Abstract

Phase sensing implementations of spectral domain optical coherence tomography (SDOCT) have demonstrated the ability to measure nanometer-scale temporal and spatial profiles of samples. However, the phase information suffers from a 2π ambiguity that limits observations of larger sample displacements to lengths less than half the source center wavelength. We introduce a synthetic wavelength phase unwrapping technique in SDOCT that uses spectral windowing and corrects the 2π ambiguity, providing accurate measurements of sample motion with information gained from standard SDOCT processing. We demonstrate this technique by using a common path implementation of SDOCT and correctly measure phase profiles from a phantom phase object and human epithelial cheek cells which produce multiple wrapping artifacts. Using a synthetic wavelength for phase unwrapping could prove useful in Doppler or other phase based implementations of OCT.

© 2009 Optical Society of America

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References

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  1. O. W. Richards, "Phase Difference Microscopy," Nature 154, 672 (1944).
    [CrossRef]
  2. H. Gundlach, "Phase contrast and differential interference contrast instrumentation and applications in cell, developmental, and marine biology," Opt. Eng. 32, 3223-3228, (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. N. Lue, W. Choi, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, "Quantitative phase imaging of live cells using fast Fourier phase microscopy," Appl. Opt. 46, 1836-1842, (2007).
    [CrossRef] [PubMed]
  8. T. Ikeda, G. Popescu, R. R. Dasari, and M.S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1167, (2005).
    [CrossRef] [PubMed]
  9. G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. 10, 060503 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
    [CrossRef] [PubMed]
  13. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30,1162-1164 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
    [CrossRef] [PubMed]
  16. Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).
  17. A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, "Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy," Opt. Express 15, 8115 - 8124, (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  27. D. L. Marks, S.C. Schlachter, A.M. Zysk, and S.A. Boppart, "Group refractive index reconstruction with broadband interferometric confocal microscopy," J. Opt. Soc. Am. A 25, 1156-1164 (2008).
    [CrossRef]
  28. R. Tripathi, N Nassif, J. S. Nelson, B. H. Park, and J. F. de Boer, "Spectral shaping for non-Gaussian source spectra in optical coherence tomography," Opt. Lett. 27, 406-408, (2002).
    [CrossRef]
  29. D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
    [CrossRef] [PubMed]
  30. A. Khmaladze, A. Restrepo-Martínez, M.K. Kim, R. Castañeda, and A. Blandón, "Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples," Appl. Opt. 47, 3203-3210 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. J.A. Izatt and M.A. Choma, "Theory of Optical Coherence Tomography," in Optical Coherence Tomography: Technology and Applications, W. Drexler and J.G. Fujimoto, eds. (Springer, 2008).
    [CrossRef]
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    [CrossRef]

2008 (3)

2007 (6)

2006 (1)

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

2005 (5)

2004 (2)

G. Popescu, L. P. Deflores, J.C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505, (2004).
[CrossRef] [PubMed]

D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
[CrossRef] [PubMed]

2003 (4)

2002 (2)

2001 (1)

1999 (1)

1997 (1)

1993 (1)

H. Gundlach, "Phase contrast and differential interference contrast instrumentation and applications in cell, developmental, and marine biology," Opt. Eng. 32, 3223-3228, (1993).
[CrossRef]

1985 (1)

1984 (1)

1977 (1)

1944 (1)

O. W. Richards, "Phase Difference Microscopy," Nature 154, 672 (1944).
[CrossRef]

Akkin, T.

Applegate, B. E.

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

Badizadegan, K.

Best, C. A.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Bevilacqua, F.

Blandón, A.

Boppart, S.A.

D. L. Marks, S.C. Schlachter, A.M. Zysk, and S.A. Boppart, "Group refractive index reconstruction with broadband interferometric confocal microscopy," J. Opt. Soc. Am. A 25, 1156-1164 (2008).
[CrossRef]

D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
[CrossRef] [PubMed]

Bouma, B. E.

Carney, P.S.

D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
[CrossRef] [PubMed]

Castañeda, R.

Cense, B.

Charrière, F.

Cheng, Y.

Choi, W.

Choma, M. A.

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30,1162-1164 (2005).
[CrossRef] [PubMed]

M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
[CrossRef] [PubMed]

Colomb, T.

Creath, K.

Creazzo, T. L.

Cuche, E.

Dakoff, A.

Dasari, R. R.

Dasari, R.R.

de Boer, J. F.

de Boer, J.F.

Deflores, L. P.

Depeursinge, C.

Doi, T.

Ellerbee, A. K.

A. K. Ellerbee and J.A. Izatt, "Phase retrieval in low-coherence interferometric microscopy," Opt. Lett. 32, 388-390, (2007).
[CrossRef] [PubMed]

A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, "Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy," Opt. Express 15, 8115 - 8124, (2007).
[CrossRef] [PubMed]

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30,1162-1164 (2005).
[CrossRef] [PubMed]

Emery, Y.

Feld, M. S.

Feld, M.S.

Fercher, A. F.

Fercher, A.F.

Gass, J.

Gundlach, H.

H. Gundlach, "Phase contrast and differential interference contrast instrumentation and applications in cell, developmental, and marine biology," Opt. Eng. 32, 3223-3228, (1993).
[CrossRef]

Hayasaki, Y.

S. Tamano, M. Otaka, Y. Hayasaki, "Two-wavelength phase-shifting low-coherence digital holography," Jpn. J. Appl. Phys. 47, 8844-8847 (2008).
[CrossRef]

Hitzenberger, C. K.

Hitzenberger, C.K.

Ikeda, T.

Iwai, H.

Izatt, J. A.

A. K. Ellerbee, T. L. Creazzo, and J. A. Izatt, "Investigating nanoscale cellular dynamics with cross-sectional spectral domain phase microscopy," Opt. Express 15, 8115 - 8124, (2007).
[CrossRef] [PubMed]

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30,1162-1164 (2005).
[CrossRef] [PubMed]

M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
[CrossRef] [PubMed]

Izatt, J.A.

Joo, C.

Khmaladze, A.

Kim, M. K.

Kim, M.K.

Kuhn, J.

Leitgeb, R.

Lo, C.

Lue, N.

Mann, C. J.

Marks, D. L.

Marks, D.L.

D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
[CrossRef] [PubMed]

Marquet, P.

McDowell, E. J.

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

Montfort, F.

Nassif, N

Nelson, J. S.

Otaka, M.

S. Tamano, M. Otaka, Y. Hayasaki, "Two-wavelength phase-shifting low-coherence digital holography," Jpn. J. Appl. Phys. 47, 8844-8847 (2008).
[CrossRef]

Park, B. H.

Pierce, M. C.

Popescu, G.

Restrepo-Martínez, A.

Richards, O. W.

O. W. Richards, "Phase Difference Microscopy," Nature 154, 672 (1944).
[CrossRef]

Sarunic, M. V.

Schlachter, S.C.

Sticker, M.

Tamano, S.

S. Tamano, M. Otaka, Y. Hayasaki, "Two-wavelength phase-shifting low-coherence digital holography," Jpn. J. Appl. Phys. 47, 8844-8847 (2008).
[CrossRef]

Tanimura, Y.

Tearney, G. J.

Tilford, C. R.

Toyoda, K.

Tripathi, R.

Vaughan, J.C.

Warnasooriya, N.

Wax, A.

Wyant, J. C.

Yang, C.

Yazdanfar, S.

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

Yu, L.

Zysk, A.M.

Appl. Opt. (6)

J. Biomed. Opt. (4)

D.L. Marks, P.S. Carney, and S.A. Boppart, "Adaptive spectral apodization for sidelobe reduction in optical coherence tomography images," J. Biomed. Opt. 9, 1281-1287 (2004).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasm streaming using spectral domain phase microscopy," J. Biomed. Opt. 11,024014 (2006).
[CrossRef] [PubMed]

Q1. E. J. McDowell, A. K. Ellerbee, M. A. Choma, B. E. Applegate, and J. A. Izatt, "Spectral domain phase microscopy for local measurements of cytoskeletal rheology in single cells," J. Biomed. Opt.04400, (2007).

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

Jpn. J. Appl. Phys. (1)

S. Tamano, M. Otaka, Y. Hayasaki, "Two-wavelength phase-shifting low-coherence digital holography," Jpn. J. Appl. Phys. 47, 8844-8847 (2008).
[CrossRef]

Nature (1)

O. W. Richards, "Phase Difference Microscopy," Nature 154, 672 (1944).
[CrossRef]

Opt. Eng. (1)

H. Gundlach, "Phase contrast and differential interference contrast instrumentation and applications in cell, developmental, and marine biology," Opt. Eng. 32, 3223-3228, (1993).
[CrossRef]

Opt. Express (6)

Opt. Lett. (11)

C.K. Hitzenberger, M. Sticker, R. Leitgeb, and A.F. Fercher, "Differential phase measurements in low-coherence interferometry without 2π ambiguity," Opt. Lett. 26, 1864-1866, (2001).
[CrossRef]

J. Gass, A. Dakoff, and M. K. Kim, "Phase imaging without 2π ambiguity by multiwavelength digital holography," Opt. Lett. 28, 1141-1143, (2003)
[CrossRef] [PubMed]

C. Yang, A. Wax, R.R. Dasari, and M.S. Feld, "2π ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer," Opt. Lett. 27, 77-79, (2002).
[CrossRef]

R. Tripathi, N Nassif, J. S. Nelson, B. H. Park, and J. F. de Boer, "Spectral shaping for non-Gaussian source spectra in optical coherence tomography," Opt. Lett. 27, 406-408, (2002).
[CrossRef]

A. K. Ellerbee and J.A. Izatt, "Phase retrieval in low-coherence interferometric microscopy," Opt. Lett. 32, 388-390, (2007).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30,1162-1164 (2005).
[CrossRef] [PubMed]

C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, "Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging," Opt. Lett. 30, 2131-2133, (2005).
[CrossRef] [PubMed]

J.F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, "Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography," Opt. Lett. 28, 2067-2069, (2003).
[CrossRef] [PubMed]

G. Popescu, L. P. Deflores, J.C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505, (2004).
[CrossRef] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M.S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1167, (2005).
[CrossRef] [PubMed]

E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital Holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293, (1999).
[CrossRef]

Other (3)

D. C. Ghilglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms, and Software. (Wiley, 1998)

J.A. Izatt and M.A. Choma, "Theory of Optical Coherence Tomography," in Optical Coherence Tomography: Technology and Applications, W. Drexler and J.G. Fujimoto, eds. (Springer, 2008).
[CrossRef]

D.R. Lide, ed. CRC Handbook of Chemistry and Physics, (CRC Press, 2001-2002).

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Figures (6)

Fig. 1.
Fig. 1.

Synthetic wavelength unwrapping procedure using two Gaussian windows. The spectra have been linearly interpolated to even k spacing.

Fig. 2.
Fig. 2.

Effects of window separation on δxsyn calculated using Eq. (12). Theoretical SNR based δxsyn is compared to experimentally measured δxsyn. The increase in δxsyn at large window separation (small Λ) is due to the SNR loss as the windows are moved further from the source center. At small window separation (large Λ), δxsyn also increases due to noise amplification by Λ. δxsyn is minimized when the SNR loss and Λ achieve a balance, which appears experimentally at a 50 nm window separation.

Fig. 3.
Fig. 3.

SDPM system schematic. (L1, L2, L3): Imaging lenses. (TL): Tube lens. (CCD) PixleLinks camera used for bright field imaging.

Fig. 4.
Fig. 4.

(a). Raw, wrapped phase data from an AFM calibration step grating (b). Synthetic wavelength phase image of the grating. The step height was measured by taking the difference of the averages in the peak and valley regions indicated in the image. (c). Cross-sectional profile taken across the center of the grating comparing the synthetic wavelength unwrapping method with that of a simple unwrapping method from Matlab.

Fig. 5.
Fig. 5.

(a). Single wavelength corrected phase image of the AFM grating. The spikes indicate regions the phase is incorrectly wrapped by +/- 2π. (b) Final corrected image. Spikes were removed by applying a 3×3 window to (a) and comparing the central point of the window to the surrounding pixels to determine locations that were wrapped by +/- λo/2. This image has a noise level reduced to the order of the single wavelength profile. Standard deviation of the indicated region was 3 nm.

Fig. 6.
Fig. 6.

Phase images of human epithelial cheek cells. (a) Wrapped phase image. (b) Filtered single wavelength phase map corrected using synthetic wavelength unwrapping. Note the difference in the colorbar scales for (a) and (b). Region in the red box indicates area used as the reference. (c) Bright field microscopy image of the cells.

Equations (17)

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

i ( k ) S ( k ) { R R + R S + R R R S cos ( 2 kn ( x + Δ x ) ) }
I ( ± 2 nx ) = S R R R S E ( 2 nx ) exp ( ± j 2 k o n Δ x )
Δ x = λ o Δ φ t j t o 4 πn + m λ o 2 n
Λ = λ 1 λ 2 λ 1 λ 2
i 1 ( k ) e ( k k 1 ) 2 Δ k 1 2 cos ( 2 kn ( x + Δ x ) )
i 2 ( k ) e ( k k 2 ) 2 Δ k 2 2 cos ( 2 kn ( x + Δ x ) )
δφ = 2 π ( SNR ) 1 2
SNR = Δ t ρ ( k ) R s ( k ) S ( k ) dk 2 e
δx = λ o δφ 4 πn
δ φ syn = δ φ 1 2 + δ φ 2 2 cov ( δ φ 1 2 , δ φ 2 2 )
cov ( δ φ 1 2 , δ φ 2 2 ) = a ( k ) ( δ φ 1 2 + δ φ 2 2 )
a ( k ) = β i 2 ( k ) dk + β + i 1 ( k ) dk 1 2 + [ i 1 ( k ) + i 2 ( k ) ] dk
SNR = Δ t ρ ( k ) R s ( k ) S ( k ) e ( k k 1 ) 2 Δ k 2 dk 2 e
δ x syn = Λ δ φ syn 4 πn
Δ x max = Λ 2 n
Δ φ Si = π p
p = tan 1 ( 2 n o k 1 n 1 2 + k 1 2 n o 2 )

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