Abstract

Spectroscopic optical coherence tomography (sOCT) enables the mapping of chromophore concentrations and image contrast enhancement in tissue. Acquisition of depth resolved spectra by sOCT requires analysis methods with optimal spectral/spatial resolution and spectral recovery. In this article, we quantitatively compare the available methods, i.e. the short time Fourier transform (STFT), wavelet transforms, the Wigner-Ville distribution and the dual window method through simulations in tissue-like media. We conclude that all methods suffer from the trade-off in spectral/spatial resolution, and that the STFT is the optimal method for the specific application of the localized quantification of hemoglobin concentration and oxygen saturation.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
    [CrossRef] [PubMed]
  6. N. Bosschaart, M. C. G. Aalders, D. J. Faber, J. J. A. Weda, M. J. C. van Gemert, T. G. van Leeuwen, “Quantitative measurements of absorption spectra in scattering media by low-coherence spectroscopy,” Opt. Lett. 34(23), 3746–3748 (2009).
    [CrossRef] [PubMed]
  7. N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
    [CrossRef] [PubMed]
  8. N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. Data tabulated from various sources compiled by S. Prahl, http://omlc.ogi.edu/spectra .
  18. N. Bosschaart, M. C. G. Aalders, T. G. van Leeuwen, D. J. Faber, “Spectral domain detection in low-coherence spectroscopy,” Biomed. Opt. Express 3(9), 2263–2272 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2013 (1)

2012 (2)

2011 (3)

F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (2)

2007 (1)

2005 (1)

2004 (1)

2003 (1)

2000 (2)

1998 (1)

1989 (1)

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

Aalders, M. C. G.

N. Bosschaart, M. C. G. Aalders, T. G. van Leeuwen, D. J. Faber, “Spectral domain detection in low-coherence spectroscopy,” Biomed. Opt. Express 3(9), 2263–2272 (2012).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

N. Bosschaart, M. C. G. Aalders, D. J. Faber, J. J. A. Weda, M. J. C. van Gemert, T. G. van Leeuwen, “Quantitative measurements of absorption spectra in scattering media by low-coherence spectroscopy,” Opt. Lett. 34(23), 3746–3748 (2009).
[CrossRef] [PubMed]

Backman, V.

Boppart, S. A.

Bosschaart, N.

N. Bosschaart, M. C. G. Aalders, T. G. van Leeuwen, D. J. Faber, “Spectral domain detection in low-coherence spectroscopy,” Biomed. Opt. Express 3(9), 2263–2272 (2012).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

N. Bosschaart, M. C. G. Aalders, D. J. Faber, J. J. A. Weda, M. J. C. van Gemert, T. G. van Leeuwen, “Quantitative measurements of absorption spectra in scattering media by low-coherence spectroscopy,” Opt. Lett. 34(23), 3746–3748 (2009).
[CrossRef] [PubMed]

Cohen, L.

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

Drexler, W.

Eckert, J.

Faber, D. J.

N. Bosschaart, M. C. G. Aalders, T. G. van Leeuwen, D. J. Faber, “Spectral domain detection in low-coherence spectroscopy,” Biomed. Opt. Express 3(9), 2263–2272 (2012).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

N. Bosschaart, M. C. G. Aalders, D. J. Faber, J. J. A. Weda, M. J. C. van Gemert, T. G. van Leeuwen, “Quantitative measurements of absorption spectra in scattering media by low-coherence spectroscopy,” Opt. Lett. 34(23), 3746–3748 (2009).
[CrossRef] [PubMed]

Fercher, A. F.

Fleming, C. P.

Fujimoto, J. G.

Gardecki, J. A.

Graf, R. N.

Grant, G.

F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
[CrossRef] [PubMed]

Halpern, E. F.

Hitzenberger, C. K.

Ippen, E. P.

Izatt, J. A.

Kamalabadi, F.

Kärtner, F. X.

Kowalczyk, A.

Leitgeb, R.

Li, X.

Li, X. D.

Marks, D. L.

Morgner, U.

Pitris, C.

Robles, F.

Robles, F. E.

F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
[CrossRef] [PubMed]

Schmitt, J. M.

Sticker, M.

Tearney, G. J.

van Gemert, M. J. C.

van Leeuwen, T. G.

N. Bosschaart, M. C. G. Aalders, T. G. van Leeuwen, D. J. Faber, “Spectral domain detection in low-coherence spectroscopy,” Biomed. Opt. Express 3(9), 2263–2272 (2012).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, M. C. G. Aalders, D. J. Faber, J. J. A. Weda, M. J. C. van Gemert, T. G. van Leeuwen, “Quantitative measurements of absorption spectra in scattering media by low-coherence spectroscopy,” Opt. Lett. 34(23), 3746–3748 (2009).
[CrossRef] [PubMed]

Wax, A.

Weda, J. J. A.

Wilson, C.

F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
[CrossRef] [PubMed]

Wojtkowski, M.

Xiang, S. H.

Xu, C.

Yang, C.

Ye, J.

Yi, J.

Yung, K. M.

Appl. Opt. (1)

Biomed. Opt. Express (2)

J. Biomed. Opt. (2)

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “In vivo low-coherence spectroscopic measurements of local hemoglobin absorption spectra in human skin,” J. Biomed. Opt. 16(10), 100504 (2011).
[CrossRef] [PubMed]

N. Bosschaart, D. J. Faber, T. G. van Leeuwen, M. C. G. Aalders, “Measurements of wavelength dependent scattering and backscattering coefficients by low-coherence spectroscopy,” J. Biomed. Opt. 16(3), 030503 (2011).
[CrossRef] [PubMed]

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

Nat. Photonics (1)

F. E. Robles, C. Wilson, G. Grant, A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (7)

Proc. IEEE (1)

L. Cohen, “Time-frequency distributions – a review,” Proc. IEEE 77(7), 941–981 (1989).
[CrossRef]

Other (2)

Data tabulated from various sources compiled by S. Prahl, http://omlc.ogi.edu/spectra .

N. Bosschaart, T. G. van Leeuwen, M. C. G. Aalders, B. Hermann, W. Drexler, and D. J. Faber, “Spectroscopic low coherence interferometry”, Chapter 23 in Optical Coherence Tomography – Technology and Applications, W. Drexler and J.G. Fujimoto, eds. (Springer Berlin Heidelberg New York USA), 2nd edition (2013)

Supplementary Material (1)

» Media 1: MOV (666 KB)     

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Figures (8)

Fig. 1
Fig. 1

Simulation of two reflectors (R1 and R2) for the DW and STFT method (Case 1): (a) recovered A-scans. (b) recovered spectra from R1, no filtering. (c) recovered spectra from R2, no filtering. (d) Fourier transform on the recovered spectra from R2, revealing an interference term at a distance of 25 µm (separation of R1 and R2) for the DW method. (d) recovered spectra from R1, low-pass filtered at 7 µm. (e) recovered spectra from R2, low-pass filtered at 7 µm. The actual, and STFT-recovered spectra overlap in figures b, c, e and f.

Fig. 2
Fig. 2

Recovered absorption spectra µa from the blood volume between R1 and R2 for the DW and STFT method (Case 1).

Fig. 3
Fig. 3

For both the DW and the STFT method: (a) fitted oxygen saturation SO2. (b) fitted total hemoglobin concentration [tHb]. (c) χ2 of µa as a function of actual SO2 for the case of two reflectors (Case 1). Error bars represent the 95% confidence intervals of the fit parameters.

Fig. 4
Fig. 4

Simulation of three reflectors (R1, R2 and R3) for the DW and STFT method (Case 2) with R2 and R3 separated at 20 µm: (a) recovered A-scans. (b) recovered absorption spectra µa from the blood volume between R1 and R2. (c) recovered A-scans in the presence of noise. (d) recovered absorption spectra µa from the blood volume between R1 and R2 in the presence of noise. Media 1 shows for panel a and b (without noise) how R3 approaches R2 and its effect on µa for both methods.

Fig. 5
Fig. 5

For the case of three reflectors (Case 2): (a) χ2 of µa. (b) fitted total hemoglobin concentration [tHb]. (c) fitted oxygen saturation SO2 as a function of the separation between R2 and R3. Error bars represent the 95% confidence intervals of the fit parameters.

Fig. 6
Fig. 6

Influence of noise on χ2 of μa estimation: (a) separation R2 & R3 = 100 μm > wL, (b) separation R2 & R3 = 20 μm < wL but larger than wS, wM. Horizontal lines in both figures show noise on χ2 of μa estimation in absence of noise.

Fig. 7
Fig. 7

Effective spatial resolution of the DW and STFT method as a function of the power ratio between R3 and R2 (Case 3). The effective spatial resolution is defined as the separation between R2 and R3 (see Fig. 4a), where the χ2 of µa between R1 and R2 deviates more than 15% from the χ2 of µa without the presence of R3.

Fig. 8
Fig. 8

(a) Effective spatial resolution of the DW and STFT method as a function of ΔzL for the large spatial window wL(ΔzL,ΔkL) of the DW method (Case 4). (b) χ2 of µa for the STFT method and for the DW method, with a selection of sizes for ΔzL.

Tables (2)

Tables Icon

Table 1 Definition of simulated window sizes and theoretical resolutions

Tables Icon

Table 2 Quantification of performance of STFT and DW method for Case 1 (filtered and unfiltered).

Equations (10)

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i D ( k , z ) = | E S + E R | 2 = | E S | 2 + | E R | 2 + 2 | E S | | E R | cos ( k 2 z ) ,
i D ( 2 z ) i D ( k ) ,
S T F T ( k , z ; w ) = i D ( z ' ) w ( z z ' ; Δ z ) e i k z ' d z ' ,
Δ λ = λ 2 2 Δ z .
W V ( k , z ) = i D ( z + z ' ) i D * ( z z ' ) e ( i k z ' ) d z ' .
S R 2 ( k ) = S R 1 ( k ) e D μ a ( k ) ,
μ a ( k ) = 0.01 [ tHb ] { SO 2 μ a , H b O 2 ( k ) + ( 1 SO 2 ) μ a , H b ( k ) } ,
μ a ( k ) = 1 D ln ( S R 2 ( k ) S R 1 ( k ) ) ,
χ 2 = 1 N i = λ 1 λ N ( μ a , a c t μ a , s i m ) 2 μ a , a c t ,
S N R = 20 log ( amplitude R1 stand .dev . of noise ) ,

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