Abstract

The role that deconvolution plays in the achievable spatial resolution in optical diffusion tomography is examined for the case of imaging an inhomogeneity in an otherwise homogeneous medium. It is shown that, in the measured data, it is the shape of the turbid medium modulation transfer function that determines the maximum spatial resolution. When the turbid medium transfer function is deconvolved from the measured data, it is the signal-to-noise ratio properties of the Fourier-transformed measured data that determine the maximum spatial resolution. It is shown that deconvolution-based methods can improve the spatial resolution in measured data up to a factor of 5 for realistic noise levels. These results are demonstrated with computer-simulated data.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
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  26. C. L. Matson is preparing a manuscript to be called “Signal-to-noise ratio expressions in optical diffusion tomography.”
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2000 (3)

1999 (5)

1998 (2)

1997 (6)

1996 (3)

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]

M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
[CrossRef] [PubMed]

1995 (2)

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[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]

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 (1)

1992 (1)

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

Arridge, S. R.

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

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97), Lecture Notes in Computer Science (Springer, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

Barton, G.

G. Barton, Elements of Green’s Functions and Propagation (Oxford University, 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]

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]

Carminati, R.

Chance, B.

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]

Clark, N.

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. D. 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]

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. D. 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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Fender, J. S.

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

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. USA 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]

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. USA 94, 6468–6473 (1997).
[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]

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]

Iftimia, N.

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Jiang, H.

N. Iftimia, H. Jiang, “Quantitative optical image reconstruction of turbid media by use of direct-current measurements,” Appl. Opt. 39, 5256–5261 (2000).
[CrossRef]

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

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]

Li, X. D.

X. D. 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]

M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
[CrossRef] [PubMed]

Lionheart, W. R. B.

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]

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Matson, C. L.

McBride, T. O.

McMackin, L.

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. USA 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.

Österberg, U. L.

Pattanayak, D. N.

X. D. 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]

Paulsen, K. D.

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, K. D. Paulsen, “Spatially variant regularization improves optical diffusion tomography,” Appl. Opt. 38, 2950–2961 (1999).
[CrossRef]

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

Pogue, B. W.

Prewitt, J.

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), Sect. 2.3.

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Schotland, J. C.

Schweiger, M.

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97), Lecture Notes in Computer Science (Springer, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

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.

Welsh, B.

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996), Sect. 2.3.

Yodh, A. G.

Appl. Opt. (5)

IEEE J. Sel. Top. Quantum Electron. (1)

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]

J. Opt. Soc. Am. A (5)

Med. Phys. (6)

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

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

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. Express (1)

Opt. Lett. (4)

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. D. 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]

Proc. Natl. Acad. Sci. USA (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. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Other (4)

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

C. L. Matson is preparing a manuscript to be called “Signal-to-noise ratio expressions in optical diffusion tomography.”

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97), Lecture Notes in Computer Science (Springer, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996), Sect. 2.3.

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Figures (12)

Fig. 1
Fig. 1

System geometry for the spatial resolution analysis. The inhomogeneity is represented by the cube, which is assumed to be embedded in an infinite homogeneous turbid medium. The face of the cube closest to the detection plane is located at z = z 1 and the detection plane is located at z 0.

Fig. 2
Fig. 2

MTF n plots: solid curve, μ a = 0.03 cm-1, μ s ′ = 15 cm-1, f t = 0, Δz = 6 cm; dotted curve, μ a = 0.03 cm-1, μ s ′ = 15 cm-1, f t = 1 GHz, Δz = 6 cm; dashed curve, μ a = 0.03 cm-1, μ s ′ = 25 cm-1, f t = 0, Δz = 6 cm; dashed–dotted curve, μ a = 0.03 cm-1, μ s ′ = 15 cm-1, f t = 0, Δz = 1 cm. For all plots, n = 1.333.

Fig. 3
Fig. 3

PSF plots corresponding to the MTF n plots in Fig. 2. Parameter values are the same as in Fig. 2.

Fig. 4
Fig. 4

MTF n ratios as a function of spatial frequency. The MTF n with the larger value of the varied parameter is divided by the MTF n with the smaller value: solid curve, μ a1 = 0.03 cm-1, μ a2 = 0.003 cm-1; dotted curve, μ s1′ = 25 cm-1, μ s2′ = 5 cm-1; dashed curve, f t1 = 1 GHz, f t2 = 0; dashed–dotted curve, Δz 1 = 6 cm, Δz 2 = 3 cm.

Fig. 5
Fig. 5

Ratio of a MTF n with μ a = 0.03 cm-1 to a MTF n with μ a = 0.003 cm-1. For both MTF n ’s, μ s ′ = 15 cm-1, Δz = 6 cm, n = 1.333, f t = 1 GHz.

Fig. 6
Fig. 6

MTF n plot (solid curve) and a 0.1% noise amplitude plot (dotted curve).

Fig. 7
Fig. 7

PSF width multiplicative scale factor produced by regularization as a function of the SNR ratio at dc. Parameter values are the same as in Fig. 2.

Fig. 8
Fig. 8

PSF width multiplicative scale factor produced by deconvolution and regularization as a function of the SNR at dc. Parameter values are the same as in Fig. 2.

Fig. 9
Fig. 9

Unblurred and noise-free resolution chart.

Fig. 10
Fig. 10

Measured data images of a resolution chart resulting from (a) continuous-wave light and (b) 1-GHz modulated light.

Fig. 11
Fig. 11

Plots of the averaged Fourier amplitudes of the two images in Fig. 10 as a function of spatial frequency.

Fig. 12
Fig. 12

Deconvolved and regularized images of a resolution chart resulting from (a) continuous-wave light and (b) 1-GHz modulated light.

Equations (10)

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isx, y; z0=isx, y; z1 * hx, y; Δz,
Hu, v; Δz=exp-Δz2πu2+2πv2+3μaμs-j6πμsftn/c1/2,
MTFnu, v; Δz=exp-ΔzAu, v-A0, 0,
Au, v=2πu2+2πv2+3μaμs-j6πμsftn/c1/2
zMTFnu, v; Δz=-exp-ΔzAu, v-A0, 0Au, v-A0, 0,
μaMTFnu, v; Δz=-3Δzμs2exp-ΔzAu, v-A0, 0×1Au, v-1A0, 0,
μsMTFnu, v; Δz=-Δz exp-ΔzAu, v-A0, 03μa2 1Au, v-1A0, 0+6πftv ×1Au, v-1A0, 0,
ftMTFnu, v; Δz=-3πΔzμsvexp-Δz×Au, v-A0, 0×1Au, v-1A0, 0,
Isu, v; z0=Isu, v; z1Hu, v; Δz+Nu, v,
Idu, v; z0=Fu, vIsu, v; z1+Fu, vNu, vHu, v; Δz,

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