Abstract

We present differential phase-contrast optical-coherence tomography (DPC-OCT) with two transversally separated probing beams to sense phase gradients in various directions by employing a rotatable Wollaston prism. In combination with a two-dimensional mathematical-reconstruction algorithm based on a regularized shape from shading method, accurate quantitative phase maps can be determined from a set of two orthogonal en-face DPC-OCT images, as exemplified on various technical samples.

© 2009 Optical Society of America

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References

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2008 (1)

2007 (2)

D. Stifter, Appl. Phys. B 88, 337 (2007).
[CrossRef]

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

2005 (2)

2004 (2)

2003 (2)

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

C. K. Hitzenberger, P. Trost, P.-W. Lo, and Q. Zhou, Opt. Express 11, 2753 (2003).
[CrossRef] [PubMed]

2001 (1)

1999 (1)

1998 (1)

R. T. Frankot and R. Chellappa, IEEE Trans. Pattern Anal. Mach. Intell. 10, 439 (1998).
[CrossRef]

Akkin, T.

Boccara, A. C.

Bruhn, A.

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

Burgholzer, P.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

Cable, A.

Cense, B.

Chellappa, R.

R. T. Frankot and R. Chellappa, IEEE Trans. Pattern Anal. Mach. Intell. 10, 439 (1998).
[CrossRef]

Chen, Y.

Choma, M. A.

Creazzo, T. L.

Davé, D. P.

de Boer, J. F.

Didas, S.

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

Diller, K. R.

Dubois, A.

Ellerbee, A. K.

Fercher, A. F.

Frankot, R. T.

R. T. Frankot and R. Chellappa, IEEE Trans. Pattern Anal. Mach. Intell. 10, 439 (1998).
[CrossRef]

Fujimoto, J. G.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

Gorczynska, I.

Götzinger, E.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

Grieve, K.

Hitzenberger, C. K.

Höglinger, O.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

Izatt, J. A.

Jiang, J.

Joo, C.

Lecaque, R.

Leitgeb, R.

Lo, P.-W.

Milner, T. E.

Moneron, G.

Park, B. H.

Potsaid, B.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

Rylander, C. G.

Srinivasan, V. J.

Sticker, M.

Stifter, D.

D. Stifter, Appl. Phys. B 88, 337 (2007).
[CrossRef]

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

Trost, P.

Vabre, L.

Vogel, O.

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

Weickert, J.

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

Welch, A. L.

Yang, C.

Zhou, Q.

Appl. Opt. (1)

Appl. Phys. A (1)

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, Appl. Phys. A 76, 947 (2003).
[CrossRef]

Appl. Phys. B (1)

D. Stifter, Appl. Phys. B 88, 337 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

R. T. Frankot and R. Chellappa, IEEE Trans. Pattern Anal. Mach. Intell. 10, 439 (1998).
[CrossRef]

Lect. Notes Comput. Sci. (1)

O. Vogel, A. Bruhn, J. Weickert, and S. Didas, Lect. Notes Comput. Sci. 4485, 871 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Other (1)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

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Figures (4)

Fig. 1
Fig. 1

(a) Scheme of the DPC-OCT setup with indicated polarization directions, (b) configuration of the probing head with rotatable Wollaston prism (f, focal length; α, divergence angle; Δ x , probing beam shear).

Fig. 2
Fig. 2

(a) Sketch of a microlens array test structure with four interfaces, (b) cross-sectional DPC-OCT image, (c), (d) en-face DPC-OCT images in x and y directions at interface (2), (e), (f) en-face DPC-OCT images at interface (4), (g) reconstructed cumulative phase map at interface (2), (h) cumulative phase map at interface (4). White scale bar, 100 μ m .

Fig. 3
Fig. 3

DPC-OCT image of an oil layer with embedded particles. (a), (b) DPC images with shear in x and y directions, respectively; (c) OPL reconstruction by numerical line integration using the single scan displayed in (b); (d) FFT-based OPL reconstruction from scans (a) and (b); (e), (f) OPL reconstruction with SfS method using scans (a) and (b). White scale bar, 100 μ m .

Fig. 4
Fig. 4

(a), (b) Wrapped DPC images of a transparent polymer layer (shear in x and y directions, respectively); (c), (d) unwrapped phase of (a) and (b), respectively; (e) total phase map reconstructed from (c) and (d). White scale bar, 40 μ m .

Equations (3)

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ϕ i ( x , y ) = Δ ϕ i τ i = ϕ 2 i ( x , y ) ϕ 1 i ( x , y ) τ i , i = ( x , y ) .
ϕ 1 , 2 x ( x , y ) = arctan H ( S 1 , 2 ( x ± τ x 2 , y , z ) ) S 1 , 2 ( x ± τ x 2 , y , z )
E ( ϕ ̂ ( x , y ) ) = Ω ( ( f ( x , y ) ) R ( ϕ ̂ x , ϕ ̂ y ) ) 2 + μ ( ϕ ̂ x x 2 + 2 ϕ ̂ x y 2 + ϕ ̂ y y 2 )) d x d y ,

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