Abstract

We describe a system for measuring sub-surface displacement fields within a scattering medium using a phase contrast version of spectral Optical Coherence Tomography. The system provides displacement maps within a 2-D slice extending into the sample with a sensitivity of order 10 nm. The data for a given deformation state is recorded in a single image, potentially allowing sub-surface displacement and strain mapping of moving targets. The system is based on low cost components and has no moving parts. The theoretical basis for the system is presented along with experimental results from a simple well-controlled geometry consisting of independently-tilting glass sheets. Results are validated using standard two-beam interferometry. A modified system was used to measure through-the-thickness phase changes within a porcine cornea due to displacements produced by an increase in the intraocular pressure.

© 2006 Optical Society of America

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2005 (8)

Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
[CrossRef]

S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. Puliafito, “Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography,” Opt. Express 13, 444–452 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-2-444
[CrossRef] [PubMed]

B. Grajciar, M. Pircher, A. Fercher, and R. Leitgeb, “Parallel Fourier domain optical coherence tomography for in vivo measurement of the human eye,” Opt. Express 13, 1131–1137 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-4-1131
[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]

B. Park, M. C. Pierce, B. Cense, S. -H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13, 3931–3944 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-3931
[CrossRef] [PubMed]

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurements by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (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]

B. Hyle Park, Mark C. Pierce, Barry Cense, and Johannes F. de Boer, “Optic axis determination accuracy for fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 30, 2587–2589 (2005).
[CrossRef] [PubMed]

2004 (6)

R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski, “Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt. Lett. 29, 171–173 (2004).
[CrossRef] [PubMed]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404
[CrossRef] [PubMed]

B. Cense, N. Nassif, T. Chen, M. Pierce, S. -H. Yun, B. Park, B. Bouma, G. Tearney, and J. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2435
[CrossRef] [PubMed]

Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express 12, 6184–6191 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6184
[CrossRef] [PubMed]

A. V. Zvyagin, “Fourier-domain optical coherence tomography: optimization of signal-to-noise ratio in full space,” Opt. Commun. 242, 97–108 (2004).
[CrossRef]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A: Pure Appl. Opt. 6, 679–683 (2004).
[CrossRef]

2003 (5)

2002 (3)

M. Wojtkowski, R. Leigeb, A. Kowalczyk, T. Bajraszewski, and A. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[CrossRef] [PubMed]

Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. 27, 1803–1805 (2002).
[CrossRef]

Mary T. Draney, et al., “Quantification of Vessel Wall Cyclic Strain Using Cine Phase Contrast Magnetic Resonance Imaging,” Annals of Biomed. Eng. 30, 1033–1045 (2002).
[CrossRef]

2000 (2)

DD Steele, TL Chenevert, AR Skovoroda, and SY. Emelianov “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Physics in Medicine and Biology 45, 1633–1648 (2000).
[CrossRef] [PubMed]

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” J. Opt. A: Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

1999 (1)

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39, 217–226 (1999).
[CrossRef]

1998 (1)

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

1994 (1)

1992 (1)

1986 (1)

1982 (1)

Abe, T.

Aben, Hillar

Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
[CrossRef]

Ainola, Leo

Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
[CrossRef]

Akkin, T.

Anton, Johan

Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
[CrossRef]

Aoki, G.

Bajraszewski, T.

R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski, “Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt. Lett. 29, 171–173 (2004).
[CrossRef] [PubMed]

M. Wojtkowski, R. Leigeb, A. Kowalczyk, T. Bajraszewski, and A. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[CrossRef] [PubMed]

Bajraszewski, Tomasz

Bay, B. K.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39, 217–226 (1999).
[CrossRef]

Berisha, F.

Bouma, B.

Bouma, Brett E.

Cense, B.

Cense, Barry

Chen, T.

Chenevert, TL

DD Steele, TL Chenevert, AR Skovoroda, and SY. Emelianov “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Physics in Medicine and Biology 45, 1633–1648 (2000).
[CrossRef] [PubMed]

Choma, M.

Choma, M. A.

Creazzo, T. L.

de Boer, J.

de Boer, J. F.

de Boer, Johannes F.

Draney, Mary T.

Mary T. Draney, et al., “Quantification of Vessel Wall Cyclic Strain Using Cine Phase Contrast Magnetic Resonance Imaging,” Annals of Biomed. Eng. 30, 1033–1045 (2002).
[CrossRef]

Dresel, T.

Drexler, W.

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]

Duker, J.

Ellerbee, A. K.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Emelianov, SY.

DD Steele, TL Chenevert, AR Skovoroda, and SY. Emelianov “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Physics in Medicine and Biology 45, 1633–1648 (2000).
[CrossRef] [PubMed]

Endo, T.

Errapart, Andrei

Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
[CrossRef]

Fercher, A.

Fercher, A. F.

R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski, “Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt. Lett. 29, 171–173 (2004).
[CrossRef] [PubMed]

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]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Fujimoto, J.

Fyhrie, D. P.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39, 217–226 (1999).
[CrossRef]

Grajciar, B.

Gregori, G.

Gülker, G.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low coherence ESPI in the investigation of ancient terracotta warriors,” in Proceedings of Speckle Metrology 2003, K. Gastinger, O. Løckberg, and S. Winther, eds., Proc. SPIE4933, 53–58 (2003).

Hausler, G.

Hinsch, K. D.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low coherence ESPI in the investigation of ancient terracotta warriors,” in Proceedings of Speckle Metrology 2003, K. Gastinger, O. Løckberg, and S. Winther, eds., Proc. SPIE4933, 53–58 (2003).

Hitzenberger, C.

Hitzenberger, C. K.

R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski, “Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt. Lett. 29, 171–173 (2004).
[CrossRef] [PubMed]

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]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Huang, X.

Huntley, J. M.

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurements by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef] [PubMed]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A: Pure Appl. Opt. 6, 679–683 (2004).
[CrossRef]

J. M. Huntley, “Automated Analysis of Speckle Interferograms,” in Proceedings of Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi ed., (Chichester, West Sussex, England, John Wiley & Sons., 2001) pp. 59–139.

A. Marañon, A. D. Nurse, J. M. Huntley, and P. D. Ruiz, “A low population genetic algorithm applied to characterization of sub-surface delamination”, in Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation (CIMCA 2004), M. Mohammadian ed. (ISBN 1740881885, 2004) pp. 12–14.

Hyle Park, B.

Ina, H.

Itoh, M.

Izatt, J.

Izatt, J. A.

Jiao, S.

Joo, C.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Kannari, F.

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” J. Opt. A: Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

Knighton, R.

Ko, T.

Kobayashi, S.

Koga, H.

Kowalczyk, A.

Kowalczyk, Andrzej

Kraft, A.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low coherence ESPI in the investigation of ancient terracotta warriors,” in Proceedings of Speckle Metrology 2003, K. Gastinger, O. Løckberg, and S. Winther, eds., Proc. SPIE4933, 53–58 (2003).

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]

Leigeb, R.

M. Wojtkowski, R. Leigeb, A. Kowalczyk, T. Bajraszewski, and A. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[CrossRef] [PubMed]

Leitgeb, R.

Leitgeb, R. A.

Makita, S.

Marañon, A.

A. Marañon, A. D. Nurse, J. M. Huntley, and P. D. Ruiz, “A low population genetic algorithm applied to characterization of sub-surface delamination”, in Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation (CIMCA 2004), M. Mohammadian ed. (ISBN 1740881885, 2004) pp. 12–14.

Mitsunaga, Y.

Mujat, M.

Nassif, N.

Nurse, A. D.

A. Marañon, A. D. Nurse, J. M. Huntley, and P. D. Ruiz, “A low population genetic algorithm applied to characterization of sub-surface delamination”, in Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation (CIMCA 2004), M. Mohammadian ed. (ISBN 1740881885, 2004) pp. 12–14.

Park, B.

Park, B. H.

Pierce, M.

Pierce, M. C.

Pierce, Mark C.

Pircher, M.

Puliafito, C.

Rastogi, P.

P. Rastogi, Optical Measurement Techniques and Applications (The Artech house publishers, 1997).

Ruiz, P. D.

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurements by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef] [PubMed]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A: Pure Appl. Opt. 6, 679–683 (2004).
[CrossRef]

A. Marañon, A. D. Nurse, J. M. Huntley, and P. D. Ruiz, “A low population genetic algorithm applied to characterization of sub-surface delamination”, in Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation (CIMCA 2004), M. Mohammadian ed. (ISBN 1740881885, 2004) pp. 12–14.

Saad, M.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39, 217–226 (1999).
[CrossRef]

Sarunic, M.

Schmetterer, L.

Schmitt, J.

Schwider, J.

Skovoroda, AR

DD Steele, TL Chenevert, AR Skovoroda, and SY. Emelianov “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Physics in Medicine and Biology 45, 1633–1648 (2000).
[CrossRef] [PubMed]

Smith, T. S.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39, 217–226 (1999).
[CrossRef]

Srinivasan, V.

Steele, DD

DD Steele, TL Chenevert, AR Skovoroda, and SY. Emelianov “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Physics in Medicine and Biology 45, 1633–1648 (2000).
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Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” J. Opt. A: Pure Appl. Opt. 2, 21–26 (2000).
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Venzke, H.

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P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A: Pure Appl. Opt. 6, 679–683 (2004).
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A. V. Zvyagin, “Fourier-domain optical coherence tomography: optimization of signal-to-noise ratio in full space,” Opt. Commun. 242, 97–108 (2004).
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[CrossRef]

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Hillar Aben, Andrei Errapart, Leo Ainola, and Johan Anton, “Photoelastic tomography for residual stress measurement in glass,” Opt. Eng. 44, 93601 (2005).
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B. Cense, N. Nassif, T. Chen, M. Pierce, S. -H. Yun, B. Park, B. Bouma, G. Tearney, and J. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2435
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Supplementary Material (2)

» Media 1: MPG (410 KB)     
» Media 2: MPG (453 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of a SOCT system consisting of a broadband source BBS, beam splitter BS, object O, reference mirror R (apparent position also shown as a dashed line), diffraction grating G, lens L of focal length f, and two-dimensional photo detector array D. θ and βc denote, respectively, the incident angle of the broadband beam and the diffraction angle for the central wavelength λc .

Fig. 2.
Fig. 2.

Optical setup for simultaneous SOCT and two beam interferometry.

Fig. 3.
Fig. 3.

(a) x and (b) y-axis image formation.

Fig. 4.
Fig. 4.

Experimental procedure for measuring tilt on S1 and S2 using SOCT, and validation using two-beam interferometry.

Fig. 5.
Fig. 5.

Sample geometry consisting of two microscope cover slips. The rear surface of the second cover slip was painted black to suppress the back reflections from it.

Fig. 6.
Fig. 6.

(a) Interference pattern with both cover slips present, (b) spectrum of intensity along line y=1.9 mm with frequency converted to optical depth by Eqn. 3 (linear scale).

Fig. 7.
Fig. 7.

(a) Wrapped and (b) unwrapped phase difference map representing out of plane displacement field at the interfaces shown in Fig. 6(b) as RS1, RS1’ and RS2.

Fig. 8.
Fig. 8.

Displacement field profiles measured using phase-contrast SOCT (solid lines) and standard two-beam interferometry (dashed lines). An arbitrary offset of 0.1µm has been added for clarity.

Fig. 9.
Fig. 9.

(a) Magnitude and (b) phase difference map from slice through porcine cornea. One fringe corresponds to a displacement of 420nm.

Fig. 10.
Fig. 10.

Movies of the wrapped phase change through-the-thickness of a porcine cornea trephinate after a change in the hydrostatic pressure from (a) (411 KB) 2.06 to 2.16 kPa and (b) (453 KB) 2.06 to 2.45 kPa. Framing rate: 3.6fps; Exposure time: 60ms.

Equations (9)

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ϕ j ( λ ) = ϕ j 0 + 4 π λ z j
ϕ j ( k ) = ϕ j 0 + 2 k z j
f k = 1 2 π ϕ k = z j π
I ( k ) = I 0 + 2 j = 1 M I R I j cos [ ϕ j ( k ) ] + 2 i = 1 M j = i + 1 M I i I j cos [ ϕ i ( k ) ϕ j ( k ) ]
Δ ϕ j = tan 1 { Re [ I ˜ 1 ( f kj ) ] Im [ I ˜ 2 ( f kj ) ] Im [ I ˜ 1 ( f kj ) ] Re [ I ˜ 2 ( f kj ) ] Im [ I ˜ 1 ( f kj ) ] Im [ I ˜ 2 ( f kj ) ] + Re [ I ˜ 1 ( f kj ) ] Re [ I ˜ 2 ( f kj ) ] }
w j = λ c 4 π Δ ϕ j
w j = ( n 0 n ) d 1 + n d j
Δ z = N λ c 2 4 Δ λ
δ z = γ λ c 2 Δ λ

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