Abstract

Diffuse optical reflection tomography is used to reconstruct absorption images from continuous-wave measurements of diffuse light re-emitted from a “semi-infinite” medium. The imaging algorithm is simple and fast and permits psuedo-3D images to be reconstructed from measurements made with a single source of light. Truly quantitative three-dimensional images will require modifications to the algorithm, such as incorporating measurements from multiple sources.

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References

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  1. A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48, 34-40 (1995).
    [CrossRef]
  2. S. R. Arridge and J. C. Hebden, "Optical Imaging in Medicine: II. Modelling and reconstruction," Phys. Med. Biol. 42, 841-854 (1997).
    [CrossRef]
  3. M. A. O'Leary, D. A. Boas, B. Chance and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography," Opt. Lett. 20, 426-428 (1995).
    [CrossRef]
  4. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue and M. S. Patterson, "Optical image reconstruction using frequency-domain data: Simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996).
    [CrossRef]
  5. M. V. Klibanov, T. R. Lucas and R. M. Frank, "A fast and accurate imaging algorithm in optical /diffusion tomography," Inverse Probl. 13, 1341-1361 (1997).
    [CrossRef]
  6. S. R. Arridge, "Forward and inverse problems in time-resolved infrared imaging," SPIE Proceedings IS11, 35-64 (1993).
  7. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  8. D. A. Boas, "A fundamental limitation of linearized algorithms for diffuse optical tomography," Opt. Express 1, 404-413 (1997).
    [CrossRef]
  9. X. D. Li, T. Durduran, A. G. Yodh, B. Chance and D. N. Pattanayak, "Diffraction tomography for biochemical imaging with diffuse-photon density waves," Opt. Lett. 22, 573-575 (1997).
    [CrossRef]
  10. X. D. Li, T. Durduran, A. G. Yodh, B. Chance and D. N. Pattanayak, "Diffraction tomography for biomedical imaging with diffuse photon density waves: errata," Opt. Lett. 22, 1198 (1997).
    [CrossRef]
  11. C. L. Matson, N. Clark, l. McMackin and J. S. Fender, "Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves," Appl. Opt. 36, 214-220 (1997).
    [CrossRef]
  12. C. L. Matson, "A diffraction tomographic model of the forward problem using diffuse photon density waves," Opt. Express 1, 6-11 (1997).
    [CrossRef]
  13. D. Boas, Diffuse Photon Probes of Structural and Dynamical Properties of Turbid Media: Theory and Biomedical Applications, A Ph.D. Dissertation in Physics, University of Pennsylvania, 1996.
  14. D. A. Boas, M. A. O'Leary, B. Chance and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications," Proc. Natl. Acad. Sci. USA 91, 4887-4891 (1994).
    [CrossRef]
  15. P. N. den Outer, T. M. Nieuwenhuizen and A. Lagendijk, "Location of objects in multiple-scattering media," J. Opt. Soc. Am. A 10, 1209-1218 (1993).
    [CrossRef]
  16. S. Feng, F. Zeng and B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
    [CrossRef]
  17. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
    [CrossRef]
  18. T. J. Farrell, M. S. Patterson and B. Wilson, "A diffusion theory model of spatially resolved, steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
    [CrossRef]

Other (18)

A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48, 34-40 (1995).
[CrossRef]

S. R. Arridge and J. C. Hebden, "Optical Imaging in Medicine: II. Modelling and reconstruction," Phys. Med. Biol. 42, 841-854 (1997).
[CrossRef]

M. A. O'Leary, D. A. Boas, B. Chance and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue and M. S. Patterson, "Optical image reconstruction using frequency-domain data: Simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996).
[CrossRef]

M. V. Klibanov, T. R. Lucas and R. M. Frank, "A fast and accurate imaging algorithm in optical /diffusion tomography," Inverse Probl. 13, 1341-1361 (1997).
[CrossRef]

S. R. Arridge, "Forward and inverse problems in time-resolved infrared imaging," SPIE Proceedings IS11, 35-64 (1993).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

D. A. Boas, "A fundamental limitation of linearized algorithms for diffuse optical tomography," Opt. Express 1, 404-413 (1997).
[CrossRef]

X. D. Li, T. Durduran, A. G. Yodh, B. Chance and D. N. Pattanayak, "Diffraction tomography for biochemical imaging with diffuse-photon density waves," Opt. Lett. 22, 573-575 (1997).
[CrossRef]

X. D. Li, T. Durduran, A. G. Yodh, B. Chance and D. N. Pattanayak, "Diffraction tomography for biomedical imaging with diffuse photon density waves: errata," Opt. Lett. 22, 1198 (1997).
[CrossRef]

C. L. Matson, N. Clark, l. McMackin and J. S. Fender, "Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves," Appl. Opt. 36, 214-220 (1997).
[CrossRef]

C. L. Matson, "A diffraction tomographic model of the forward problem using diffuse photon density waves," Opt. Express 1, 6-11 (1997).
[CrossRef]

D. Boas, Diffuse Photon Probes of Structural and Dynamical Properties of Turbid Media: Theory and Biomedical Applications, A Ph.D. Dissertation in Physics, University of Pennsylvania, 1996.

D. A. Boas, M. A. O'Leary, B. Chance and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications," Proc. Natl. Acad. Sci. USA 91, 4887-4891 (1994).
[CrossRef]

P. N. den Outer, T. M. Nieuwenhuizen and A. Lagendijk, "Location of objects in multiple-scattering media," J. Opt. Soc. Am. A 10, 1209-1218 (1993).
[CrossRef]

S. Feng, F. Zeng and B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
[CrossRef]

T. J. Farrell, M. S. Patterson and B. Wilson, "A diffusion theory model of spatially resolved, steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic illustration of the set-up for diffuse optical reflectance tomography. The phantom is 30 × 30 × 20 cm with μs ′ = 10.0 cm-1 and μa = 0.05 cm-1. The properties of the objects are given in the text.

Fig. 2
Fig. 2

Difference of the images obtained by the CCD camera without and with the absorbing objects. The absorbing objects cause the measured diffuse reflectance to decrease. The color scale is linear where red corresponds to maximum change and blue corresponds to zero change. The peak attenuation for the first (second) object corresponds to a 24% (8%) change in the signal.

Fig.3.
Fig.3.

Images reconstruction at different depths from the raw data presented in fig. 2. The objects can be localized in depth by minimizing the size of the object in the X and Y directions. The color scale is linear. Reconstruct absorption coefficients are given in the text.

Fig. 4.
Fig. 4.

Measured reflectance versus radial position from the source. Experimental data with the absorbing objects present given by symbols. Theoretical fit for a semi-infinite homogeneous medium is given by the solid line. The object is to the left resulting in the difference between theory and experiment.

Fig. 5. A)
Fig. 5. A)

Reconstruction of the upper left object by subtracting a theoretical background from the experimental data. B) Reconstruction of the lower center object by subtracting the theoretical background from the experimental data.

Equations (9)

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ϕ sc ( r d ) = dr ϕ inc r s r νδ μ a ( r ) D G r r d .
ϕ ˜ sc ω x ω y = G ˜ ω x ω y z A ω x ω y z dz ,
A ω x ω y z = ∫∫ d x d y ϕ inc r s x y z νδ μ a x y z D exp ( x x + y y )
G r r d = exp k ( ( x x d ) 2 + ( y y d ) 2 + z 2 ) 1 / 2 4 πD ( ( x x d ) 2 + ( y y d ) 2 + z 2 ) 1 / 2
exp [ k ( ( x x d ) 2 + ( y y d ) 2 + ( z + 2 z e ) 2 ) 1 / 2 ] 4 πD ( ( x x d ) 2 + ( y y d ) 2 + ( z + 2 z e ) 2 ) 1 / 2
z e = 2 3 μ s ' 1 + R eff 1 R eff
G ˜ ω x ω y = 1 2 D ω x 2 + ω y 2 + k 2
{ exp ( z ω x 2 + ω y 2 + k 2 ) exp [ ( z + z e ) ω x 2 + ω y 2 + k 2 ] } .
δμ a x y z = D vhϕ inc x y z FT 1 [ ϕ ˜ sc ω x ω y z G ˜ ω x ω y z ]

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