phys. 23, 1857–1861 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
[CrossRef]

A. H. Gandjbakhche, G. H. Weiss, “Random walk and diffusion-like model of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1995), Vol. 34, pp. 333–402.
[CrossRef]

Gratton, E.

Hall, D. J.

J. C. Hebden, D. J. Hall, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

Hebden, J. C.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Biol. Med. 42, 841–853 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, “Imaging through scattering media using an analytical model of perturbation amplitudes in the time-domain,” Appl. Opt. 35, 6788–6796 (1996).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

J. C. Hebden, R. A. Kruger, K. S. Wong, “Time-resolved imaging through a highly scattering medium,” Appl. Opt. 30, 788–794 (1991).
[CrossRef] [PubMed]

Jiang, H. B.

Kruger, R. A.

Moon, J. A.

Nossal, R.

V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling argument,” Med. Phys. 23, 1857–1861 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
[CrossRef]

O’Leary, M. A.

Osterberg, U. L.

Page, D. L.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical tomography,” J. Biomed. Opt. 1, 342–355 (1996).
[CrossRef] [PubMed]

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Reintjes, J.

Sevick-Muraca, E. M.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical tomography,” J. Biomed. Opt. 1, 342–355 (1996).
[CrossRef] [PubMed]

Troy, T. L.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical tomography,” J. Biomed. Opt. 1, 342–355 (1996).
[CrossRef] [PubMed]

Walker, S. A.

Weiss, G. H.

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. 35, 1767–1774 (1996).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

A. H. Gandjbakhche, G. H. Weiss, “Random walk and diffusion-like model of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1995), Vol. 34, pp. 333–402.
[CrossRef]

Wong, K. S.

Yodh, A. G.

Appl. Opt. (5)

J. Biomed. Opt. (1)

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical tomography,” J. Biomed. Opt. 1, 342–355 (1996).
[CrossRef] [PubMed]

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

J. Stat. Phys. (1)

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
[CrossRef]

Med. Phys. (3)

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities embedded in tissues,” Med. Phys. 22, 185–191 (1994).

J. C. Hebden, D. J. Hall, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling argument,” Med. Phys. 23, 1857–1861 (1996).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Biol. Med. (2)

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Biol. Med. 42, 825–840 (1997).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Biol. Med. 42, 841–853 (1997).
[CrossRef]

Phys. Rev. E (1)

A. H. Gandjbakhche, R. F. Bonner, R. Nossal, G. H. Weiss, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

Other (3)

B. Chance, R. R. Alfano, eds., Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389 (1995).

R. R. Alfano, ed., Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, Proc. SPIE2387 (1995).

A. H. Gandjbakhche, G. H. Weiss, “Random walk and diffusion-like model of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1995), Vol. 34, pp. 333–402.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Comparison between (a) absorptive and (b) scattering perturbations [Eq. (1) ff.] of the diffusion model of Arridge8 (solid curves) and the random-walk model (dotted curves) as a function of the gating time Δt for a detector collinear with the source and point s.

Fig. 2
Fig. 2

Behavior of absorbing (dotted curve) and scattering (dotted–dashed curve) contrasts and their sum (solid curve) as a function of the gating time Δt. At short Δt the scattering perturbation is dominant, whereas at large Δt the total contrast is exclusively dependent on the absorptive perturbation.

Fig. 3
Fig. 3

Time-of-flight curve of maximum intensity obtained in the line-scan measurement (solid curve; see text). The dotted curve is the theoretical fit, from which the optical properties of the background are calculated.

Fig. 4
Fig. 4

Experimental total contrast (solid curves) as a function of position x (fan geometry) at Δt = (a) 800, (b) 900, (c) 1500, and (d) 2500 ps for N a = 4. The dotted curves are the theoretical fits to the data from Eq. (1). Values of fitting parameters are presented in Section 3. Systematic data fitting to contrast functions for a set of Δt enables one to obtain both the optical coefficients and an estimate for the size of the inclusion (see text).

Equations (20)

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

C s ,   r | r 0 ,   n = p n r | r 0 - q n s ,   r | r 0 p n r | r 0 = 1 - q n s ,   r | r 0 p n r | r 0 ,
C A r | r 0 ,   n = η   W s ,   r ,   r 0 n + 1 p n r | r 0 ,
C D s ,   r | r 0 ,   n = W s ,   r ,   r 0 n - W s ,   r ,   r 0 n - 1 p n r | r 0   Δ n D .
μ     μ a μ s ,     n     μ s ct ,     r     r ¯ μ s 2 , N     T μ s 2 ,     η     μ ˜ a - μ a μ s ,
Δ τ = τ 1 - τ 2 = d 2 μ ˜ s - μ s 2 c ,
Δ n D = c μ s Δ τ = d 2 μ s μ ˜ s - μ s 2 .
W s ,   r ,   r 0 n = 9 16 π 5 / 2 Δ n 3 / 2 × k = - m = - F n α - k ,   β - m ,   x + F n α + k ,   β + m ,   x - F n α + k ,   β - m ,   x - F n α - k ,   β + m ,   x ,
Δ n = μ s c Δ t , F n a ,   b = 1 a + 1 b exp - a + b 2 Δ n , α ± k = ³ / s 1 2 + s 3 + 2 kN ± 1 2 1 / 2 , β ± m ,   x = ³ / x - s 1 2 + N - s 3 + 2 mN ± 1 2 1 / 2 .
σ = 0.816 c Δ t μ s 1 / 2 1 - s 3 ¯ T s 3 ¯ T 1 / 2 ,
I f x ,   Δ t I t Δ t exp - 3 μ s x 2 / 4 c Δ t .
C T x ,   Δ t = 1 - I f x ,   Δ t I 0 f x 0 ,   Δ t p Δ t x 0 p Δ t x × W t s ,   x Δ t W f s ,   x Δ t p Δ t x p Δ t 0 ,
ĥ ξ = n = 0   h n exp - ξ n ,
Q ˆ ξ = 1 - ψ ˆ ξ p ˆ ξ s | r 0 p ˆ ξ r | s ψ ˆ ξ + 1 - ψ ˆ ξ p ˆ ξ s | s .
Q ˆ ξ = Δ n D ξ p ˆ ξ s | r 0 p ˆ ξ r | s .
I 0 f x ,   Δ t = I 0 t 0 ,   Δ t p Δ t x p Δ t 0 = I 0 t 0 ,   Δ t exp - 3 μ s x 2 / 4 c Δ t ,
I 0 f x ,   Δ t = I 0 f x 0 ,   Δ t p Δ t x p Δ t x 0 = I 0 f x 0 ,   Δ t exp - 3 μ s x 2 - x 0 2 4 c Δ t .
δ I f x ,   Δ t I 0 f x ,   Δ t = 1 - I f x ,   Δ t I 0 f x ,   Δ t = η eff W f s ,   x n p n x ,
C T x ,   Δ t = δ I t x ,   Δ t I 0 t Δ t = η eff W t s ,   x Δ t p Δ t 0 = K f η eff W f s ,   x n p n x ,
K f = W t s ,   x Δ t p Δ t x W f s ,   x Δ t p Δ t 0 .
C T x ,   Δ t = K f 1 - I f x ,   Δ t I 0 f x 0 ,   Δ t I 0 f x 0 ,   Δ t I 0 f x ,   Δ t = 1 - I f x ,   Δ t I 0 f x 0 ,   Δ t p Δ t x 0 p Δ t x × W t s ,   x Δ t W f s ,   x Δ t p Δ t x p Δ t 0 .

Metrics