Abstract

We combine diffuse optical tomography for detecting and localizing an inhomogeneity in a two-layered tissue and diffuse optical spectroscopy (DOS) for characterizing the spectrum of that inhomogeneity. For detecting and localizing an inhomogeneity, we reduce the number of unknowns substantially by seeking only the location and size of the inhomogeneity. Then, we seek to recover an unknown specific tumor component of that inhomogeneity from spectral data. In doing so, we develop a method for distinguishing between healthy and tumorous lesions. We demonstrate the utility of this theory with numerical simulations.

© 2012 Optical Society of America

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References

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  1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
    [CrossRef]
  2. S. R. Arridge, and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
    [CrossRef]
  3. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
  4. A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
    [CrossRef]
  5. N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).
  6. S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
    [CrossRef]
  7. Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
    [CrossRef]
  8. K. Sokolov, R. A. Drezek, K. Gossage, and R. Richards-Kortum, “Reflectance spectroscopy with polarized light: is it sensitive to cellular and nuclear morphology,” Opt. Express 5, 302–317 (1999).
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    [CrossRef]
  10. P. Gonzalez-Rodriguez and A. D. Kim, “Light propagation in tissues with forward-peaked and large-angle scattering,” Appl. Opt. 47, 2599–2609 (2008).
    [CrossRef]
  11. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1996).
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    [CrossRef]
  13. T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy, Appl. Opt. 44, 2072–2081 (2005).
    [CrossRef]
  14. V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).
  15. A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
    [CrossRef]
  16. A. D. Kim and M. Moscoso, “Beam propagation in sharply peaked forward scattering media,” J. Opt. Soc. Am. A 21, 797–803 (2004).
    [CrossRef]
  17. P. González-Rodríguez and A. D. Kim, “Reflectance optical tomography in epithelial tissues,” Inverse Probl. 25, 015001 (2009).
    [CrossRef]

2009 (3)

S. R. Arridge, and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

P. González-Rodríguez and A. D. Kim, “Reflectance optical tomography in epithelial tissues,” Inverse Probl. 25, 015001 (2009).
[CrossRef]

2008 (1)

2007 (1)

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

2006 (1)

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

2005 (3)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef]

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy, Appl. Opt. 44, 2072–2081 (2005).
[CrossRef]

2004 (1)

2003 (3)

A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
[CrossRef]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

2001 (1)

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

1999 (1)

1998 (1)

Andersson-Engels, S.

Arridge, S. R.

S. R. Arridge, and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Backman, V.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Bean, S. M.

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Bentley, R. C.

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Butler, J.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Cartwright, P. S.

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Cerussi, A.

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

Cerussi, A. E.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Chang, V. Tuan-Chyan

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Chen, K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Collier, T.

Drezek, R. A.

Durkin, A.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

Follen, M.

Goldberg, M. J.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Gonzalez-Rodriguez, P.

González-Rodríguez, P.

P. González-Rodríguez and A. D. Kim, “Reflectance optical tomography in epithelial tissues,” Inverse Probl. 25, 015001 (2009).
[CrossRef]

Gossage, K.

Gratton, E.

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

Hsiang, D.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1996).

Jakubowski, D.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Keller, J. B.

Kim, A. D.

Kim, Y. L.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Kromin, A. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Kukreti, S.

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

Liu, D. L.

Liu, Y.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Malpica, A.

McBride, T. O.

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

Moscoso, M.

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef]

A. D. Kim and M. Moscoso, “Beam propagation in sharply peaked forward scattering media,” J. Opt. Soc. Am. A 21, 797–803 (2004).
[CrossRef]

Nilsson, A. M. K.

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Osterberg, U. L.

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

Osterman, K. S.

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

Palmer, G. M.

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Paulsen, K. D.

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

Pogue, B. W.

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

Poplack, S. P.

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

Ramanujam, N.

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Richards-Kortum, R.

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Roy, H. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Schotland, J. C.

S. R. Arridge, and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Shah, N.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Sokolov, K.

Sturesson, C.

Tromberg, B.

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

Tromberg, B. J.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

Wali, R. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Wells, W. A.

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

Appl. Opt. (3)

Dis. Markers (1)

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “The role of diffuse optical spectroscopy in the clinical management of breast cancer,” Dis. Markers 19, 95–105 (2003).

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

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture in its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Inverse Probl. (2)

S. R. Arridge, and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

P. González-Rodríguez and A. D. Kim, “Reflectance optical tomography in epithelial tissues,” Inverse Probl. 25, 015001 (2009).
[CrossRef]

J. Biomed. Opt. (3)

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005(2006).
[CrossRef]

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef]

S. Kukreti, A. Cerussi, B. Tromberg, and E. Gratton, “Intrinsic tumor biomarkers revealed by novel double-differential spectroscopic analysis of near-infrared spectra,” J. Biomed. Opt. 12, 020509 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Neoplasia (1)

V. Tuan-Chyan Chang, P. S. Cartwright, S. M. Bean, G. M. Palmer, R. C. Bentley, and N. Ramanujam, “Quantitative physiology of the precancerous cervix in vivo through optical spectroscopy,” Neoplasia 11, 325–332 (2009).

Opt. Express (1)

Radiology (1)

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

Other (1)

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1996).

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Figures (8)

Fig. 1.
Fig. 1.

Absorption spectra of healthy (solid black curve) and tumorous (red dashed curve with ○ symbols) inhomogeneities. The inset shows the STC added to the spectrum of the tumorous tissue. The STC is used only to calculate the forward data. It is not known during the inversion.

Fig. 2.
Fig. 2.

Rnorm(x) defined in Eq. (12). (Left inset) Detail of the normalized data. (Right inset) Spectrally resolved reflectance Eq. (11) for constant λ=958nm.

Fig. 3.
Fig. 3.

Data amplitude as a function of the contrast A(λ) between the inhomogeneity and the background for λ=650nm (solid line), λ=818nm (line with dots), and λ=1000nm (line with open circles). Note that RmaxRmin is a linear function of A(λ) for small inhomogeneity to background contrast.

Fig. 4.
Fig. 4.

Simulated reflectance data at λj=958nm with no noise (solid line), with 1% noise (dashed line with open circles), and with 6% (dotted–dashed line with crosses).

Fig. 5.
Fig. 5.

Solid lines, recovered spectra for (left) a benign inhomogeneity and (right) a malignant inhomogeneity. Dashed curves with dots, four-component fittings. 1% data noise level.

Fig. 6.
Fig. 6.

Images (Left) of the real inhomogeneity, (middle) of the residual for the tumorous inhomogeneity, and (right) of the residual for the benign inhomogeneity. The images are reconstructed using the data at 958 nm.

Fig. 7.
Fig. 7.

Retrieved STC in the spectra for 1% noise level (dashed line) and 6% noise level (dotted–dashed line with open circles). The true STC is depicted with a solid line.

Fig. 8.
Fig. 8.

Differences between the calculated spectra and their four-component fitting for tissues with (solid line with open circles) and without (dashed line with crosses) STC. The real STC is represented by a black solid line.

Tables (2)

Tables Icon

Table 1. Component Concentrations of the Background and the Inhomogeneitya

Tables Icon

Table 2. Depths and Sizes Obtained for Different Noise Levelsa

Equations (13)

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

μa(r;λ)=ici(r)ϵi(λ)+STC(r;λ),
Ω·I+μaIμsLI=0.
LI=I+S2f(Ω·Ω)I(r,Ω;λ)dΩ.
S2f(Ω·Ω)dΩ=1.
g=2π1+1f(Ω·Ω)(Ω·Ω)d(Ω·Ω).
μa1(x,z;λ)=μa10(λ)+μ˜a1(x,z;λ)+n1(x,z),
μa2(x,z;λ)=μa20(λ)+n2(x,z),
μ˜a1(x,z;λ)=A(λ)e((xxa)2+(zza)2)/w2
μs1=μs2=qλp,
LgFPEI=(1α0)I+α1Ω2(1α2Ω2)1I+14πS2[b0f0(Ω·Ω)+3b1(Ω·Ω)]I(r,Ω;λ)dΩ,
R(x;λ)=Ω·z^<0I(x,0,Ω;λ)Ω·z^dΩ,
Rnorm(x)=Rmax(λ)R(x;λ)maxx(Rmax(λ)R(x;λ)),
f[za,w]=R˜normRnorm[za,w]2,

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