Abstract

We present a polarization Linnik interference microscope with a nematic liquid-crystal (NLC) phase shifter for full-field optical coherence tomography of high-quality images. The rotating half-wave plate in conventional achromatic phase shifters was replaced by three liquid-crystal (LC) half-wave plates for implementing three-step phase-shifting interferometry. Thus, the NLC device generates phase shifts quickly and has no vibrations. In addition, the phase shift can be set to an arbitrary value between 0 and 2π by altering the azimuth angles of the LC cells. A tomographic image is retrieved from three sequential phase-shifted interferograms by using a three-step algorithm. The experimental results confirm the feasibility of the proposed technology.

© 2012 Optical Society of America

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References

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2010

O. Aharon and I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49, 034002 (2010).
[CrossRef]

M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt. 49, D30–D61 (2010).
[CrossRef]

2007

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

2005

2004

2002

A. Dubois, L. Vabre, A.-C. Boccara, and E. Beaurepaire, “High-resolution full-field optical coherence tomography with a Linnik microscope,” Appl. Opt. 41, 805–812 (2002).
[CrossRef]

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

1999

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

1996

1994

P. Hariharan and M. Roy, “White-light phase-steppping interferometry for surface profiling,” J. Mod. Opt. 41, 2197–2201 (1994).
[CrossRef]

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

1992

1978

Abdulhalim, I.

O. Aharon and I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49, 034002 (2010).
[CrossRef]

Aharon, O.

O. Aharon and I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49, 034002 (2010).
[CrossRef]

Azzam, R. M. A.

Beaurepaire, E.

Boccara, A.-C.

Boccara, C.

Brugioni, S.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Chipman, R. A.

Ciddor, P. E.

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Cox, G.

Dubois, A.

Faetti, S.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Goldstein, D. H.

Grieve, K.

Hariharan, P.

M. Roy, G. Cox, and P. Hariharan, “Low-coherence interference microscopy with an improved switchable achromatic phase-shifter,” Opt. Express 13, 9125–9130 (2005).
[CrossRef]

M. Roy, C. Sheppard, and P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
[CrossRef]

P. Hariharan and M. Roy, “White-light phase-steppping interferometry for surface profiling,” J. Mod. Opt. 41, 2197–2201 (1994).
[CrossRef]

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Hayasaka, Y.

Helen, S. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Kothiyal, M. P.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Lecaque, R.

Li, J.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Lu, S. Y.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), Chap. 14.

Meucci, R.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Moneron, G.

Roy, M.

M. Roy, G. Cox, and P. Hariharan, “Low-coherence interference microscopy with an improved switchable achromatic phase-shifter,” Opt. Express 13, 9125–9130 (2005).
[CrossRef]

M. Roy, C. Sheppard, and P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
[CrossRef]

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

P. Hariharan and M. Roy, “White-light phase-steppping interferometry for surface profiling,” J. Mod. Opt. 41, 2197–2201 (1994).
[CrossRef]

Sato, M.

Sheppard, C.

Sheppard, C. J. R.

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

Stifter, D.

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

Tanno, N.

Vabre, L.

Watanabe, Y.

Wojtkowski, M.

Wu, S. T.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. B

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

J. Appl. Phys.

J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

J. Mod. Opt.

P. Hariharan and M. Roy, “White-light phase-steppping interferometry for surface profiling,” J. Mod. Opt. 41, 2197–2201 (1994).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

P. Hariharan and P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Opt. Eng.

O. Aharon and I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49, 034002 (2010).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

Opt. Lett.

Other

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), Chap. 14.

W. Drexler and J. G. Fujimoto, eds., Optical Coherence Tomography (Springer-Verlag, 2008), pp. 565–591.

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Figures (9)

Fig. 1.
Fig. 1.

(a) QHQ phase shifter, (b) NLC phase shifter.

Fig. 2.
Fig. 2.

Three activation ways for generating phase shifts of (a) 4θ, (b) 0, and (c) 4θ.

Fig. 3.
Fig. 3.

Full-field optical coherence microscope with NLC phase shifter.

Fig. 4.
Fig. 4.

Variations in measured retardations with wavelength for the LC cells in (a) field-on and (b) field-off states.

Fig. 5.
Fig. 5.

(a) Phase-shift error and (b) amplitude ratio of two orthogonal polarizations as a function of wavelength for design phase shifts of 120°, 0°, and 120°.

Fig. 6.
Fig. 6.

(a) Three recorded interferograms with phase step of 120°. (b) Horizontal fitted intensity curves through their center.

Fig. 7.
Fig. 7.

(a) Intensity profile of the interferogram of a tilted mirror. (b) Recovered fringe envelope by using three-step phase-shifting method.

Fig. 8.
Fig. 8.

(a) Photograph of a Taiwanese coin. (b) 3D structure (1900μm×1400μm×140μm) of the rectangular region indicated in image (a).

Fig. 9.
Fig. 9.

(a) Side view of the coin covered with diffusion and clear tapes. (b) xz sectional image 1400μm×390μm. (c) 3D tomographic image of the Chinese number 10 covered with diffusion and clear tapes (1900μm×1400μm×390μm).

Equations (4)

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

WP(δ,θ)=[cos(δ2)+jsin(δ2)cos2θjsin(δ2)sin2θjsin(δ2)sin2θcos(δ2)jsin(δ2)cos2θ].
WP(π2,π4)WP(π,θ)WP(π2,π4)[ErEt]=[Erei(2θ+π2)Etei(2θ+π2)],
Iβ(x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)+β],
B(x,y)=({[1cos(4θ)](I4θI4θ)}2+[sin(4θ)(2I0I4θI4θ)]2)1/22sin(4θ)[1cos(4θ)],

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