Abstract

Optical diffusion tomography is a technology that is employed to obtain images of the heterogeneous nature of turbid media by using optical radiation. Noise ultimately limits the achievable spatial resolution in these reconstructed images; therefore it is of interest to develop signal-to-noise-ratio expressions that relate spatial resolution in the images to the underlying system and material properties. In this study, Fourier-domain signal-to-noise-ratio expressions are derived for two types of optical diffusion tomography systems: those that use amplitude-modulated illumination sources and those that use continuous-wave illumination sources. The signal-to-noise-ratio expressions are compared for these two types of systems and are validated by laboratory data.

© 2002 Optical Society of America

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2001 (1)

2000 (2)

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

1999 (6)

L. Gobin, L. Blanchot, H. Saint-Jalmes, “Integrating the digitized backscattered image to measure absorption and reduced-scattering coefficients in vivo,” Appl. Opt. 38, 4217–4227 (1999).
[CrossRef]

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

C. L. Matson, H. Liu, “Backpropagation in turbid media,” J. Opt. Soc. Am. A 16, 1254–1265 (1999).
[CrossRef]

J. Ripoll, M. Nieto-Vesperinas, “Spatial resolution of diffuse photon density waves,” J. Opt. Soc. Am. A 16, 1466–1476 (1999).
[CrossRef]

C. L. Matson, H. Liu, “Analysis of the forward problem with diffuse photon density waves in turbid media by use of a diffraction tomography model,” J. Opt. Soc. Am. A 16, 455–466 (1999).
[CrossRef]

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

1998 (1)

1997 (4)

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

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

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–368 (1997).
[CrossRef] [PubMed]

H. Wabnitz, H. Rinneberg, “Imaging in turbid media by photon density waves: spatial resolution and scaling relations,” Appl. Opt. 36, 64–74 (1997).
[CrossRef] [PubMed]

1996 (5)

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]

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

A. Kienle, L. Lige, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

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

1995 (3)

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

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

J. C. Hebden, D. J. Hall, D. T. Delpy, “The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

1994 (2)

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

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

1993 (2)

1992 (3)

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (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]

P. S. Idell, A. Webster, “Resolution limits for coherent optical imaging: signal-to-noise analysis in the spatial-frequency domain,” J. Opt. Soc. Am. A 9, 43–56 (1992).
[CrossRef]

Barbieri, B.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Barton, G.

G. Barton, Elements of Green’s Functions and Propagation (Oxford U. Press, Oxford, UK, 1989).

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]

Blanchot, L.

Boas, D. A.

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.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

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

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

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Cheng, X.

Chernomordik, V.

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

Colak, S. B.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Culver, J. P.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 255–320.

Delpy, D. T.

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–368 (1997).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[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]

Durduran, T.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

Fantini, S.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Fishkin, J. B.

Franceschini, M. A.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Franceschini-Fantini, M. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Gaida, G.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

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

Gobin, L.

Gratton, E.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

J. B. Fishkin, E. Gratton, “Propagation 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] [PubMed]

Hall, D. J.

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–368 (1997).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

Hebden, J. C.

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–368 (1997).
[CrossRef] [PubMed]

J. C. Hebden, D. J. Hall, D. T. Delpy, “The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[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]

Hibst, R.

Hooft, G. W.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Hoogenraad, J. H.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Idell, P. S.

Janesick, J. R.

J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, Bellingham, Wash., 2001).

Jess, H.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Jiang, H.

Kaschke, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Kienle, A.

Kingston, R. H.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1979).

Kuijpers, F. A.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Lau, K.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

Li, X.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

Lige, L.

Liu, H.

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]

Maier, J. S.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Mantulin, W. W.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Mapakshi, R. R.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

Matson, C. L.

McBride, T. O.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

Moesta, K. T.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

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

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]

Nieto-Vesperinas, M.

Nossal, R.

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

O’Leary, M. A.

Osterberg, U. L.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

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

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 439.

Pattanayak, D. N.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

Patterson, M. S.

Paulsen, K. D.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

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

Pogue, B. W.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

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

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

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.

Ripoll, J.

Roggemann, M. C.

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Saint-Jalmes, H.

Schlag, P. M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Seeber, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Steiner, R.

van der Linden, E. S.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

van der Mark, M. B.

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Wabnitz, H.

Walker, S. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Webster, A.

Welsh, B.

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Willscher, C.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

Wilson, B. C.

Yodh, A. G.

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

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

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

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Appl. Opt. (5)

IEEE J. Sel. Top. Quantum Electron. (2)

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden, F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

J. Biomed. Opt. (1)

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (6)

Med. Phys. (6)

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography,” Med. Phys. 27, 2693–2700 (2000).
[CrossRef]

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]

V. Chernomordik, R. Nossal, A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling arguments,” Med. Phys. 23, 1857–1861 (1996).
[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, D. J. Hall, D. T. Delpy, “The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation,” Med. Phys. 22, 201–208 (1995).
[CrossRef] [PubMed]

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–368 (1997).
[CrossRef] [PubMed]

Opt. Eng. (1)

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (2)

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]

X. Li, D. N. Pattanayak, T. Durduran, J. P. Culver, B. Chance, A. G. Yodh, “Near-field diffraction tomography with diffuse photon density waves,” Phys. Rev. E 61, 4295–4309 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Other (6)

J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, Bellingham, Wash., 2001).

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1979).

G. Barton, Elements of Green’s Functions and Propagation (Oxford U. Press, Oxford, UK, 1989).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 439.

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 255–320.

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Figures (5)

Fig. 1
Fig. 1

Plots of SNRs with modulated light: solid curve, theory; asterisks, data.

Fig. 2
Fig. 2

Plots of Fourier amplitudes with modulated light: solid curve, theory; asterisks, data.

Fig. 3
Fig. 3

Plots of SNRs with unmodulated light: solid curve, theory; asterisks, data.

Fig. 4
Fig. 4

Plots of Fourier amplitudes with unmodulated light, with corrections for laser speckle and nonuniform camera responsivity: solid curve, theory; asterisks, data.

Fig. 5
Fig. 5

Plots of Fourier amplitudes with unmodulated light, without corrections for laser speckle and nonuniform camera responsivity: solid curve, theory; asterisks, data.

Equations (44)

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SNR(u, v)=|E[Iˆs(u, v)]|{var[Iˆs(u, v)]}1/2,
ıˆs(x, y)=ii(x, y)-ih(x, y),
E[ıˆs(x, y)]=E[ii(x, y)]-E[ih(x, y)],
ii(x, y)=si(x, y)+na(x, y),
ih(x, y)=sh(x, y)+na(x, y),
E[ıˆs(x, y)]=Δtαuηups,u(x, y)/hυ,
|E[Iˆs(u, v)]|=Δtαuηu|Ps,u(u, v)|/hυ.
var[Iˆs(u, v)]=x, yvar[ıˆs(x, y)].
var[Iˆs(u, v)]=x, yΔtαuηu[pi(x, y)+ph(x, y)]/hυ+2σ2(x, y).
SNRu(u, v)=Δtαuηu|Ps,u(u, v)|/hυx, yΔtαuηu[pi(x, y)+ph(x, y)]/hυ+2σ2(x, y)1/2.
SNRu,p(u, v)=Δtαuηuhυ1/2|Ps,u(u, v)|[Pi(0, 0)+Ph(0, 0)]1/2.
v(x, y, t)=Gs(x, y, t)+na(x, y, t).
p(x, y, t)=pdc(x, y)+pac(x, y)cos[2πf0t+θ(x, y)],
vˆre(x, y)=lp(t)*{2 cos(2πf0t)[Gs(x, y, t)+na(x, y, t)]},
vˆim(x, y)=lp(t)*{2 sin(2πf0t)[Gs(x, y, t)+na(x, y, t)]},
E[vˆre(x, y)]=αmηmGpac(x, y)cos[θ(x, y)]/hυ,
E[vˆim(x, y)]=αmηmGpac(x, y)sin[θ(x, y)]/hυ,
var[vˆre(x, y)]=var[vˆim(x, y)]=4αmηmΓG2Blppdc(x, y)/hυ+4Blpσ2(x, y),
|E[Vˆs(u, v)]|=αmηmG|Ps,m(u, v)|/hυ,
var[Iˆs(u, v)]=x, y8BlpαmηmΓG2[pi,dc(x, y)+ph,dc(x, y)]/hυ+16σ2(x, y)Blp,
SNRm(u, v)=αmηmG|Ps,m(u, v)|/hυ8Blpx, yαmηmΓG2[pi,dc(x, y)+ph,dc(x, y)]/hυ+2σ2(x, y)1/2.
SNRm,p(u, v)
=αmηm8BlpΓhυ1/2|Ps,m(u, v)|[Pi,dc(0, 0)+Ph,dc(0, 0)]1/2.
SNRm,p(u, v)
=Δtαmηm4Γhυ1/2|Ps,m(u, v)|[Pi,dc(0, 0)+Ph,dc(0, 0)]1/2.
SNRratio(u, v)SNRm,p(u, v)SNRu,p(u, v)=14Γαmηmαuηu1/2|Ps,m(u, v)||Ps,u(u, v)|.
SNRh,m(u, v)
=αmηmG|Ph,m(u, v)|/hυ8Blpx, yαmηmΓG2ph,dc(x, y)/hυ+σ2(x, y)1/2.
SNRh,u(u, v)=Δtαuηu|Ph,u(u, v)|/hυx, yΔtαuηuph(x, y)/hυ+σ2(x, y)1/2.
vˆre(x, y)=lp(t)*{2 cos(2πf0t)[Gs(x, y, t)+na(x, y, t)]}.
E[vˆre(x, y)]=lp(t)*(2 cos(2πf0t){GE[s(x, y, t)]+E[na(x, y, t)]})=lp(t)*(2 cos(2πf0t)Gαmηm{pdc(x, y)+pac(x, y)cos[2πf0t+θ(x, y)]}/hυ)=αmηmGpac(x, y)cos[θ(x, y)]/hυ,
E[vˆim(x, y)]=αmηmGpac(x, y)sin[θ(x, y)]/hυ.
var[vˆre(x, y)]Evˆre(x, y)2-E[vˆre(x, y)]2.
var[vˆre(x, y)]=lp(t-α)lp(t-β)×E({2 cos(2πf0α)[Gs(x, y, α)+na(x, y, α)]}{2 cos(2πf0β)×[Gs(x, y, β)+na(x, y, β)]})dαdβ-E[vˆre(x, y)]2=lp(t-α)lp(t-β)×4 cos(2πf0α)cos(2πf0β)×{G2E[s(x, y, α)s(x, y, β)]+E[na(x, y, α)na(x, y, β)]}dαdβ-E[vˆre(x, y)]2,
E[s(x, y, α)s(x, y, β)]
=αm2ηm2p(x, y, α)p(x, y, β)/h2υ2
+αmηmp(x, y, α)δ(α-β)/hυ,
E[na(x, y, α)na(x, y, β)]=σ2(x, y)δ(α-β).
var[vˆre(x, y)]
=4G2Γαmηm lp2(t-α)cos2(2πf0α)p(x, y, α)dα/hυ+4σ2(x, y) lp2(t-α)cos2(2πf0α)dα+[2Gαmηm lp(t-α)cos(2πf0α)×p(x, y, α)dα/hυ]2-E[vˆre(x, y)]2.
var[vˆre(x, y)]=[2αmηmΓG2pdc(x, y)/hυ+2σ2(x, y)] lp2(t)dt.
 lp2(t)dt=LP2(f)df,
var[vˆre(x, y)]=4αmηmΓG2Blppdc(x, y)/hυ+4Blpσ2(x, y).
var[vˆim(x, y)]=4αmηmΓG2Blppdc(x, y)/hυ+4Blpσ2(x, y),

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