Abstract

A novel differential-phase optical coherence reflectometer (DP-OCR) was proposed using a low-coherence source, integrating it with an analog differential-phase decoding method. In the experiment, the DP-OCR performed a localized surface profile measurement of an optical grating (1200 lp/mm) and demonstrated its ability to measure the translation speed of a tilted mirror. Experimentally, the resolution of the axial displacement of proposed DP-OCR at 185 pm was demonstrated.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. S. Yazdanfar and J. A. Izatt, "Self-referenced Doppler optical coherence tomography," Opt. Lett. 27, 2085-2087 (2002).
    [CrossRef]
  6. C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 96-99 (2001).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 3rd ed., (Roberts and Company, Englewood, 2005).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. 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]
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    [CrossRef] [PubMed]
  18. M. Sticker, M. Pircher, E. Gotzinger, H. Sattmann, A. F. Fercher, and C. K. Hitzenberger, "En Face imaging of single cell layers by differential phase-contrast optical coherence microscopy," Opt. Lett. 27, 1126-1128 (2002).
    [CrossRef]
  19. M. A. Choma, A. K. Ellerbee, and C. Yang, "Spectral-domain phase microscopy," Opt. Lett. 30, 1162-1164 (2005).
    [CrossRef] [PubMed]
  20. 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]
  21. C. Joo, K. H. Kim, and J. F. de Boer, "Spectral-domain optical coherence phase and multiphoton microscopy," Opt. Lett. 32, 623-625 (2007).
    [CrossRef] [PubMed]
  22. D. C. Adler, R. Huber, and J. G. Fujimoto, "Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers," Opt. Lett. 32, 626-628 (2007).
    [CrossRef] [PubMed]
  23. C. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. Fercher, "Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography," Opt. Express 9, 780-790 (2001).
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  24. C. J. Pedersen, D. Huang, M. A. Shure, A. M. Rollins, "Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography," Opt. Lett. 32, 506-508, (2007).
    [CrossRef] [PubMed]
  25. R. E. Ziemer and W. H. Tranter, Principle of communications: Systems, modulation, and noise, (Houghton Mifflin Co., Boston, MA, 1976).
  26. C. Chou, H. K. Teng, C. C. Tsai, and L. P. Yu, "Balanced detector interferometric ellipsometer," J. Opt. Soc. Am. A,  23, 2871-2879 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  28. H. Lim, J. F. de Boer, B. H. Park, E. C. Lee, R. Yelin, and S. H. Yun, "Optical frequency domain imaging with a rapidly swept laser in the 815-870 nm range," Opt. Express 14, 5937-5944 (2006).
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  29. C. Tsai, H. Wei, S. Huang, C. Lin, C. Yu, and C. Chou, "High speed interferometric ellipsometer," Opt. Express 16, 7778-7788 (2008).
    [CrossRef] [PubMed]
  30. D. P. Davé and T. E. Milner, "Optical low-coherence reflectometer for differential phase measurement," Opt. Lett. 25, 227-229 (2000).
    [CrossRef]
  31. C. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
    [CrossRef]

2008 (1)

2007 (3)

2006 (3)

2005 (2)

2004 (2)

2002 (2)

2001 (2)

2000 (4)

1999 (1)

1998 (1)

1997 (2)

1994 (1)

1992 (1)

1991 (2)

G. Lai and T. Yatagai, "Generalized phase-shifting interferometry," J. Opt. Soc. Am. A 8, 822-827 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1987 (1)

Adler, D. C.

Akkin, T.

Badizadegan, K.

Brun, G.

Cense, B.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Chen, Z.

Choma, M. A.

Chou, C.

Dasari, R. R.

Dave, D. P.

Davé, D. P.

de Boer, J. F.

de Groot, P.

Deck, L.

Diller, K. R.

Dresel, T.

Drexler, W.

Ellerbee, A. K.

Feld, M. S.

Fercher, A.

Fercher, A. F.

Flottee, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

Georgakoudi, I.

Goetzinger, E.

Gotzinger, E.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hanlon, E. B.

Hausler, G.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hitzenberger, C.

Hitzenberger, C. K.

Huang, D.

C. J. Pedersen, D. Huang, M. A. Shure, A. M. Rollins, "Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography," Opt. Lett. 32, 506-508, (2007).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Huang, S.

Huang, Y. C.

Huber, R.

Ippen, E. P.

Izatt, J. A.

Jacquot, M.

Joo, C.

Kartner, F. X.

Kim, K. H.

Ko, T. H.

Kubota, T.

Lai, G.

Lee, E. C.

Li, X. D.

Lim, H.

Lin, C.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Lyu, C. W.

C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 96-99 (2001).
[CrossRef]

Malekafzali, A.

Milner, T. E.

Morgner, U.

Nara, M.

Nelson, J. S.

Park, B. H.

Pedersen, C. J.

Peng, L. C.

C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 96-99 (2001).
[CrossRef]

Pircher, M.

Pitris, C.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Reolon, D.

Rollins, A. M.

Rylander, C. G.

Sattmann, H.

Shuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Shure, M. A.

Shyu, J.C.

Srinivas, S.

Sticker, M.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, 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. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Teng, H. K.

Tsai, C.

Tsai, C. C.

van Gemert, M. C. J.

van Gemert, M. J. C.

Veillas, C.

Venzke, H.

Verrier, I.

Wang, X.

Wax, A.

Wei, H.

Welch, A. J.

Yang, C.

Yatagai, T.

Yazdanfar, S.

Yelin, R.

Yoshino, T.

Yu, C.

Yu, L. P.

Yuan, C. K.

Yun, S. H.

Appl. Opt. (4)

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

Opt. Express (5)

Opt. Lett. (16)

C. G. Rylander, D. P. Dave, T. Akkin, T. E. Milner, K. R. Diller, and A. J. Welch, "Quantitative phase-contrast imaging of cells with phase-sensitive optical coherence microscopy," Opt. Lett. 29, 1509-1511 (2004).
[CrossRef] [PubMed]

M. Sticker, M. Pircher, E. Gotzinger, H. Sattmann, A. F. Fercher, and C. K. Hitzenberger, "En Face imaging of single cell layers by differential phase-contrast optical coherence microscopy," Opt. Lett. 27, 1126-1128 (2002).
[CrossRef]

M. A. Choma, A. K. Ellerbee, and C. Yang, "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]

C. Joo, K. H. Kim, and J. F. de Boer, "Spectral-domain optical coherence phase and multiphoton microscopy," Opt. Lett. 32, 623-625 (2007).
[CrossRef] [PubMed]

D. C. Adler, R. Huber, and J. G. Fujimoto, "Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers," Opt. Lett. 32, 626-628 (2007).
[CrossRef] [PubMed]

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

D. P. Dave and T. E. Milner, "Optical low-coherence reflectometer for differential phase measurement," Opt. Lett. 25, 227-229 (2000).
[CrossRef]

T. Kubota, M. Nara, and T. Yoshino, "Interferometer for measuring displacement and distance," Opt. Lett. 12, 310-312 (1987).
[CrossRef] [PubMed]

C. K. Hitzenberger and A. F. Fercher, "Differential phase contrast in optical coherence tomography," Opt. Lett. 24, 622-624 (1999).
[CrossRef]

S. Yazdanfar and J. A. Izatt, "Self-referenced Doppler optical coherence tomography," Opt. Lett. 27, 2085-2087 (2002).
[CrossRef]

D. P. Davé and T. E. Milner, "Optical low-coherence reflectometer for differential phase measurement," Opt. Lett. 25, 227-229 (2000).
[CrossRef]

C. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
[CrossRef]

C. J. Pedersen, D. Huang, M. A. Shure, A. M. Rollins, "Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography," Opt. Lett. 32, 506-508, (2007).
[CrossRef] [PubMed]

Z. Chen, T. E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M. J. C. van Gemert, and J. S. Nelson, "Noninvasive imaging of in vivo blood flow velocity using optical Doppler tomography," Opt. Lett. 22, 1119-1121 (1997).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flottee, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed., (Roberts and Company, Englewood, 2005).

S. Haykin, Communication Systems, 4th Ed., (Wiley, New York, 2001).

R. E. Ziemer and W. H. Tranter, Principle of communications: Systems, modulation, and noise, (Houghton Mifflin Co., Boston, MA, 1976).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of DP-OCR: HWP, half wave plate; QWP, quarter wave plate; BS, beam splitter; PBS1, PBS2, PBS3, polarization beam splitters; D1, D2, photo detectors; DA, differential amplifier; ADC, analog-to-digital converter; S, sample; M, mirror; PZT, piezoelectric-supported mirror.

Fig. 2.
Fig. 2.

Stability test of DP-OCR on axial displacement.

Fig. 3.
Fig. 3.

The measured data (dots) and computer simulation (solid line) of a plane mirror axially displaced at 28 nm in each step by use of DP-OCR. The error bar of the measurement is smaller than the size of dots.

Fig. 4.
Fig. 4.

Surface profile of an optical grating (1200 lp/mm) measured by DP-OCR (dots) and by AFM (solid line). The error bar of the measured data by DP-OCR is less than the size of the dots.

Fig. 5.
Fig. 5.

Linear relationship between the translational speed of tilted mirror and Doppler shift by DP-OCR.

Equations (46)

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

E = E 0 ( 1 ± i ) ,
E 1 = 1 2 E 0 ( 1 i ) ,
E 2 = 1 2 E 0 ( 1 i ) ,
E P 2 = R S 2 E 0 ( 1 0 ) exp ( i 2 k l P 2 ) ,
E S 2 = R M 2 E 0 ( 0 i ) exp ( i 2 k l S 2 ) ,
E P 1 = R 1 2 E 0 ( 1 0 ) exp ( i 2 k l P 1 ) ,
E P 2 = R S 2 E 0 ( 1 0 ) exp ( i 2 k l P 2 ) ,
E S 1 = R 1 2 E 0 ( 0 i ) exp ( i 2 k l S 1 ) ,
E S 2 = R M 2 E 0 ( 0 i ) exp ( i 2 k l S 2 ) ,
E P = 1 2 E 0 [ R 1 exp ( i 2 k l P 1 ) + R S exp ( i 2 k l P 2 ) ] ,
E S = i 2 E 0 [ R 1 exp ( i 2 k l S 1 ) + R M exp ( i 2 k l S 2 ) ] ,
i p = γ E P 2
= γ A 0 2 ( k ) 4 [ R 1 + R S + 2 R 1 R S cos ( 2 k Δ l P ) ] ,
i S = γ E S 2
= γ A 0 2 ( k ) 4 [ R 1 + R M + 2 R 1 R M cos ( 2 k Δ l S ) ] ,
A 0 2 ( k ) = P 0 S ( k ) ,
S ( k ) = 2 ln 2 Δ k π exp { [ ( k k 0 ) 2 ln 2 Δ k ] 2 } ,
I P = i P d k
= γ P 0 4 S ( k ) [ R 1 + R S + 2 R 1 R S cos ( 2 k Δ l P ) ] d k
= γ P 0 4 exp [ ( 2 Δ l P ln 2 l ω ) 2 ] [ R 1 + R S + 2 R 1 R S cos ( 2 k 0 Δ l P ) ] ,
I S = i S d k
= γ P 0 4 S ( k ) [ R 1 + R M + 2 R 1 R M cos ( 2 k Δ l S ) ] d k
= γ P 0 4 exp [ ( 2 Δ l S ln 2 l ω ) 2 ] [ R 1 + R M + 2 R 1 R M cos ( 2 k 0 Δ l S ) ] ,
l ω = 4 ln 2 Δ k = 2 ( ln 2 ) λ 0 2 π Δ λ ,
I diff = I P I S
γ P 0 4 exp [ ( 2 Δ l ln 2 l ω ) 2 ] { ( R S R M ) + 2 R 1 [ R S cos ( 2 k 0 Δ l P ) R M cos ( 2 k 0 Δ l S ) ] } .
I diff γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] R S cos ( 2 k 0 Δ l P ) R M cos ( 2 k 0 Δ l S ) ,
I diff γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] R S cos ( ω D t + ϕ P ) R M cos ( ω D t + ϕ S )
= γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] R S cos ( ω D t + ϕ P ϕ S ) R M cos ( ω D t )
= γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] cos ( ω D t ) [ R S cos ( Δ ϕ ) R M ] + sin ( ω D t ) [ R S sin ( Δ ϕ ) ]
= γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] R S + R M 2 R S R M cos ( Δ ϕ ) cos ( ω D t θ ) ,
cos θ = R S cos ( Δ ϕ ) R M R S + R M 2 R S R M cos ( Δ ϕ ) ,
sin θ = R S sin ( Δ ϕ ) R S + R M 2 R S R M cos ( Δ ϕ ) .
I P M = Max { γ P 0 R 1 R S 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] cos ( 2 k 0 Δ l P ) } ,
I S M = Max { γ P 0 R 1 R M 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] cos ( 2 k 0 Δ l S ) } ,
I diff M = Max { γ P 0 R 1 2 exp [ ( 2 Δ l ln 2 l ω ) 2 ] R S + R M 2 R S R M cos ( Δ ϕ ) cos ( ω t θ ) } .
Δ h = 1 2 · λ 0 2 π · Δ ϕ
= λ 0 4 π cos 1 [ ( I S M ) 2 + ( I P M ) 2 ( I diff M ) 2 2 I S M I P M ] .
Δ h = λ 0 4 π cos 1 [ ( I S M ) 2 + ( I P M ) 2 ( I diff M ) 2 2 I S M I P M ] Δ h 0 .
I diff = γ P 0 R · exp [ ( 2 Δ l ln 2 l ω ) 2 ] cos ( Δ ϕ 2 ) cos ( ω D t θ ) ,
cos θ = cos ( Δ ϕ 2 ) ,
sin θ = sin ( Δ ϕ 2 ) .
V = ( I diff M ) 2 ( I V M ) 2 ( I H M ) 2 2 I V M I H M = cos ( Δ ϕ )
f D = Δ ϕ 2 π T
= 1 2 π T cos 1 [ ( I S M ) 2 + ( I P M ) 2 ( I diff M ) 2 2 I S M I P M ] ,
V = f D λ 0 2 cos θ ,

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