Abstract

Instrumentation is described that is suitable for acquiring multisource, multidetector, time-series optical data at high sampling rates (up to 150 Hz) from tissues having arbitrary geometries. The design rationale, calibration protocol, and measured performance features are given for both a currently used, CCD-camera-based instrument and a new silicon-photodiode-based system under construction. Also shown are representative images that we reconstructed from data acquired in laboratory studies using the described CCD-based instrument.

© 2000 Optical Society of America

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1999

Y. Yamashita, A. Maki, H. Koizumi, “Measurement system for noninvasive dynamic optical topography,” J. Biomed. Opt. 4, 414–417 (1999).
[CrossRef] [PubMed]

Y. Pei, F.-B. Lin, R. L. Barbour, “Modeling of sensitivity and resolution to an included object in homogeneous scattering media and in MRI-derived breast maps,” Opt. Exp. 5, 203–219 (1999).
[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
[CrossRef]

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Exp. 4, 287–298 (1999).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41–93 (1999).
[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

1998

S. R. Arridge, W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

1997

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

D. A. Boas, A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A. 14, 192–215 (1997).
[CrossRef]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Kochinsky, J. Sandahl-Christiansen, H. Orskov, M. Essenpreiss, G. Schmelzeisen-Redeker, D. Böcker, “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

J. Chang, W. Zhu, Y. Wang, H. L. Graber, R. L. Barbour, “Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data,” J. Opt. Soc. Am. A 14, 306–312 (1997).
[CrossRef]

S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical imhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

1996

R. B. King, G. M. Raymond, J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24, 352–372 (1996).
[CrossRef] [PubMed]

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

1995

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

1992

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

1991

1989

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

1988

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

1986

S. Sundberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1986).
[CrossRef] [PubMed]

1980

C. R. Honig, C. L. Odoroff, J. L. Frierson, “Capillary recruitment in exercise: rate, extent, uniformity and relation to blood flow,” Am. J. Physiol. 238, H31–H42 (1980).
[PubMed]

1973

’t Hooft, G. W.

Abdoulaev, G.

S. Bartel, G. Abdoulaev, A. H. Hielscher, “Parallelization of gradient-based iterative image reconstruction scheme,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Phototonics Series (Optical Society of America, Washington, D.C., 2000), pp. 433–435.

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Alfano, R. R.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Andronica, R.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general-purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Arif, I.

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Arnold, M.

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

Aronson, R.

H. L. Graber, R. Aronson, R. L. Barbour are preparing a manuscript to be called “Dependence of object sensitivity and resolution on optical thickness of scattering media.”

Arridge, S. R.

Barbour, R. L.

Y. Pei, F.-B. Lin, R. L. Barbour, “Modeling of sensitivity and resolution to an included object in homogeneous scattering media and in MRI-derived breast maps,” Opt. Exp. 5, 203–219 (1999).
[CrossRef]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

J. Chang, W. Zhu, Y. Wang, H. L. Graber, R. L. Barbour, “Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data,” J. Opt. Soc. Am. A 14, 306–312 (1997).
[CrossRef]

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

H. L. Graber, R. Aronson, R. L. Barbour are preparing a manuscript to be called “Dependence of object sensitivity and resolution on optical thickness of scattering media.”

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general-purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Y. Pei, H. L. Graber, R. L. Barbour are preparing a manuscript to be called “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging.”

R. L. Barbour, S. Blattman, T. Panetta, “Dynamic optical tomography: a new approach for investigating tissue–vascular coupling in large tissue structures,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 336–338.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz are preparing a manuscript to be called “Optical tomographic imaging of dynamic features of dense-scattering media.”

H. L. Graber, R. L. Barbour, J. Chang, “Algebraic reconstruction of images of a diffusive medium containing strong absorbers: comparative study of different illumination schemes and the effect of restricted view angle,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 431–447 (1995).
[CrossRef]

Bartel, S.

S. Bartel, G. Abdoulaev, A. H. Hielscher, “Parallelization of gradient-based iterative image reconstruction scheme,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Phototonics Series (Optical Society of America, Washington, D.C., 2000), pp. 433–435.

Bassingthwaighte, J. B.

R. B. King, G. M. Raymond, J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24, 352–372 (1996).
[CrossRef] [PubMed]

Berger, M.

Bertuglia, S.

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

Bishop, Y. M. M.

Y. M. M. Bishop, S. E. Fienberg, P. W. Holland, “Maximum likelihood estimates for complete tables,” in Discrete Multivariate Analysis: Theory and Practice (MIT, Cambridge, Mass., 1991), Chap. 3.

Blattman, S.

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

R. L. Barbour, S. Blattman, T. Panetta, “Dynamic optical tomography: a new approach for investigating tissue–vascular coupling in large tissue structures,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 336–338.

Boas, D. A.

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Exp. 4, 287–298 (1999).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical imhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

D. A. Boas, A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A. 14, 192–215 (1997).
[CrossRef]

Böcker, D.

Bruulsema, J. T.

Castrén, M.

S. Sundberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1986).
[CrossRef] [PubMed]

Chance, B.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical imhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

S. Zhao, M. A. O’Leary, S. Nioka, B. Chance, “Breast tumor detection using continuous wave light source,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 809–817 (1995).
[CrossRef]

B. Chance, “Near-infrared images using continuous, phase-modulated, and pulsed light with quantitation of blood and blood oxygenation,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 29–45 (1998).
[CrossRef]

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

Chang, J.

J. Chang, W. Zhu, Y. Wang, H. L. Graber, R. L. Barbour, “Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data,” J. Opt. Soc. Am. A 14, 306–312 (1997).
[CrossRef]

H. L. Graber, R. L. Barbour, J. Chang, “Algebraic reconstruction of images of a diffusive medium containing strong absorbers: comparative study of different illumination schemes and the effect of restricted view angle,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 431–447 (1995).
[CrossRef]

Chen, W.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Chernomordik, V.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Chesler, D. A.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Colak, S. B.

Colantuoni, A.

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

Conolly, S.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Cope, M.

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Corballis, P.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Cubeddu, R.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Danlewski, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Dawson, J. B.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Delpy, D. T.

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Demos, S. G.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Driver, I.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Eda, H.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Essenpreiss, M.

Fabiani, M.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Fantini, S.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Farrell, T. J.

Feather, J. W.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Fienberg, S. E.

Y. M. M. Bishop, S. E. Fienberg, P. W. Holland, “Maximum likelihood estimates for complete tables,” in Discrete Multivariate Analysis: Theory and Practice (MIT, Cambridge, Mass., 1991), Chap. 3.

Flock, S. T.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Franceschini, M. A.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Friedman, D.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Frierson, J. L.

C. R. Honig, C. L. Odoroff, J. L. Frierson, “Capillary recruitment in exercise: rate, extent, uniformity and relation to blood flow,” Am. J. Physiol. 238, H31–H42 (1980).
[PubMed]

Fry, M. E.

Galland, P.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Gandjbakhche, A. H.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Gayen, S. K.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Glass, L.

L. Glass, M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University, Princeton, N.J., 1988).

Graber, H. L.

J. Chang, W. Zhu, Y. Wang, H. L. Graber, R. L. Barbour, “Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data,” J. Opt. Soc. Am. A 14, 306–312 (1997).
[CrossRef]

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

H. L. Graber, R. Aronson, R. L. Barbour are preparing a manuscript to be called “Dependence of object sensitivity and resolution on optical thickness of scattering media.”

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general-purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Y. Pei, H. L. Graber, R. L. Barbour are preparing a manuscript to be called “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging.”

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz are preparing a manuscript to be called “Optical tomographic imaging of dynamic features of dense-scattering media.”

H. L. Graber, R. L. Barbour, J. Chang, “Algebraic reconstruction of images of a diffusive medium containing strong absorbers: comparative study of different illumination schemes and the effect of restricted view angle,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 431–447 (1995).
[CrossRef]

Grable, R. J.

R. J. Grable, P. D. Rohler, K. L. A. Sastry, “Optical tomography breast imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 197–210 (1997).

Gratton, E.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Gratton, G.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef] [PubMed]

Grosenick, D.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Guo, Y.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Haida, M.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

Hale, G. M.

Hattery, D.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Hayward, J. E.

Hebden, J. C.

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Heinemann, L.

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

S. Bartel, G. Abdoulaev, A. H. Hielscher, “Parallelization of gradient-based iterative image reconstruction scheme,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Phototonics Series (Optical Society of America, Washington, D.C., 2000), pp. 433–435.

Hillman, E. C.

Hira, J.

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Ho, P. P.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Hoberman, C. S.

C. S. Hoberman, “Reversibly expandable three-dimensional structure,” U.S. patent4,780,344 (25October1988).

Holland, P. W.

Y. M. M. Bishop, S. E. Fienberg, P. W. Holland, “Maximum likelihood estimates for complete tables,” in Discrete Multivariate Analysis: Theory and Practice (MIT, Cambridge, Mass., 1991), Chap. 3.

Honig, C. R.

C. R. Honig, C. L. Odoroff, J. L. Frierson, “Capillary recruitment in exercise: rate, extent, uniformity and relation to blood flow,” Am. J. Physiol. 238, H31–H42 (1980).
[PubMed]

Hu, X.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Ito, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Jacques, S. L.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Johnson, M. L.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

Kakihana, Y.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

Kessler, M.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

King, P. R.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

King, R. B.

R. B. King, G. M. Raymond, J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24, 352–372 (1996).
[CrossRef] [PubMed]

Kochinsky, T.

Koizumi, H.

Y. Yamashita, A. Maki, H. Koizumi, “Measurement system for noninvasive dynamic optical topography,” J. Biomed. Opt. 4, 414–417 (1999).
[CrossRef] [PubMed]

Krug, A.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

Kwong, K. K.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Lakowicz, J. R.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

Liang, X.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Lin, F.-B.

Y. Pei, F.-B. Lin, R. L. Barbour, “Modeling of sensitivity and resolution to an included object in homogeneous scattering media and in MRI-derived breast maps,” Opt. Exp. 5, 203–219 (1999).
[CrossRef]

Lionheart, W. R. B.

Liu, F.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Mackey, M. C.

L. Glass, M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University, Princeton, N.J., 1988).

Macovski, A.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Maki, A.

Y. Yamashita, A. Maki, H. Koizumi, “Measurement system for noninvasive dynamic optical topography,” J. Biomed. Opt. 4, 414–417 (1999).
[CrossRef] [PubMed]

Marota, J. J. A.

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Exp. 4, 287–298 (1999).
[CrossRef]

Mcbride, T.

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

McBride, T. O.

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
[CrossRef]

Melissen, J. B. M.

Miwa, M.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

Moes, C. J. M.

Moesta, K.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Nioka, S.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

S. Zhao, M. A. O’Leary, S. Nioka, B. Chance, “Breast tumor detection using continuous wave light source,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 809–817 (1995).
[CrossRef]

Nowaczyk, K.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical imhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

S. Zhao, M. A. O’Leary, S. Nioka, B. Chance, “Breast tumor detection using continuous wave light source,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 809–817 (1995).
[CrossRef]

Oda, I.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Oda, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Oda, T.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

Odoroff, C. L.

C. R. Honig, C. L. Odoroff, J. L. Frierson, “Capillary recruitment in exercise: rate, extent, uniformity and relation to blood flow,” Am. J. Physiol. 238, H31–H42 (1980).
[PubMed]

Oikawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Orel, S.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

Orskov, H.

Osterberg, U.

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Osterberg, U. L.

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
[CrossRef]

Paasschens, J. C. J.

Panetta, T.

R. L. Barbour, S. Blattman, T. Panetta, “Dynamic optical tomography: a new approach for investigating tissue–vascular coupling in large tissue structures,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 336–338.

Papaioannou, D. G.

Patel, M.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Patterson, M. S.

Paulsen, K.

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Paulsen, K. D.

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
[CrossRef]

Pauly, J.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Pei, Y.

Y. Pei, F.-B. Lin, R. L. Barbour, “Modeling of sensitivity and resolution to an included object in homogeneous scattering media and in MRI-derived breast maps,” Opt. Exp. 5, 203–219 (1999).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz are preparing a manuscript to be called “Optical tomographic imaging of dynamic features of dense-scattering media.”

Y. Pei, “Optical tomographic imaging using finite element method,” Ph.D. dissertation (Polytechnic University, Brooklyn, N.Y., 1999).

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Y. Pei, H. L. Graber, R. L. Barbour are preparing a manuscript to be called “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging.”

Pifferi, A.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Pogue, B. W.

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Exp. 4, 270–286 (1999).
[CrossRef]

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Prahl, S. A.

Querry, M. R.

Raymond, G. M.

R. B. King, G. M. Raymond, J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24, 352–372 (1996).
[CrossRef] [PubMed]

Reynolds, E. O. R.

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Rinneberg, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Rohler, P. D.

R. J. Grable, P. D. Rohler, K. L. A. Sastry, “Optical tomography breast imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 197–210 (1997).

Rousseeuw, P. J.

P. J. Rousseeuw, “Robust estimation and identifying outliers,” in Handbook of Statistical Methods for Engineers and Scientists, H. M. Wadsworth, ed. (McGraw-Hill, New York, 1990), Chap. 16.

Sandahl-Christiansen, J.

Sassaroli, A.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Sastry, K. L. A.

R. J. Grable, P. D. Rohler, K. L. A. Sastry, “Optical tomography breast imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 197–210 (1997).

Schenk, J.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Schlag, P.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Schmelzeisen-Redeker, G.

Schmidt, F. E. W.

Schmitz, C. H.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz are preparing a manuscript to be called “Optical tomographic imaging of dynamic features of dense-scattering media.”

Schomberg, H.

Schweiger, M.

Sevick, E. M.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

Sha, Q.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general-purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Shnall, M.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

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A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Exp. 4, 287–298 (1999).
[CrossRef]

Soller, I.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general-purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Star, W. M.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
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S. Sundberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1986).
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E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

Takada, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Tamura, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Taroni, P.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Testorf, M.

B. W. Pogue, M. Testorf, T. Mcbride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Torricelli, A.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
[CrossRef]

Tsuchiya, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Tsunasawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Ugurbil, K.

S. Conolly, A. Macovski, J. Pauly, J. Schenk, K. K. Kwong, D. A. Chesler, X. Hu, W. Chen, M. Patel, K. Ugurbil, “Magnetic resonance imaging,” in The Biomedical Engineering Handbook, 2nd ed., J. D. Bronzino, ed. (CRC Press, Boca Raton, Fla., 2000), Chap. 63.

Valentini, G.

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, J. C. Hebden, “Quantitative imaging in time-resolved transillumination experiments using time-dependent contrast functions,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 398–402 (1999).
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O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (Royal Vangorcum Ltd., Assen, The Netherlands, 1970).

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van der Mark, M. B.

van Gemert, M. J. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
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H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
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van Staveren, H. J.

Wabnitz, H.

H. Rinneberg, D. Grosenick, H. Wabnitz, H. Danlewski, K. Moesta, P. Schlag, “Time-domain optical mammography: results on phantoms, healthy volunteers, and patients,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1998), pp. 278–280.

Wada, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Wang, L.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Wang, Q. Z.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Wang, W. B.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear imaging for medical applications,” in Advances in Optical Biopsy and Optical MammographyR. R. Alfano, ed., Ann. N. Y. Acad. Sci.838, 14–28 (1998).

Wang, Y.

Wilson, B. C.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Witte, H.

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

Wray, S.

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Wyatt, J. S.

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Yamada, H.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

Yamada, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Yamashira, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunasawa, M. Takada, Y. Tsuchiya, Y. Yamashira, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multi-channel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Yamashita, Y.

Y. Yamashita, A. Maki, H. Koizumi, “Measurement system for noninvasive dynamic optical topography,” J. Biomed. Opt. 4, 414–417 (1999).
[CrossRef] [PubMed]

Yodh, A. G.

D. A. Boas, A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A. 14, 192–215 (1997).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical imhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

Yoshimura, N.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

Zhao, S.

S. Nioka, M. Miwa, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” in Oxygen Transport to Tissue XVI, Vol. 361 of Advances in Experimental Medicine and Biology, M. C. Hogan, O. Mathieu-Costello, D. C. Poole, P. D. Wagner, eds. (Plenum, New York, 1994), pp. 171–179.

S. Zhao, M. A. O’Leary, S. Nioka, B. Chance, “Breast tumor detection using continuous wave light source,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 809–817 (1995).
[CrossRef]

Zhong, S.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz are preparing a manuscript to be called “Optical tomographic imaging of dynamic features of dense-scattering media.”

S. Blattman, H. L. Graber, S. Zhong, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Zhu, W.

Am. J. Physiol.

C. R. Honig, C. L. Odoroff, J. L. Frierson, “Capillary recruitment in exercise: rate, extent, uniformity and relation to blood flow,” Am. J. Physiol. 238, H31–H42 (1980).
[PubMed]

Ann. Biomed. Eng.

R. B. King, G. M. Raymond, J. B. Bassingthwaighte, “Modeling blood flow heterogeneity,” Ann. Biomed. Eng. 24, 352–372 (1996).
[CrossRef] [PubMed]

Appl. Opt.

Biochim. Biophys. Acta

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, E. O. R. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation,” Biochim. Biophys. Acta 933, 184–192 (1988).
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Inverse Probl.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41–93 (1999).
[CrossRef]

J. Biomed. Opt.

Y. Yamashita, A. Maki, H. Koizumi, “Measurement system for noninvasive dynamic optical topography,” J. Biomed. Opt. 4, 414–417 (1999).
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G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
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J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

D. A. Boas, A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A. 14, 192–215 (1997).
[CrossRef]

J. Photochem. Photobiol. B

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol. B 16, 169–185 (1992).
[CrossRef] [PubMed]

Lasers Surg. Med.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

Microvasc. Res.

Y. Kakihana, M. Kessler, A. Krug, H. Yamada, T. Oda, N. Yoshimura, “Dynamic changes in intracapillary hemoglobin oxygenation in human skin following various temperature changes,” Microvasc. Res. 56, 104–112 (1998).
[CrossRef] [PubMed]

S. Bertuglia, A. Colantuoni, M. Arnold, H. Witte, “Dynamic coherence analysis of vasomotion and flow motion in skeletal muscle microcirculation,” Microvasc. Res. 52, 235–244 (1996).
[CrossRef] [PubMed]

Opt. Exp.

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Figures (17)

Fig. 1
Fig. 1

Block diagram of the existing CCD-based instrument. LD, laser diodes at two different wavelengths λ1, λ2; ES, electronic shutter; RM, rotating mirror; T, target facing end of fiber bundle; S, source fiber; D, detector fiber; BS, beam splitter. Numbers indicate different functional features of instrument described in text.

Fig. 2
Fig. 2

Photograph of the iris measurement head.

Fig. 3
Fig. 3

Photograph of the pad measurement head showing the arrangement of the source fibers. Inset: The array of 9 × 7 detector fibers.

Fig. 4
Fig. 4

Photograph of a folding hemisphere structure, consisting of a folding hemitrapezoidal icosatethrahedron. Top-most device is an additional folding iris. Various functional features described in the text are identified.

Fig. 5
Fig. 5

Detailed schematic of the variable attenuator array. O.D., optical density.

Fig. 6
Fig. 6

Timing scheme for dynamic measurements performed with the existing setup.

Fig. 7
Fig. 7

Block diagram showing the principle of the new instrument design. LD, laser diodes; LDD, laser diode driver; AM, amplitude modulation; SC, signal conditioning circuitry (i.e., gain switch, lock-in, sample-and-hold circuit); DPS, digital phase shifter; RM, rotating mirror; BS, beam splitter; f1, f2, modulation frequencies; PCI, peripheral component interconnect.

Fig. 8
Fig. 8

Detailed layout of one detector channel, shown for the case of simultaneous measurements at two wavelengths. I-to-V, current-to-voltage converting amplifier; PGA, programmable gain amplifier; f1, f2, modulation frequencies; PCI, peripheral component interconnect.

Fig. 9
Fig. 9

Plot of mean relative detector coupling efficiencies d j versus detector number j, as calculated from phantom studies for two values of IL concentration at two wavelengths. Each data point represents the mean value according to Eq. (4). Error bars indicate the standard deviations for one set of data.

Fig. 10
Fig. 10

Plot of mean relative source coupling efficiencies s i versus detector number i, as calculated from phantom studies for two values of IL concentration at two wavelengths. Error bars indicate the sample standard deviations for one set of data. Symbols are the same as in Fig. 9.

Fig. 11
Fig. 11

Plot of the matrix elements m ji versus the source–detector separation angle for two values of IL concentration at two wavelengths. Symbols are the same as in Fig. 9.

Fig. 12
Fig. 12

Histogram indicating the number of source–detector pairs (out of a total of 324) for which the calculated detector response lies within a certain deviation Δ ji from the measured value.

Fig. 13
Fig. 13

(a) Schematic of the phantom used to demonstrate dynamic imaging capabilities. (b) Cross section of the target used for experimental studies.

Fig. 14
Fig. 14

Reconstructed images showing snapshots of dynamic phantom at different times: (a) 2 s, (b) 5 s.

Fig. 15
Fig. 15

Amplitude maps of the Fourier transform of the reconstructed image time series at two beat frequencies: (a) 0.1 Hz, (b) 0.24 Hz.

Fig. 16
Fig. 16

Measurement of dynamic performance of the detector channel.

Fig. 17
Fig. 17

Schematic drawing of the arrangement of source and detector fibers on the pad.

Tables (1)

Tables Icon

Table 1 Performance Characteristics of the SiPD Detector Module

Equations (11)

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Is,i=αs,iβs,iγs,iPlsiPl.
Id,j=αd,jβd,jγd,jδjIt,jdjIt,j.
R=cPlSMD,
r11r12r1Nr21r22r2NrN1rN2rNN =s1000s2000sN×m1m2mNmNm1m2m2mNm1d1000d2000dN,
M=m1m2m9m10m9m3m2m2m1m3m9m9m10m10m9m9m3m1m2m2m3m9m10m9m2m1.
r1,1r2,2r1,2r2,11/2=s1m1d1s2m1d2s1m2d2s2m2d11/2=m1m2=r2,2r3,3r2,3r3,21/2=r3,3r4,4r3,4r4,31/2=.
r1,1r2,1=s1m1d1s2m2d1=m1m2s1s2, r1,1r1,2=s1m1d1s1m2d2=m1m2d1d2,
Rij=rijj=1N rij, Rij=riji=1N rij, ,
nij=msidjj msidj=djj dj=mdj,
Δij=100 rij-nsimijdjrij.
n=i,j riji,j simijdj.

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