Abstract

We propose a computational calibration method for optical tomography. The model of the calibration scheme is based on the rotation symmetry of source and detector positions in the measurement setup. The relative amplitude losses and phase shifts at the optic fibers are modeled by complex-valued coupling coefficients. The coupling coefficients can be estimated when optical tomography data from a homogeneous and isotropic object are given. Once these coupling coefficients have been estimated, any data measured with the same measurement setup can be corrected for the relative variation in the data due to source and detector losses. The final calibration of the data for the source and detector losses and the source calibration between the data and the forward model are obtained as part of the initial estimation for reconstruction. The calibration method was tested with simulations and measurements. The results show that the coupling coefficients of the sources and detectors can be estimated with good accuracy. Furthermore, the results show that the method can significantly improve the quality of reconstructed images.

© 2005 Optical Society of America

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2003 (3)

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

J. J. Stott, J. P. Culver, S. R. Arridge, D. A. Boas, “Optode positional calibration in diffuse optical tomography,” Appl. Opt. 42, 3154–3162 (2003).
[CrossRef] [PubMed]

2002 (4)

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

J. Heino, E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559–573 (2002).
[CrossRef]

S. Oh, A. B. Milstein, R. P. Millane, C. A. Bouman, K. J. Webb, “Source–detector calibration in three-dimensional Bayesian optical diffusion tomography,” J. Opt. Soc. Am. A 19, 1983–1993 (2002).
[CrossRef]

2001 (2)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

2000 (3)

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

1997 (1)

M. Schweiger, S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

1995 (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Andronica, R.

Arif, I.

Arridge, S. R.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

J. J. Stott, J. P. Culver, S. R. Arridge, D. A. Boas, “Optode positional calibration in diffuse optical tomography,” Appl. Opt. 42, 3154–3162 (2003).
[CrossRef] [PubMed]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Austin, T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Barbour, R. L.

Barbour, S.-L. S.

Bluestone, A.

Boas, D.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Boas, D. A.

Bouman, C. A.

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Choe, R.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Culver, J. P.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

J. J. Stott, J. P. Culver, S. R. Arridge, D. A. Boas, “Optode positional calibration in diffuse optical tomography,” Appl. Opt. 42, 3154–3162 (2003).
[CrossRef] [PubMed]

Dehghani, H.

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

Delby, D. T.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

Delpy, D. T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Durduran, T.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Everdell, N.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Fallström, K.

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

Franceschini, M. A.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Fry, M. E.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

Gibson, A.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Graber, H. L.

Hebden, J. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

Heino, J.

J. Heino, E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559–573 (2002).
[CrossRef]

Hillman, E. M. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

Hira, J.

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Holboke, M. J.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Jiang, S.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Kaipio, J. P.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Kajava, T.

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Katila, T.

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Kolehmainen, V.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, “Novel approaches to image reconstruction in diffusion tomography,” Ph.D. thesis (University of Kuopio, Kuopio, Finland, 2001).

Kotilahti, K.

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Luo, H.

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[CrossRef]

McBride, T. O.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, U. L. Österberg, K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXIV, J. F. Dunn, H. M. Swartz, eds. (Kluwer Academic–Plenum, New York, 2003), pp. 85–99.
[CrossRef]

Meek, J. H.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Meriläinen, P.

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Millane, R. P.

Milstein, A. B.

Nissilä, I.

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Noponen, T.

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Oh, S.

Osterberg, U. L.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Österberg, U. L.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

T. O. McBride, B. W. Pogue, U. L. Österberg, K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXIV, J. F. Dunn, H. M. Swartz, eds. (Kluwer Academic–Plenum, New York, 2003), pp. 85–99.
[CrossRef]

Paloheimo, M.

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

Paulsen, K. D.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

T. O. McBride, B. W. Pogue, U. L. Österberg, K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXIV, J. F. Dunn, H. M. Swartz, eds. (Kluwer Academic–Plenum, New York, 2003), pp. 85–99.
[CrossRef]

Pei, Y.

Pogue, B. W.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, U. L. Österberg, K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXIV, J. F. Dunn, H. M. Swartz, eds. (Kluwer Academic–Plenum, New York, 2003), pp. 85–99.
[CrossRef]

Poplack, S. P.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Prince, S.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Ramirez, N.

Schmidt, F. E. W.

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

Schmitz, C. H.

Schweiger, M.

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

M. Schweiger, S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Slemp, A.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Soller, I.

Somersalo, E.

J. Heino, E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559–573 (2002).
[CrossRef]

Stott, J. J.

Sunshine Osterman, K.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Webb, K. J.

Wells, W. A.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Wyatt, J. S.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Yodh, A. G.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Yusof, R. M.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

Zhong, S.

Zubkov, L.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Appl. Opt. (2)

Inverse Probl. (2)

J. Heino, E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559–573 (2002).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Med. Phys. (4)

M. Schweiger, S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

Phys. Med. Biol. (2)

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef] [PubMed]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Radiology (1)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (4)

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[CrossRef]

I. Nissilä, K. Kotilahti, K. Fallström, T. Katila, “Instrumentation for the accurate measurement of phase and amplitude in optical tomography,” Rev. Sci. Instrum. 73, 3306–3312 (2002).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).
[CrossRef]

Other (8)

D. A. Boas, T. Gaudette, S. R. Arridge, “Simultaneous imaging and optode calibration with diffuse optical tomography,” Opt. Express8, 263–270 (2001), http://www.opticsexpress.org .
[CrossRef]

M. A. Franceschini, V. Toronov, M. E. Filiaci, E. Gratton, S. Fantini, “On-line optical imaging of the human brain with 1603ms temporal resolution,” Opt. Express6, 49–57 (2000), http://www.opticsexpress.org .
[CrossRef]

A. V. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express9, 272–286 (2001), http://www.opticsexpress.org .
[CrossRef]

T. Noponen, M. Paloheimo, P. Meriläinen, T. Kajava, K. Kotilahti, I. Nissilä, T. Katila, “Multi-channel near-infrared spectroscopy on the human forehead during hypo- and hypercapnia,” in Biomedical Topical Meetings on CD-ROM (Optical Society of America, Washington, D.C., 2004), paper WF8.

R. Williams, M. Beck, eds., Process Tomography, Principles, Techniques and Applications (Butterworth-Heinemann, Oxford, UK, 1995).

V. Kolehmainen, “Novel approaches to image reconstruction in diffusion tomography,” Ph.D. thesis (University of Kuopio, Kuopio, Finland, 2001).

S. R. Arridge, M. Schweiger, “The UCL optical tomography software system (TOAST),” available at http://www.medphys.ucl.ac.uk/~martins/toast/index.html .

T. O. McBride, B. W. Pogue, U. L. Österberg, K. D. Paulsen, “Strategies for absolute calibration of near infrared tomographic tissue imaging,” in Oxygen Transport to Tissue XXIV, J. F. Dunn, H. M. Swartz, eds. (Kluwer Academic–Plenum, New York, 2003), pp. 85–99.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Left image, logarithm of the amplitude of the simulated data plotted against the source–detector angle index for raw data (dotted curve) and for calibrated data (solid curve). Right image, phase shift of the simulated data plotted against the source–detector angle index for raw data (dotted curve) and for calibrated data (solid curve).

Fig. 2
Fig. 2

Top row, relative source amplitude loss coefficient (left image) and phase shift (right image) shown as + and the corresponding estimated values shown as circles. Bottom row, relative detector amplitude loss coefficient (left image) and phase shift (right image) shown as + and the corresponding estimated values shown as circles.

Fig. 3
Fig. 3

Absorption coefficients (left column) and scattering coefficients (right column). Top row, simulated distributions; middle row, reconstructions from calibrated data; bottom row, reconstructions from raw data.

Fig. 4
Fig. 4

Left image, logarithm of the amplitude of the measured data plotted against the source–detector angle index for raw data (dotted curves) and for calibrated data (solid curves). Right image, phase shift of the measured data plotted against the source–detector angle index for raw data (dotted curves) and for calibrated data (solid curves).

Fig. 5
Fig. 5

Absorption coefficients (left column) and scattering coefficients (right column). Top row, difference images; middle row, absolute images from calibrated data; bottom row, absolute images from raw uncalibrated data.

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

Z = ( z 1 , 1 z 2 , 1 z m , 1 z 1 , 2 z 2 , 2 z m , 2 z 1 , m z 2 , m z m , m ) = ( y 1 exp ( j η 1 ) y m exp ( j η m ) y 2 exp ( j η 2 ) y 2 exp ( j η 2 ) y 1 exp ( j η 1 ) y 3 exp ( j η 3 ) y m exp ( j η m ) y m - 1 exp ( j η m - 1 ) y 1 exp ( j η 1 ) ) ,
y ^ = ( y 1 exp ( j η 1 ) ,     ,     y m exp ( j η m ) ) T ,
x i , k = s ^ i d ^ k z i , k = s i exp ( j σ i ) d k exp ( j δ k ) z i , k ,
X = [ x 1 , 1 x m , 1 x 1 , m x m , m ] = [ d 1 exp ( j δ 1 ) d m exp ( j δ m ) ] [ y 1 exp ( j η 1 ) y 2 exp ( j η 2 ) y m exp ( j η m ) y 1 exp ( j η 1 ) ] [ s 1 exp ( j σ 1 ) s m exp ( j σ m ) ] = D Y S ,
s ˜ i = s i / s 1 ,             i = 1 ,     ,     m ,
d ˜ i = d i / d 1 ,             i = 1 ,     ,     m ,
y ˜ i = y i s 1 d 1 ,             i = 1 ,     ,     m .
σ ˜ i = σ i - σ 1 ,             i = 1 ,     ,     m ,
δ ˜ i = δ i - δ 1 ,             i = 1 ,     ,     m ,
η ˜ i = η i + σ 1 + δ 1 ,             i = 1 ,     ,     m .
X = [ 1 d ˜ 2 exp ( j δ ˜ 2 ) d ˜ m exp ( j δ ˜ m ) ] [ y ˜ 1 exp ( j η ˜ 1 ) y ˜ 2 exp ( j η ˜ 2 ) y ˜ 2 exp ( j η ˜ 2 ) y ˜ 3 exp ( j η ˜ 3 ) y ˜ m exp ( j η ˜ m ) y ˜ 1 exp ( j η ˜ 1 ) ] [ 1 s ˜ 2 exp ( j η ˜ 2 ) s ˜ m exp ( j η ˜ m ) ] = D ˜ Y ˜ S ˜ .
Ψ = L { [ Γ 0 ang ( Γ 0 ) ] - [ X ( y ˜ ,     s ˜ ,     d ˜ ) ang ( X ( η ˜ , σ ˜ ,     δ ˜ ) ) ] } 2 2 ,
L = diag [ Γ 0 ang ( Γ 0 ) ] - 1 .
θ i + 1 = θ i + c i ( J i T W J i ) - 1 J i T W { [ Γ 0 ang ( Γ 0 ) ] - [ X ( θ i ) ang ( X ( θ i ) ) ] } ,
θ = ( y ˜ 1 ,     ,     y ˜ m ,     s ˜ 2 ,     ,     s ˜ m , d ˜ 2 ,     ,     d ˜ m ,     η ˜ 1 ,     ,     η ˜ m ,     σ ˜ 2 ,     ,     σ ˜ m ,     δ ˜ 2 ,     ,     δ ˜ m ) T R 6 m - 4
θ i + 1 = θ i + c i ( J i T W J i + λ I ) - 1 J i T W { [ Γ 0 ang ( Γ 0 ) ] - [ X ( θ i ) ang ( X ( θ i ) ) ] } ,
Γ ˜ = D ˜ - 1 Γ S ˜ - 1 ,
Γ = F mod ( μ a ,     μ s ) ,
ang ( Γ ) = F ang ( μ a ,     μ s ) ,
Γ ˜ = G mod ( μ a ,     μ s ,     ξ ) = ξ F mod ( μ a ,     μ s ) ,
ang ( Γ ˜ ) = G ang ( μ a ,     μ s ,     ɛ ) = F ang ( μ a ,     μ s ) + ɛ ,
Ψ = L { [ Γ ˜ ang ( Γ ˜ ) ] - [ G mod ( μ a , 0 ,     μ s , 0 ,     ξ ) G ang ( μ a , 0 ,     μ s , 0 ,     ɛ ) ] } 2 2 ,
Γ ˜ = ξ - 1 Γ ˜ ,             ang ( Γ ˜ ) = ang ( Γ ˜ ) - ɛ
- κ Φ ( r ; ω ) + μ a Φ ( r ; ω ) + ( j ω / c ) Φ ( r ; ω ) = q 0 ( r ; ω ) ,
κ = 1 n ( μ a + μ s ) ,
Φ ( r ) + 1 2 γ n κ A Φ ( r ) n ^ = 0 ,             r Ω ,
q 0 ( r ) = s ^ i δ ( r - r s ) ,
Φ ( r ) + 1 2 γ n κ A Φ ( r ) n ^ = { - s ^ i w i γ n r i ɛ i 0 r Ω \ i ɛ i ,
Γ ( r ) = - d ^ i κ Φ ( r ) n ^ = d ^ i 2 γ n A Φ ( r ) ,             r i ζ i ,
( K + C + R + j ω Z ) a = G ˜ + E ˜ ,
K ( p , k ) = Ω κ φ k φ p d r ,
C ( p , k ) = Ω μ a φ k φ p d r ,
Z ( p , k ) = 1 c Ω φ k φ p d r ,
R ( p , k ) = Ω 2 γ n A φ k φ p d S ,
G ˜ = 0 ,
E ˜ ( p ) = s i exp ( j σ i ) Ω δ ( r - r s ) φ p d r ,
G ˜ ( p ) = s i exp ( j σ i ) Ω - 2 w i A φ p d S ,
E ˜ = 0.
Γ = M a ,
M ( i , k ) = { [ 2 d i exp ( j δ i ) γ n / A ] if node k ζ i Ω 0 otherwise } ,

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