Abstract

In spectroscopic optical coherence tomography, it is important and useful to separately estimate the absorption and the scattering properties of tissue. In this paper, we propose a least-squares fitting algorithm to separate absorption and scattering profiles when near-infrared absorbing dyes are used. The algorithm utilizes the broadband Ti:sapphire laser spectrum together with joint time-frequency analysis. Noise contribution to the final estimation was analyzed using simulation. The validity of our algorithm was demonstrated using both single-layer and multi-layer tissue phantoms.

© 2004 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
    [CrossRef] [PubMed]
  3. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys, 66, 239–303 (2003).
    [CrossRef]
  4. U. Morgner, W. Drexler, F. C. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25, 111–113 (2000).
    [CrossRef]
  5. R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, “Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography,” Opt. Lett. 25, 820–822 (2000).
    [CrossRef]
  6. D. J. Faber, E. G. Mik, M. C. G. Aalders, and T. G. van Leeuwen, “Light absorption of (oxy-) hemoglobin assessed by spectroscopic optical coherence tomography,” Opt. Lett. 28, 1436–1438 (2003).
    [CrossRef] [PubMed]
  7. C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. 29, (2004).
    [CrossRef] [PubMed]
  8. B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher, and W. Drexler, “Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography,” Opt. Express 12, 1677–1688 (2004).
    [CrossRef] [PubMed]
  9. K. D. Rao, M. A. Choma, S. Yazdanfar, A. M. Rollins, and J. A. Izatt, “Molecular contrast in optical coherence tomography by use of a pump-probe technique,” Opt. Lett. 28, 340–342 (2003).
    [CrossRef] [PubMed]
  10. C. Yang, M. A. Choma, L. E. Lamb, J. D. Simon, and J. A. Izatt, “Protein-based molecular contrast optical coherence tomography with phytochrome as the contrast agent,” Opt. Lett. 29, 1396–1398 (2004).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge,1999).
  12. C. Yang, M. A. Choma, J. D. Simon, and J. A. Izatt. “Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper SB3.
  13. C. Xu and S. A. Boppart. “Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper FH9.
  14. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Differential absorption imaging with optical coherence tomography,” J. Opt. Soc. Am. A 15, 2288–2296 (1998).
    [CrossRef]
  15. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. 42, 204–217 (2003).
    [CrossRef] [PubMed]

2004 (3)

2003 (4)

2000 (2)

1998 (1)

1995 (1)

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Aalders, M. C. G.

Bizheva, K.

Boppart, S. A.

C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. 29, (2004).
[CrossRef] [PubMed]

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. 42, 204–217 (2003).
[CrossRef] [PubMed]

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

C. Xu and S. A. Boppart. “Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper FH9.

Born, M.

M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge,1999).

Bouma, B. E.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

Brezinski, M. E.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Choma, M. A.

Drexler, W.

Faber, D. J.

Fercher, A. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

U. Morgner, W. Drexler, F. C. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25, 111–113 (2000).
[CrossRef]

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys, 66, 239–303 (2003).
[CrossRef]

R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, “Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography,” Opt. Lett. 25, 820–822 (2000).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ippen, E. P.

Izatt, J. A.

Kartner, F. C.

Kowalczyk, A.

Lamb, L. E.

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys, 66, 239–303 (2003).
[CrossRef]

Leeuwen, T. G. van

Leitgeb, R.

Li, X. D.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Marks, D. L.

C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. 29, (2004).
[CrossRef] [PubMed]

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. 42, 204–217 (2003).
[CrossRef] [PubMed]

Mik, E. G.

Morgner, U.

Oldenburg, A. L.

Pitris, C.

Povazay, B.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rao, K. D.

Reynolds, J. J.

Rollins, A. M.

Sattmann, H.

Schmetterer, L.

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Simon, J. D.

C. Yang, M. A. Choma, L. E. Lamb, J. D. Simon, and J. A. Izatt, “Protein-based molecular contrast optical coherence tomography with phytochrome as the contrast agent,” Opt. Lett. 29, 1396–1398 (2004).
[CrossRef] [PubMed]

C. Yang, M. A. Choma, J. D. Simon, and J. A. Izatt. “Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper SB3.

Southern, J. F.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

Sticker, M.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

Unterhuber, A.

Wojtkowski, M.

Wolf, E.

M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge,1999).

Xiang, S. H.

Xu, C.

C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. 29, (2004).
[CrossRef] [PubMed]

C. Xu and S. A. Boppart. “Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper FH9.

Yang, C.

C. Yang, M. A. Choma, L. E. Lamb, J. D. Simon, and J. A. Izatt, “Protein-based molecular contrast optical coherence tomography with phytochrome as the contrast agent,” Opt. Lett. 29, 1396–1398 (2004).
[CrossRef] [PubMed]

C. Yang, M. A. Choma, J. D. Simon, and J. A. Izatt. “Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper SB3.

Yazdanfar, S.

Ye, J.

C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. 29, (2004).
[CrossRef] [PubMed]

Yung, K. M.

Appl. Opt. (1)

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

Nature Medicine (1)

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine 1, 970–972 (1995).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (6)

Rep. Prog. Phys, (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys, 66, 239–303 (2003).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge,1999).

C. Yang, M. A. Choma, J. D. Simon, and J. A. Izatt. “Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper SB3.

C. Xu and S. A. Boppart. “Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper FH9.

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Figures (6)

Fig. 1.
Fig. 1.

Errors in retrieved absorption fa as a function of SNR in SOCT I(λ, z).

Fig. 2.
Fig. 2.

Emission spectrum of the Ti:Al2O3 laser (black curve) and absorption spectrum of dye ADS830WS (red curve). Also shown is the FWHM region used for determining W(λ).

Fig. 3.
Fig. 3.

Absorption/scattering attenuation loss due to various absorbers/scatterers as measured by a spectrometer: 40 μM ADS830WS NIR dye solution, 1% 160 nm silica microbead solution, 0.5% 330 nm silica microbead solution, and 0.5 % 800 nm silica microbead solution, potato slice, and murine skin.

Fig. 4.
Fig. 4.

Separation of absorption and scattering losses from distinctive interfaces: total attenuation profile measured by SOCT (black curve), resolved absorption profile by the separation algorithm (green curve), resolved scattering profile by the separation algorithm (red curve), the sum of the resolved absorption profile and the resolved scattering profile (blue curve).

Fig. 5.
Fig. 5.

Resolved absorber and scatterer concentrations in turbid media. (a) Resolved cumulative dye concentrations from solutions with different dye concentrations but the same microbead concentration. (b) Resolved cumulative microbead concentrations from solutions with different microbead concentrations but the same dye concentration. The smooth lines represent the least-squares-fitted model of Eq. (10). The resolved concentrations retrieved from the slopes of the fitted lines are shown as well. The insets show the diagrams of the samples.

Fig. 6.
Fig. 6.

Resolved absorber and scatter concentrations in a turbid multi-layer phantom. (a) Resolved cumulative dye concentration. (b) Resolved cumulative microbead concentration. The lines represent the least-squares-fitted model of Eq. (10). The resolved concentrations retrieved from the slopes of the fitted lines are also shown. The inset in (a) shows the diagram of the samples.

Equations (24)

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

I ( λ , z ) = S ( λ ) H r ( λ , z ) H m ( λ , z ) H s ( λ , z ) .
H m ( λ , z ) = exp { 2 0 z [ μ a ( λ , z ) + μ s ( λ , z ) ] dz } .
H r ( λ , z ) = H r ( λ ) H r ( z ) ,
H s ( λ , z ) = H s ( λ ) H s ( z ) .
I ( λ , z ) = S ( λ ) H s ( λ ) H r ( λ ) R ( z ) exp [ 2 0 z [ μ a ( λ , z ) + μ s ( λ , z ) ] dz ] ,
I ( λ , z = 0 ) = S ( λ ) H r ( λ ) H s ( λ ) R ( z = 0 ) .
I ( λ , z ) I ( λ , z ) I ( λ , z = 0 ) = R ( z ) exp { 2 0 z [ μ a ( λ , z ) + μ s ( λ , z ) ] dz } .
μ a ( λ , z ) = ε a ( λ ) f a ( z ) ,
μ s ( λ , z ) = ε s ( λ ) f s ( z ) ,
2 0 z [ μ a ( λ , z ) + μ s ( λ , z ) ] dz = 2 [ ε a ( λ ) 0 z f a ( z ) dz + ε s ( λ ) 0 z f s ( z ) dz ] .
Y ( λ , z ) log [ I ( λ , z ) ]
= log R ( z ) 2 [ ε a ( λ ) 0 z f a ( z ) dz + ε s ( λ ) 0 z f s ( z ) dz ]
= ε a ( λ ) F a ( z ) ε s ( λ ) F s ( z ) + C ( z ) .
F a ( z ) 2 0 z f a ( z ) dz , F s ( z ) 2 0 z f s ( z ) dz , C ( z ) log R ( z ) .
E ( z ) = λ 1 λ 2 [ F a ( z ) ε a ( λ ) F s ( z ) ε s ( λ ) + C ( z ) Y ( λ , z ) ] 2 W ( λ ) d λ ,
[ λ 1 λ 2 ε a 2 ( λ ) W ( λ ) d λ λ 1 λ 2 ε s ( λ ) ε a ( λ ) W ( λ ) d λ λ 1 λ 2 ε a ( λ ) W ( λ ) d λ λ 1 λ 2 ε a ( λ ) ε s W ( λ ) d λ λ 1 λ 2 ε s 2 ( λ ) W ( λ ) d λ λ 1 λ 2 ε s ( λ ) W ( λ ) d λ λ 1 λ 2 ε a ( λ ) W ( λ ) d λ λ 1 λ 2 ε s ( λ ) W ( λ ) d λ λ 1 λ 2 W ( λ ) d λ ] A [ F a ( z ) F s ( z ) C ( z ) ] X = [ λ 1 λ 2 Y ( λ , z ) ε a ( λ ) W ( λ ) d λ λ 1 λ 2 Y ( λ , z ) ε s ( λ ) W ( λ ) d λ λ 1 λ 2 Y ( λ , z ) W ( λ ) d λ ] Y .
[ λ 1 λ 2 ε a 2 W ( λ ) d λ λ 1 λ 2 λ ε s ( λ ) W ( λ ) d λ λ 1 λ 2 ε a ( λ ) W ( λ ) d λ λ 1 λ 2 λ ε a ( λ ) W ( λ ) d λ λ 1 λ 2 λ 2 W ( λ ) d λ λ 1 λ 2 λ W ( λ ) d λ λ 1 λ 2 ε a ( λ ) W ( λ ) d λ λ 1 λ 2 λ W ( λ ) d λ λ 1 λ 2 W ( λ ) d λ ] [ F a ( z ) a F s ( z ) D ( z ) ] = [ λ 1 λ 2 Y ( λ , z ) ε a ( λ ) W ( λ ) d λ λ 1 λ 2 λ Y ( λ , z ) W ( λ ) d λ λ 1 λ 2 Y ( λ , z ) W ( λ ) d λ ] ,
AX = Y ,
X α = arg min { Y AX 2 + α 2 LX 2 } .
X = ( A T A + α 2 L T L ) 1 A T Y .
X = A 1 Y .
σ x i 2 = j = 1 3 b ij 2 σ y j 2 ,
F = λ LD [ F LD ( F high F low ) + F low ] λ ( F high F low ) + F low
δ λ = λ c 2 2 l STFT ,

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