Abstract

Frequency-domain near-infrared (NIR) diffuse spectral tomography with a mode-locked Ti:sapphire laser is presented, providing tunable multiwavelength quantitative spectroscopy with maximal power for thick tissue imaging. The system was developed to show that intrinsically high stability can be achieved with many wavelengths in the NIR range, using a mode-locked signal of 80MHz with heterodyned lock-in detection. The effect of cumulative noise from multiple wavelengths of data on the reconstruction process was studied, and it was shown that inclusion of more wavelengths can reduce skew in the noise distribution. This normalization of the data variance then minimizes errors in estimation of chromophore concentrations. Simulations and tissue phantom experiments were used to quantify this improvement in image accuracy for recovery of tissue hemoglobin and oxygen saturation.

© 2009 Optical Society of America

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  1. L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
    [CrossRef]
  2. T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
    [CrossRef]
  3. T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]
  4. J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]
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    [CrossRef] [PubMed]
  6. A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256-258 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
    [CrossRef] [PubMed]
  10. F. Bevilacqua, A. J. Berger, A. E. Cerussi, D. Jakubowski, and B. J. Tromberg, “Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods,” Appl. Opt. 39, 6498-6510 (2000).
    [CrossRef]
  11. C. D'Andrea, L. Spinellil, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14, 1888-1898 (2006).
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    [PubMed]
  13. M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
    [CrossRef]
  14. K. D. Paulsen, and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691-701 (1995).
    [CrossRef] [PubMed]
  15. B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
    [CrossRef]
  16. A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44, 2082-2093 (2005).
    [CrossRef] [PubMed]
  17. S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
    [PubMed]
  18. B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
    [CrossRef] [PubMed]
  19. B. Brooksby, “Combined near-infrared tomography and MRI to improve breast tissue chromophore and scattering assessment,” Ph.D. dissertation (Dartmouth College, 2005).
  20. S. Jiang, B. W. Pogue, and K. D. Paulsen, “Dynamic frequency domain tomography system and phantom test,” Proc. SPIE 6431, 64310G (2007).
    [CrossRef]
  21. H. Xu, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44, 2177-2188 (2005).
    [CrossRef] [PubMed]
  22. M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
    [CrossRef] [PubMed]
  23. B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).
  24. S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
    [CrossRef] [PubMed]
  25. D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
    [CrossRef] [PubMed]

2008 (2)

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

2007 (2)

2006 (2)

2005 (7)

B. Brooksby, “Combined near-infrared tomography and MRI to improve breast tissue chromophore and scattering assessment,” Ph.D. dissertation (Dartmouth College, 2005).

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44, 2082-2093 (2005).
[CrossRef] [PubMed]

H. Xu, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44, 2177-2188 (2005).
[CrossRef] [PubMed]

D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (4)

V Toronov , E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2717-2729 (2003).
[PubMed]

A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. Hillman, S. R. Arridge, and A. G. Yodh, “Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography,” Opt. Lett. 28, 2339-2341 (2003).
[CrossRef] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

2001 (1)

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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 (2)

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

F. Bevilacqua, A. J. Berger, A. E. Cerussi, D. Jakubowski, and B. J. Tromberg, “Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods,” Appl. Opt. 39, 6498-6510 (2000).
[CrossRef]

1998 (1)

E. L. Hull, M. G. Nichols, and T. H. Foster, “Quantitative broadband near-infrared spectroscopy of tissue-simulating phantoms containing erythrocytes,” Phys. Med. Biol. 43, 3381-3404 (1998).
[CrossRef] [PubMed]

1997 (1)

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

1995 (1)

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

1990 (1)

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
[CrossRef]

Anderson, E.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

Arridge, S. R.

Barbieri, B.

Bassi, A.

Berger, A. J.

Bevilacqua, F.

Boas, D. A.

Brooksby, B.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

B. Brooksby, “Combined near-infrared tomography and MRI to improve breast tissue chromophore and scattering assessment,” Ph.D. dissertation (Dartmouth College, 2005).

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

Cerussi, A. E.

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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.

Contini, D.

Coquoz, O.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

Corlu, A.

Cubeddu, R.

Culver, J. P.

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256-258 (2004).
[CrossRef] [PubMed]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

D'Amico, E.

D'Andrea, C.

Davis, S. C.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

Dehghani, H.

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

H. Xu, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44, 2177-2188 (2005).
[CrossRef] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
[CrossRef] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

Dunn, J. F.

Durduran, T.

Eames, M. E.

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

Fantini, S.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Fishkin, J. B.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

Foster, T. H.

E. L. Hull, M. G. Nichols, and T. H. Foster, “Quantitative broadband near-infrared spectroscopy of tissue-simulating phantoms containing erythrocytes,” Phys. Med. Biol. 43, 3381-3404 (1998).
[CrossRef] [PubMed]

Franceschini, M. A.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Giusto, A.

Gratton, E.

Hillman, E. M.

Holboke, M. J.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

Hueber, D.

Hull, E. L.

E. L. Hull, M. G. Nichols, and T. H. Foster, “Quantitative broadband near-infrared spectroscopy of tissue-simulating phantoms containing erythrocytes,” Phys. Med. Biol. 43, 3381-3404 (1998).
[CrossRef] [PubMed]

Innocente, S.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Jakubowski, D.

Jiang, H.

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

Jiang, S.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

S. Jiang, B. W. Pogue, and K. D. Paulsen, “Dynamic frequency domain tomography system and phantom test,” Proc. SPIE 6431, 64310G (2007).
[CrossRef]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
[CrossRef] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

Kogel, C.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

Lee, K.

Li, A.

Mannarino, E.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

McBride, T. O.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

Miller, E. L.

Nichols, M. G.

E. L. Hull, M. G. Nichols, and T. H. Foster, “Quantitative broadband near-infrared spectroscopy of tissue-simulating phantoms containing erythrocytes,” Phys. Med. Biol. 43, 3381-3404 (1998).
[CrossRef] [PubMed]

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

Osterberg, U. L.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

Palumbo, R.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Paoletti, F.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Pasqualini, L.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Patterson, M. S.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
[CrossRef]

Paulsen, K. D.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

S. Jiang, B. W. Pogue, and K. D. Paulsen, “Dynamic frequency domain tomography system and phantom test,” Proc. SPIE 6431, 64310G (2007).
[CrossRef]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

H. Xu, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44, 2177-2188 (2005).
[CrossRef] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

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

Pham, T. H.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

Piao, D.

Pogue, B. W.

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

S. Jiang, B. W. Pogue, and K. D. Paulsen, “Dynamic frequency domain tomography system and phantom test,” Proc. SPIE 6431, 64310G (2007).
[CrossRef]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
[CrossRef] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

H. Xu, R. Springett, H. Dehghani, B. W. Pogue, K. D. Paulsen, and J. F. Dunn, “Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies,” Appl. Opt. 44, 2177-2188 (2005).
[CrossRef] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

Poplack, S.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Poplack, S. P.

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

Schweiger, M.

Slemp, A.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

Spinellil, L.

Springett, R.

Srinivasan, S.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

D. Piao, S. Jiang, S. Srinivasan, H. Dehghani, and B. W. Pogue, “Video-rate near-infrared optical tomography using spectrally-encoded parallel light delivery,” Opt. Lett. 30, 2593-2595 (2005).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering NIR tomography provides quantitative and robust reconstruction,” Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

Swartling, J.

Toronov, V

Torricelli, A.

Tromberg, B. J.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

F. Bevilacqua, A. J. Berger, A. E. Cerussi, D. Jakubowski, and B. J. Tromberg, “Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods,” Appl. Opt. 39, 6498-6510 (2000).
[CrossRef]

Vaudo, G.

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

Wang, J.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066-4082 (2007).
[CrossRef] [PubMed]

Weaver, J. B.

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

Webb, A.

Wells, W. A.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Wilson, B. C.

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
[CrossRef]

Wyman, D. R.

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
[CrossRef]

Xu, H.

Yodh, A. G.

Zhang, Q.

Zubkov, L.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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. (4)

Atherosclerosis (1)

L. Pasqualini, G. Vaudo, S. Fantini, M. A. Franceschini, F. Paoletti, S. Innocente, R. Palumbo, and E. Mannarino, “Near-infrared spectroscopy, scintigraphy and transcutaneous oximetry in the diagnosis of peripheral arterial disease,” Atherosclerosis 135, S17-S17 (1997).
[CrossRef]

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

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
[CrossRef]

J. Biomed. Opt. (4)

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency-domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef] [PubMed]

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimisation in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B. Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate MR structure,” J. Biomed. Opt. 10, 050504 (2005).

Lasers Med. Sci. (1)

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155-168 (1990).
[CrossRef]

Med. Phys. (2)

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

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and 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]

Opt. Express (3)

Opt. Lett. (3)

Phys. Med. Biol. (1)

E. L. Hull, M. G. Nichols, and T. H. Foster, “Quantitative broadband near-infrared spectroscopy of tissue-simulating phantoms containing erythrocytes,” Phys. Med. Biol. 43, 3381-3404 (1998).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. Jiang, B. W. Pogue, and K. D. Paulsen, “Dynamic frequency domain tomography system and phantom test,” Proc. SPIE 6431, 64310G (2007).
[CrossRef]

Rev. Sci. Instrum. (2)

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2512 (2000).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and 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]

Technol. Cancer Res. Treat. (1)

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in-vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Other (1)

B. Brooksby, “Combined near-infrared tomography and MRI to improve breast tissue chromophore and scattering assessment,” Ph.D. dissertation (Dartmouth College, 2005).

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Figures (10)

Fig. 1
Fig. 1

System diagram of the frequency-domain NIR imaging instrument that incorporates a mode-locked Ti:sapphire laser as the broadband light source, with a 10 MHz lock to an external signal generator for a reference signal, and heterodyne mixers after the PMT detectors.

Fig. 2
Fig. 2

(a) Measurement noise levels (normalized standard deviation) for amplitude (Amp.) and the phase (unnormalized standard deviation) are shown as a function of the wavelength when using the Ti:sapphire-laser-based approach. (b) Amplitude noise levels and (c) and phase noise levels shown as a function of mean signal amplitude (on a logarithm scale) to compare the Ti:sapphire laser to a diode laser system, showing they have overall similar error values.

Fig. 3
Fig. 3

Histograms of noise distribution of two noise models with 5 and 11 wavelengths: zero-mean noise distribution (a) for the 5- wavelength data set and (b) for the 11-wavelength data set; non-zero-mean noise distribution (c) for the 5-wavelength data set and (d) for the 11-wavelength data set.

Fig. 4
Fig. 4

Reconstructed images using the simulated zero-mean noise data. The first row shows the true properties of chromophores (total hemoglobin, Hbt; oxygen saturation, StO 2 ; water) and scatter parameters (amplitude and power). The second and third rows show the reconstruction results with 5-wavelength and 11-wavelength data sets, respectively.

Fig. 5
Fig. 5

Bar graphs of reconstruction errors of the region of interest are shown for (a) the results with the zero-mean noise model (b) the results with non-zero-mean noise model.

Fig. 6
Fig. 6

Reconstructed images using the simulated non-zero-mean noise data. The first row shows the true properties of chromophores and scatter parameters. The second and third row display the reconstruction results with 5-wavelength and 11-wavelength data sets, respectively.

Fig. 7
Fig. 7

Experimental results of gelatin phantom with blood solution contrast in Hbt. The first row shows reconstructed results with the 5-wavelength data set; the second row shows reconstructed results with the 11-wavelength data set.

Fig. 8
Fig. 8

Experimental results of gelatin phantom with blood solution contrast in Hbt and StO 2 . The first row shows reconstructed results with the 5-wavelength data set; the second row shows reconstructed results with the 11-wavelength data set.

Fig. 9
Fig. 9

Bar graphs of reconstruction errors of inclusion in two phantom experiments with (a) contrast in Hbt and (b) contrast in both Hbt and StO 2 .

Fig. 10
Fig. 10

Noise distribution of experimental data from the phantom with contrast in Hbt: histogram of noise distribution for the (a) 5-wavelength data set and (b) 11-wavelength data set.

Equations (8)

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

D ( r ) Φ ( r , ω ) + [ μ a ( r ) + i ω c ] Φ ( r , ω ) = q 0 ( r , ω ) ,
χ 2 = j = 1 M Φ j m Φ j c ,
μ a ( λ ) = i ε i ( λ ) C i ,
μ s ( λ ) = a λ b ,
[ J T J + λ I ] Δ c = J T Δ Φ ,
I sim λ = I theory λ + N ( 0 , ε I theory λ ) ,
I sim λ = I theory λ + N ( a ( λ ) , ε I theory λ ) ,
ε = I expt I theory ,

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