Abstract

Spatial resolution of transillumination imaging through highly scattering media normalized to sample thickness d depends on only the normalized wavelength Λ/d of photon density waves and normalized penetration depth δ/d. This was concluded theoretically and verified experimentally by the derivation of edge-spread functions from measured time-resolved transmittance and its Fourier transform by the use of dilute milk at various concentrations as scatterer in cuvettes of d = 2 cm and d = 4 cm. In the frequency domain and the time domain, spatial resolution was found experimentally to be given by approximately 0.3d obtained at Λ ≈ d or when only the first arriving 1% of all photons detected were taken into account.

© 1997 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

1997

1996

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

1995

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

D. G. Papaioannou, G. W. ’t Hooft, J. J. M. Baselmans, M. J. C. van Gemert, “Image quality in time-resolved transillumination of highly scattering media,” Appl. Opt. 34, 6144–6157 (1995).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

1994

G. Mitic, J. Kölzer, J. Otto, E. Plies, G. Sölkner, W. Zinth, “Time-gated transillumination of biological tissues and tissue-like phantoms,” Appl. Opt. 33, 6699–6710 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

1993

J. A. Moon, R. Mahon, M. D. Duncan, J. Reintjes, “Resolution limits for imaging through turbid media with diffuse light,” Opt. Lett. 18, 1591–1593 (1993).
[CrossRef] [PubMed]

J. B. Fishkin, E. Gratton, “Progagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J.Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

J. C. Hebden, “Time-resolved imaging of opaque and transparent spheres embedded in a highly scattering medium,” Appl. Opt. 32, 3837–3841 (1993).
[CrossRef] [PubMed]

1992

J. C. Haselgrove, N. G. Wang, B. Chance, “Investigation of the nonlinear aspects of imaging through a highly scattering medium,” Med. Phys. 19, 17–23 (1992).
[CrossRef] [PubMed]

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

K. M. Yoo, B. B. Das, R. R. Alfano, “Imaging of a translucent object hidden in a highly scattering medium from the early portion of the diffuse component of a transmitted ultrafast laser pulse,” Opt. Lett. 17, 958–960 (1992).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, “Effects of optical constants on time-gated transillumination of tissue and tissue-like media,” J. Photochem. Photobiol. B 16, 155–167 (1992).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

1991

1990

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15, 1179–1181 (1990).
[CrossRef] [PubMed]

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

1989

1973

’t Hooft, G. W.

Alfano, R. R.

Andersson-Engels, S.

S. Andersson-Engels, R. Berg, S. Svanberg, “Effects of optical constants on time-gated transillumination of tissue and tissue-like media,” J. Photochem. Photobiol. B 16, 155–167 (1992).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Bartelt, H.

P. Krämmer, H. Bartelt, H. Fischer, B. Schmauss, “Imaging in scattering media using the phase of modulated light sources,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 65–74 (1995).
[CrossRef]

Baselmans, J. J. M.

Bashkansky, M.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Battle, P. R.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Berg, R.

S. Andersson-Engels, R. Berg, S. Svanberg, “Effects of optical constants on time-gated transillumination of tissue and tissue-like media,” J. Photochem. Photobiol. B 16, 155–167 (1992).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

Bonner, R. F.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Chance, B.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

J. C. Haselgrove, N. G. Wang, B. Chance, “Investigation of the nonlinear aspects of imaging through a highly scattering medium,” Med. Phys. 19, 17–23 (1992).
[CrossRef] [PubMed]

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

Cope, M.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Das, B. B.

Delpy, D. T.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Duncan, M. D.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

J. A. Moon, R. Mahon, M. D. Duncan, J. Reintjes, “Resolution limits for imaging through turbid media with diffuse light,” Opt. Lett. 18, 1591–1593 (1993).
[CrossRef] [PubMed]

Fischer, H.

P. Krämmer, H. Bartelt, H. Fischer, B. Schmauss, “Imaging in scattering media using the phase of modulated light sources,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 65–74 (1995).
[CrossRef]

Fishkin, J.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Fishkin, J. B.

J. B. Fishkin, E. Gratton, “Progagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J.Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef]

Gandjbakhche, A. H.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Gratton, E.

J. B. Fishkin, E. Gratton, “Progagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J.Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef]

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Grosenick, D.

Hale, G. M.

Haselgrove, J. C.

J. C. Haselgrove, N. G. Wang, B. Chance, “Investigation of the nonlinear aspects of imaging through a highly scattering medium,” Med. Phys. 19, 17–23 (1992).
[CrossRef] [PubMed]

Hebden, J. C.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

J. C. Hebden, “Time-resolved imaging of opaque and transparent spheres embedded in a highly scattering medium,” Appl. Opt. 32, 3837–3841 (1993).
[CrossRef] [PubMed]

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

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

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

Jarlman, O.

Kölzer, J.

Krämmer, P.

P. Krämmer, H. Bartelt, H. Fischer, B. Schmauss, “Imaging in scattering media using the phase of modulated light sources,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 65–74 (1995).
[CrossRef]

Krüger, R. A.

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

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

Mahon, R.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

J. A. Moon, R. Mahon, M. D. Duncan, J. Reintjes, “Resolution limits for imaging through turbid media with diffuse light,” Opt. Lett. 18, 1591–1593 (1993).
[CrossRef] [PubMed]

Mantulin, W. W.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Mitic, G.

Moon, J. A.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

J. A. Moon, R. Mahon, M. D. Duncan, J. Reintjes, “Resolution limits for imaging through turbid media with diffuse light,” Opt. Lett. 18, 1591–1593 (1993).
[CrossRef] [PubMed]

Neukammer, J.

H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

Nossal, R.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

Otto, J.

Papaioannou, D. G.

Patterson, M. S.

Plies, E.

Pulvermacher, H.

H. Pulvermacher “Transillumination using photon density waves: dependence of resolution on object position and detector size,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 86–97 (1995).
[CrossRef]

Querry, M. R.

Reintjes, J.

J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time-resolved transillumination imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

J. A. Moon, R. Mahon, M. D. Duncan, J. Reintjes, “Resolution limits for imaging through turbid media with diffuse light,” Opt. Lett. 18, 1591–1593 (1993).
[CrossRef] [PubMed]

Rinneberg, H.

D. Grosenick, H. Wabnitz, H. Rinneberg, “Time-resolved imaging of solid phantoms for optical mammography,” Appl. Opt. 36, 221–231 (1997).
[CrossRef] [PubMed]

H. Rinneberg, “Scattering of laser light in turbid media: optical tomography for medical diagnostics?,” in The Inverse Problem, H. Lübbig, ed. (Akademie Verlag, Berlin1995), pp. 107–141.

H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

Schmauss, B.

P. Krämmer, H. Bartelt, H. Fischer, B. Schmauss, “Imaging in scattering media using the phase of modulated light sources,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 65–74 (1995).
[CrossRef]

Sölkner, G.

Sommerfeld, A.

A. Sommerfeld, Optik, Vol. 4 of the Series Vorlesungen über Theoretische Physik (Verlag H. Deutsch, Thun, Frankfurt am Main, 1989), pp. 206–215.

Sukowski, U.

H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

Svaasand, L. O.

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. SPIE1525, 41–51 (1991).
[CrossRef]

Svanberg, S.

S. Andersson-Engels, R. Berg, S. Svanberg, “Effects of optical constants on time-gated transillumination of tissue and tissue-like media,” J. Photochem. Photobiol. B 16, 155–167 (1992).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Tromberg, B. J.

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. SPIE1525, 41–51 (1991).
[CrossRef]

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J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

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D. Grosenick, H. Wabnitz, H. Rinneberg, “Time-resolved imaging of solid phantoms for optical mammography,” Appl. Opt. 36, 221–231 (1997).
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H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

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H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

R. Willenbrock, “Streuung von ps Laserimpulsen in turbiden Medien: Abbildung mittels Photonendichtewellen,” Diploma thesis (Freie Universität Berlin, Berlin, 1993).

Wilson, B. C.

Wong, K. S.

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

Yoo, K. M.

Zinth, W.

Appl. Opt.

J. Photochem. Photobiol. B

S. Andersson-Engels, R. Berg, S. Svanberg, “Effects of optical constants on time-gated transillumination of tissue and tissue-like media,” J. Photochem. Photobiol. B 16, 155–167 (1992).
[CrossRef] [PubMed]

J.Opt. Soc. Am. A

J. B. Fishkin, E. Gratton, “Progagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J.Opt. Soc. Am. A 10, 127–140 (1993).
[CrossRef]

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J. C. Haselgrove, N. G. Wang, B. Chance, “Investigation of the nonlinear aspects of imaging through a highly scattering medium,” Med. Phys. 19, 17–23 (1992).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
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[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

Phys. Today

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Proc. Nat. Acad. Sci. USA

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Nat. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Other

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P. Krämmer, H. Bartelt, H. Fischer, B. Schmauss, “Imaging in scattering media using the phase of modulated light sources,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. J. Müller, A. V. Priezzhev, V. V. Tuchin, eds., Proc. SPIE2326, 65–74 (1995).
[CrossRef]

H. Wabnitz, R. Willenbrock, J. Neukammer, U. Sukowski, H. Rinneberg, “Spatial resolution in photon diffusion imaging from measurements of time-resolved transmittance,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 48–61 (1993).
[CrossRef]

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. SPIE1525, 41–51 (1991).
[CrossRef]

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[CrossRef]

R. Willenbrock, “Streuung von ps Laserimpulsen in turbiden Medien: Abbildung mittels Photonendichtewellen,” Diploma thesis (Freie Universität Berlin, Berlin, 1993).

G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).

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Figures (16)

Fig. 1
Fig. 1

Photon density Φinf [see Eq. (16)], normalized to its maximum, versus scaled time Θ = Dct/d2 for several values of normalized penetration depth δ/d.

Fig. 2
Fig. 2

Fourier spectrum [see Eq. (17)] of photon density Φinf versus scaled modulation frequency Ω = ωd2/(Dc) for several values of normalized penetration depth δ/d; (a) modulus normalized to Sp/(4πd3), (b) phase.

Fig. 3
Fig. 3

Experimental setup for recording time-resolved diffuse transmittance. SHG, second-harmonic generation; MCP-PMT, microchannel-plate photomultiplier; TCSPC, time-correlated single photon counting.

Fig. 4
Fig. 4

Cuvette with movable absorbing baffle at z = d/2 for measuring ESF’s (d = 2 cm, d = 4 cm).

Fig. 5
Fig. 5

Transport scattering coefficient μs and absorption coefficient μa of dilute milk at λ = 680 nm. The absorption coefficient of pure water (□) at λ = 680 nm was taken from the literature.28

Fig. 6
Fig. 6

Distributions N(x, t) of times of flight of photons (λ = 680 nm) through d = 4 cm of dilute milk at 40% volume concentration for different separations x of the edge of the movable baffle from the optic axis (see Fig. 4). The curves shown correspond to separations (from top to bottom) x/cm = 3.9, 2.7, 1.5, 1.2, 0.9, 0.6, 0.3, 0.0, -0.3, -0.6, and -0.9. All distributions are normalized to the maximum of the distribution for x = 3.9 cm. Time zero was determined from the cuvette filled with pure water. Vertical (dotted) lines indicate fractions f = 0.01 and f = 0.3 of all photons detected at x = xmax.

Fig. 7
Fig. 7

ESF’s E(x, tf) [see Eq. (20)] versus distance x of edge (see Fig. 4) from optic axis (x = 0) derived from data shown in Fig. 6. The upper integration limits tf = 1, 2.5, and 20 ns correspond to fractions f = 0.01, 0.3, and 1.0, respectively. Spatial resolution Δx as defined in Eq. (21) is indicated.

Fig. 8
Fig. 8

Fraction f of total number of photons detected versus scaled upper integration limit Θf = Dctf/d2 calculated from Eq. (16) (infinite medium) and Eq. (14) of Ref. 25 (infinite slab). The solid curves correspond to normalized penetration depth δ/d = 1, the dashed curves to δ/d = 0.5.

Fig. 9
Fig. 9

ESF’s E(x, tf) versus distance x of edge from optic axis (x = 0) for whole milk and upper integration limits tf corresponding to fractions f = 0.01, 0.3, and 1.0 (cf. Fig. 7).

Fig. 10
Fig. 10

Normalized spatial resolution Δxf/d versus volume concentration of dilute milk for d = 2 cm and d = 4 cm. Spatial resolution Δxf [see Eq. (21)] was derived from ESF’s (see Figs. 7 and 9) corresponding to fractions f = 0.01 (□), 0.03 (+), 0.1 (×), 0.3 (△), 0.5 (*) and 1.0 (●). For clarity, error bars are omitted (see Fig. 11).

Fig. 11
Fig. 11

Normalized spatial resolution Δxf/d versus fraction f obtained for various volume concentrations of milk with the data of Fig. 10 (d = 4 cm). Typical error limits are indicated to the right of data points.

Fig. 12
Fig. 12

Fourier spectra obtained from distributions of times of flight N(t) measured for whole milk (solid curves) and dilute milk at 40% volume concentration (dashed curves) in a cuvette of thickness d = 2 cm without absorbing object; (a) modulus of normalized Fourier amplitudes |(ν)/(ν = 0)|, (b) phase φ(ν = -arg (ν). Frequencies indicated by vertical lines correspond to a wavelength of Λ ≈ 4 cm of photon density waves (see Figs. 13 and 14).

Fig. 13
Fig. 13

ESF’s E(x, ω) [see Eq. (23)] versus position x for (a) whole milk, (b) milk at 40% volume concentration at selected wavelengths Λ of photon density waves.

Fig. 14
Fig. 14

Phase difference Δφ(x, ω) = arg (xmax, ω) - arg (x, ω) versus position x of absorbing edge for (a) whole milk, (b) milk at 40% volume concentration at selected wavelengths Λ of photon density waves (see Fig. 13).

Fig. 15
Fig. 15

Normalized spatial resolution Δxω/d versus square root of normalized wavelength Λ/d of photon density waves for cuvettes of (a) d = 2 cm, (b) d = 4 cm. Spatial resolution Δxω was derived from the ESF’s (cf. Fig. 13) determined for various concentrations of dilute milk.

Fig. 16
Fig. 16

Normalized spatial resolution Δxω/d versus square root of normalized wavelength Λ/d derived from ESF’s calculated according to Ref. 16 (infinite medium). Curves are shown for selected values of normalized penetration depth δ/d. Limiting values of Δxω/d for Λ → ∞ are indicated on the right-hand side.

Tables (1)

Tables Icon

Table 1 Transport Scattering and Absorption Coefficients as well as Penetration Depth of Dilute Milk at Various Volume Concentrations (λ = 680 nm)

Equations (23)

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Dc2Φr, t-Φr, tt-cμaΦr, t=-Sr, t,
2Φˆr, ω+k2Φˆr, ω=-SpDcδr,
k=kre-ikim=-iμac+iω/Dc1/2,
Φˆinfr, ωexpiωt=SpDcexp-kimωr4πr×exp-ikreωr-ωt.
δ=D/μa1/2,
kre=k04+14δ41/2-12δ21/2,
kim=k04+14δ41/2+12δ21/2,
Λ0=2π/k0=2π2Dc/ω1/2.
Λ=2π/kre=Λ01+14δ4k041/2+12δ2k021/2.
Λ0/d=const.
δ/d=const.
Θ=Dcd2t,
Ω=d2Dcω,
Λ0/d=2π2/Ω1/2.
Φinfd, t=Sp4πDct-3/2 exp-d24Dctexp-μact,
Φinfd, Θ=Spd34πΘ-3/2 exp-14Θexp-Θδ/d2.
Φˆinfd, Ω=Sp4πd3exp-kimΩdexp-ikreΩd,
kreΩd=12Ω2+1δ/d41/2-1δ/d21/2,
kimΩd=12Ω2+1δ/d41/2+1δ/d21/2.
Ex, tf=0tfNx, tdt0tfNxmax, tdt.
Δx=1Exxmax.
0tfNxmax, tdt=f0Nxmax, tdt=fNtotxmax.
Ex, ω=Nˆx, ωNˆxmax, ω.

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