Abstract

Current methods for analysis of spectroscopic optical coherence tomography (SOCT) signals suffer from an inherent tradeoff between time (depth) and frequency (wavelength) resolution. Here, we present a dual window (DW) method for reconstructing time frequency distributions (TFDs) that applies two orthogonal Gaussian windows that independently determine the spectral and temporal resolution. The effectiveness of the method is demonstrated in simulations and in processing of measured OCT signals that contain fields which vary in time and frequency. The DW method yields TFDs that maintain high spectral and temporal resolution and are free from the artifacts and limitations commonly observed with other processing methods.

© 2009 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. U. Morgner, W. Drexler, F. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, "Spectroscopic optical coherence tomography," Opt. Lett. 25, 111-113 (2000).
    [CrossRef]
  3. J. F. deBoer, T. E. Milner, M. J. C. vanGemert, and J. S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography," Opt. Lett. 22, 934-936 (1997).
    [CrossRef]
  4. J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, "In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomograghy," Opt. Lett. 22, 1439-1441 (1997).
    [CrossRef]
  5. Y. H. Zhao, Z. P. Chen, C. Saxer, S. H. Xiang, J. F. de Boer, and J. S. Nelson, "Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity," Opt. Lett. 25, 114-116 (2000).
    [CrossRef]
  6. C. Y. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, "Spectroscopic spectral-domain optical coherence microscopy," Opt. Lett. 31, 1079-1081 (2006).
    [CrossRef] [PubMed]
  7. A. Wax, C. H. Yang, and J. A. Izatt, "Fourier-domain low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 28, 1230-1232 (2003).
    [CrossRef] [PubMed]
  8. R. N. Graf and A. Wax, "Nuclear morphology measurements using Fourier domain low coherence interferometry," Opt. Express 13, 4693-4698 (2005).
    [CrossRef]
  9. M. Bayram and R. G. Baraniuk, "Multiple window time-frequency analysis," Proceedings of the IEEE-Sp International Symposium on Time-Frequency and Time-Scale Analysis  535, 173-176 (1996).
    [CrossRef]
  10. D. J. Thomson, "Spectrum Estimation and Harmonic-Analysis," Proceedings of the IEEE 70, 1055-1096 (1982).
    [CrossRef]
  11. C. Y. Xu, F. Kamalabadi, and S. A. Boppart, "Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography," Appl. Opt. 44, 1813-1822 (2005).
    [CrossRef] [PubMed]
  12. R. N. Graf and A. Wax, "Temporal coherence and time-frequency distributions in spectroscopic optical coherence tomography," J. Opt. Soc. Am. A 24, 2186-2195 (2007).
    [CrossRef]
  13. L. Cohen, "Time Frequency-Distributions - a Review," Proc. IEEE 77, 941-981 (1989).
    [CrossRef]
  14. K. F. Lee, F. Reil, S. Bali, A. Wax, and J. E. Thomas, "Heterodyne measurement of Wigner distributions for classical optical fields," Opt. Lett. 24, 1370-1372 (1999)
    [CrossRef]
  15. R. N. Graf, W. J. Brown, and A. Wax, "Parallel frequency domain optical coherence tomography scatter-mode imaging of the hamster cheek pouch using a thermal light source," Opt. Lett. 33, 1285-1287 (2008).
    [CrossRef] [PubMed]
  16. F. H. White and K. Gohari, "Cellular and Nuclear Volumetric Alterations during Differentiation of Normal Hamster-Cheek Pouch Epithelium," Arch. Dermatol. Res. 273, 307-318 (1982).
    [CrossRef] [PubMed]
  17. A. Knuttel and M. Boehlau-Godau, "Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography," J. Biomed. Opt. 5, 83- 92 (2000).
    [CrossRef] [PubMed]
  18. H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
    [CrossRef]
  19. V. Tuchin, "Tissue optics: light scattering methods and instruments for medical diagnosis," SPIE (2000).
  20. T. Hillman and D. Sampson, "The effect of water dispersion and absorption on axial resolution in ultrahigh-resolution optical coherence tomography," Opt. Express 13, 1860-1874 (2005).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2006 (1)

2005 (4)

2003 (1)

2000 (3)

1999 (1)

1997 (2)

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]

1989 (1)

L. Cohen, "Time Frequency-Distributions - a Review," Proc. IEEE 77, 941-981 (1989).
[CrossRef]

1982 (2)

F. H. White and K. Gohari, "Cellular and Nuclear Volumetric Alterations during Differentiation of Normal Hamster-Cheek Pouch Epithelium," Arch. Dermatol. Res. 273, 307-318 (1982).
[CrossRef] [PubMed]

D. J. Thomson, "Spectrum Estimation and Harmonic-Analysis," Proceedings of the IEEE 70, 1055-1096 (1982).
[CrossRef]

Bali, S.

Baraniuk, R. G.

M. Bayram and R. G. Baraniuk, "Multiple window time-frequency analysis," Proceedings of the IEEE-Sp International Symposium on Time-Frequency and Time-Scale Analysis  535, 173-176 (1996).
[CrossRef]

Barton, J. K.

Bayram, M.

M. Bayram and R. G. Baraniuk, "Multiple window time-frequency analysis," Proceedings of the IEEE-Sp International Symposium on Time-Frequency and Time-Scale Analysis  535, 173-176 (1996).
[CrossRef]

Boehlau-Godau, M.

A. Knuttel and M. Boehlau-Godau, "Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography," J. Biomed. Opt. 5, 83- 92 (2000).
[CrossRef] [PubMed]

Boppart, S. A.

Brown, W. J.

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]

Chen, Z. P.

Cohen, L.

L. Cohen, "Time Frequency-Distributions - a Review," Proc. IEEE 77, 941-981 (1989).
[CrossRef]

de Boer, J. F.

deBoer, J. F.

Ding, H.

H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
[CrossRef]

Drexler, W.

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. X. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, "Spectroscopic optical coherence tomography," Opt. Lett. 25, 111-113 (2000).
[CrossRef]

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]

Gohari, K.

F. H. White and K. Gohari, "Cellular and Nuclear Volumetric Alterations during Differentiation of Normal Hamster-Cheek Pouch Epithelium," Arch. Dermatol. Res. 273, 307-318 (1982).
[CrossRef] [PubMed]

Graf, R. N.

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.

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]

Hillman, T.

Hu, X.

H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
[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.

Jacobs, K.

H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
[CrossRef]

Kamalabadi, F.

Kartner, F. X.

Knuttel, A.

A. Knuttel and M. Boehlau-Godau, "Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography," J. Biomed. Opt. 5, 83- 92 (2000).
[CrossRef] [PubMed]

Kulkami, M. D.

Lee, K. F.

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]

Lu, J.

H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
[CrossRef]

Luo, W.

Milner, T. E.

Morgner, U.

Nelson, J. S.

Pitris, C.

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]

Ralston, T. S.

Reil, F.

Sampson, D.

Saxer, C.

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]

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.

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]

Tan, W.

Thomas, J. E.

Thomson, D. J.

D. J. Thomson, "Spectrum Estimation and Harmonic-Analysis," Proceedings of the IEEE 70, 1055-1096 (1982).
[CrossRef]

vanGemert, M. J. C.

Vinegoni, C.

Wax, A.

Welch, A. J.

White, F. H.

F. H. White and K. Gohari, "Cellular and Nuclear Volumetric Alterations during Differentiation of Normal Hamster-Cheek Pouch Epithelium," Arch. Dermatol. Res. 273, 307-318 (1982).
[CrossRef] [PubMed]

Xiang, S. H.

Xu, C. Y.

Yang, C. H.

Yazdanfar, S.

Zhao, Y. H.

Appl. Opt. (1)

Arch. Dermatol. Res. (1)

F. H. White and K. Gohari, "Cellular and Nuclear Volumetric Alterations during Differentiation of Normal Hamster-Cheek Pouch Epithelium," Arch. Dermatol. Res. 273, 307-318 (1982).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

A. Knuttel and M. Boehlau-Godau, "Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography," J. Biomed. Opt. 5, 83- 92 (2000).
[CrossRef] [PubMed]

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

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

H. Ding, J. Lu, K. Jacobs, and X. Hu, "Determination of refractive indices of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A. 22, 1151-1157 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

C. Y. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, "Spectroscopic spectral-domain optical coherence microscopy," Opt. Lett. 31, 1079-1081 (2006).
[CrossRef] [PubMed]

R. N. Graf, W. J. Brown, and A. Wax, "Parallel frequency domain optical coherence tomography scatter-mode imaging of the hamster cheek pouch using a thermal light source," Opt. Lett. 33, 1285-1287 (2008).
[CrossRef] [PubMed]

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

Y. H. Zhao, Z. P. Chen, C. Saxer, S. H. Xiang, J. F. de Boer, and J. S. Nelson, "Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity," Opt. Lett. 25, 114-116 (2000).
[CrossRef]

J. F. deBoer, T. E. Milner, M. J. C. vanGemert, and J. S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography," Opt. Lett. 22, 934-936 (1997).
[CrossRef]

J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, "In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomograghy," Opt. Lett. 22, 1439-1441 (1997).
[CrossRef]

K. F. Lee, F. Reil, S. Bali, A. Wax, and J. E. Thomas, "Heterodyne measurement of Wigner distributions for classical optical fields," Opt. Lett. 24, 1370-1372 (1999)
[CrossRef]

A. Wax, C. H. Yang, and J. A. Izatt, "Fourier-domain low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 28, 1230-1232 (2003).
[CrossRef] [PubMed]

Proc. IEEE (1)

L. Cohen, "Time Frequency-Distributions - a Review," Proc. IEEE 77, 941-981 (1989).
[CrossRef]

Proceedings of the IEEE (1)

D. J. Thomson, "Spectrum Estimation and Harmonic-Analysis," Proceedings of the IEEE 70, 1055-1096 (1982).
[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 (2)

M. Bayram and R. G. Baraniuk, "Multiple window time-frequency analysis," Proceedings of the IEEE-Sp International Symposium on Time-Frequency and Time-Scale Analysis  535, 173-176 (1996).
[CrossRef]

V. Tuchin, "Tissue optics: light scattering methods and instruments for medical diagnosis," SPIE (2000).

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Figures (9)

Fig. 1.
Fig. 1.

(a). Ideal TFD with E1 centered at z0 = 5 and k1 = 13 and E2 centered at z0 = 0 and k2 = 26. (b). Wigner TFD. (c). MH TFD. (d). Dual Window method.

Fig. 2.
Fig. 2.

(a). Ideal TFD with simulated source bandwidth of Δk = 35 length-1 units. (b). Narrow spectral window STFT with standard deviation = 2 length-1 units. (c). Wide spectral window STFT with standard deviation = 45 length -1 units. (d). Double window method using the two windows used in (b) and (c). (e). Time marginals (depth profile) of (a), (b), and (d). (f). Spectral profile at t = 4.5 in (a), (c), and (d).

Fig. 3.
Fig. 3.

(a). TFD of simulation 2 generated by the DW processing method. (b). Spectral profile corresponding to the dashed red line in (a). (c). Correlation plot with peak corresponding to sample spacing distance of 1.5 units.

Fig. 4.
Fig. 4.

(a). Illustration of absorption phantom. (b). pfdOCT image of absorption phantom. (c). Transmission spectrum of absorbing dye used in absorption phantom compared to source spectrum.

Fig. 5.
Fig. 5.

TFD of absorption phantom reconstructed with (a). Narrow spectral window STFT (b). Wide spectral window STFT (c). Moderate spectral window STFT (d). Double window method.

Fig. 6.
Fig. 6.

(a). Spectral cross-section at depth 245 μm in 5(c) and (d), along with dye transmission spectrum. (b). Spectral cross-section at depth 220 μm in 5(c) and (d), along with source spectrum. (c). Time marginals from 5(c) and (d), along with corresponding A-scan

Fig. 7.
Fig. 7.

(a). Spectral profiles of Fig. 6(a) with high frequency modulations removed. (b). Spectral profiles of Fig. 6(b) with high frequency modulations removed.

Fig. 8.
Fig. 8.

(a). Absorption phantom TFD generated with the DW method. (b). Spectrum corresponding to the dashed red line in (a). (c). Correlation plot with peak corresponding to phantom spacing distance of 20.60 μm ± 0.57 μm, in good agreement with the OCT thickness measurement.

Fig. 9.
Fig. 9.

(a). Histopathology of hamster cheek pouch used for experiments in section 5.2 with basal layer depth indicated. (b). TFD from hamster cheek pouch tissue generated with the DW method. Basal layer indicated by red dashed box. (c). Average spectrum from a 15.45 μm depth segment corresponding to the basal tissue layer (red box in part (b)). (d). Correlation plot with peak corresponding to scatterer diameter of 4.94 μm.

Tables (1)

Tables Icon

Table 1. Chi-squared calculations

Equations (15)

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

I ( k ) = I R ( k ) + I S ( k ) + 2 E R ( k ) E S * ( k ) · cos ( k · d ) ,
S ( k , z ) = 2 E R ( κ′ ) E S * ( κ′ ) · cos ( κ · d ) · e ( κ′ k ) 2 2 u 2 · e · z .
DW ( k , z ) = S 1 ( k , z ) · S 2 * ( k , z )
= 4 E S * ( k 1 ) E S ( k 2 ) · cos ( k 1 · d ) cos ( k 1 · d )
× e ( k 1 k ) 2 2 a 2 · e ( k 2 k ) 2 2 a 2 · e i ( k 1 k 2 ) z d k 1 d k 2 ,
Ω = k 1 + k 2 2 , q = k 1 k 2 , k 1 = Ω + q 2 , and k 2 = Ω q 2 ,
DW ( k , z ) = 4 E S * ( Ω + q 2 ) E S ( Ω q 2 ) · cos ( ( Ω + q 2 ) · d ) cos ( ( Ω + q 2 ) · d )
× e ( Ω + q 2 k ) 2 2 a 2 · e ( Ω - q 2 k ) 2 2 b 2 · e iqz dΩdq .
E S * ( Ω + q 2 ) E S ( Ω q 2 ) = W S ( Ω , ζ ) · e iqζ ,
DW ( k , z ) = 4 · W S ( Ω , ζ ) · e iqζ · cos ( 2 Ω · d ) cos ( q · d )
× e ( ( Ω k ) + q 2 ) 2 · ( 1 2 a 2 + 1 2 b 2 ) + q ( Ω k ) b 2 · e iqz d Ω dq .
DW ( k , z ) = 4 b π W S ( Ω , ζ ) · e 2 ( Ω k ) 2 b 2 e 2 ( d + ζ + z ) 2 a 2 cos ( 2 Ω · d ) · d Ω .
DW ( k , z ) | a 0 , b > > Δ k = S 1 ( k , z ) | a 0 S 2 ( k , z ) | b > > Δ k = 1 2 π f ( z ) F ( k ) e i · k·z .
W ( k , z ) = 1 2 π E S * ( z ζ 2 ) E S ( z + ζ 2 ) e ikζ ,
MH ( k , z ) = Re 1 2 π E ̄ s ( k ) E S ( z ) e ikz ,

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