Abstract

We report the measurement of birefringence of nematic liquid crystal (NLC) material using multiple-wavelength interferometry. A nearly common path single-stage Mach–Zehnder interferometer was used for recording interferograms of high stability. The Fourier transform fringe analysis technique was used to reconstruct the two-dimensional phase maps of interferograms consisting of the entire active area of the liquid crystal cell. Change in phase as a function of applied voltage to a liquid-crystal cell was measured for blue, green, and red color laser light, keeping the temperature constant during the experiment. From the change in phase, the birefringence for three colors, i.e., red, green, and blue light, was determined. It is found that the birefringence of NLC material for red, green, and blue colors decreases with the increase in wavelength in the visible range. The present method is noncontact, nonmechanical scanning and highly stable due to a common path interferometer.

© 2013 Optical Society of America

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  1. I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).
  2. J. Gandhi and J. E. Anderson, “P-96: experimental measurement of Cauchy values for Δn of nematic liquid crystals,” SID Symp. Digest Tech. Papers 96, 582–586 (2002).
    [CrossRef]
  3. S. T. Wu and D. K. Yang, Reflective LC Displays (Wiley, 2001).
  4. M. F. Vuks, “Determination of optical anisotropy of aromatic molecules from double refraction of crystal,” Opt. Spektrosk. 20, 644–651 (1966).
  5. S. T. Wu, “A semiempirical model for liquid‐crystal refractive index dispersions,” J. Appl. Phys. 69, 2080–2087 (1991).
    [CrossRef]
  6. S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
    [CrossRef]
  7. J. Li and S. T. Wu, “Two-coefficient Cauchy model for low birefringence liquid crystals,” Appl. Phys. 96, 170–174 (2004).
  8. S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
    [CrossRef]
  9. A. A. Zaki, “Optical measurement of mixture thermotropic liquid crystals,” Opt. Lasers Eng. 48, 538–542 (2010).
    [CrossRef]
  10. S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23, 3911–3915 (1984).
    [CrossRef]
  11. M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
    [CrossRef]
  12. Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
    [CrossRef]
  13. M. H. Lui, W. C. Kuo, H. C. Wei, C. C. Tsai, C. J. Yu, B. J. Liang, and C. Chou, “Cell parameter measurement of a twisted nematic liquid crystal device using interferometric polarimeter under normal incidence,” Opt. Express 18, 8759–8766 (2010).
    [CrossRef]
  14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  15. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [CrossRef]
  16. H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
    [CrossRef]

2011

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

2010

2006

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

2004

J. Li and S. T. Wu, “Two-coefficient Cauchy model for low birefringence liquid crystals,” Appl. Phys. 96, 170–174 (2004).

2002

J. Gandhi and J. E. Anderson, “P-96: experimental measurement of Cauchy values for Δn of nematic liquid crystals,” SID Symp. Digest Tech. Papers 96, 582–586 (2002).
[CrossRef]

2001

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

1999

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

1993

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

1991

S. T. Wu, “A semiempirical model for liquid‐crystal refractive index dispersions,” J. Appl. Phys. 69, 2080–2087 (1991).
[CrossRef]

1986

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[CrossRef]

1984

1982

1966

M. F. Vuks, “Determination of optical anisotropy of aromatic molecules from double refraction of crystal,” Opt. Spektrosk. 20, 644–651 (1966).

Anderson, J. E.

J. Gandhi and J. E. Anderson, “P-96: experimental measurement of Cauchy values for Δn of nematic liquid crystals,” SID Symp. Digest Tech. Papers 96, 582–586 (2002).
[CrossRef]

Biradar, A. M.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Chen, P. H.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Chou, C.

Efron, U.

Francescangeli, O.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Gandhi, J.

J. Gandhi and J. E. Anderson, “P-96: experimental measurement of Cauchy values for Δn of nematic liquid crystals,” SID Symp. Digest Tech. Papers 96, 582–586 (2002).
[CrossRef]

Guenther, B. D.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Hess, L. D.

Ina, H.

Inam, M.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Ismaili, M.

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

Joshi, T.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Kang, L.

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

Khoo, I. C.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Kobayashi, S.

Kuo, W. C.

Li, B.

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

Li, J.

J. Li and S. T. Wu, “Two-coefficient Cauchy model for low birefringence liquid crystals,” Appl. Phys. 96, 170–174 (2004).

Liang, B. J.

Lucchetti, L.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Lui, M. H.

Mehta, D. S.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Nie, X.

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

Prakash, J.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Shih, M.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Simoni, F.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Singh, G.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Slussarenko, S. S.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Srivastava, V.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Su, X.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Takeda, M.

Tsai, C. C.

Vuks, M. F.

M. F. Vuks, “Determination of optical anisotropy of aromatic molecules from double refraction of crystal,” Opt. Spektrosk. 20, 644–651 (1966).

Wang, H.

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

Warenghem, M.

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

Wei, H. C.

Wood, M. V.

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

Wu, C. S.

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

Wu, S.

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

Wu, S. T.

J. Li and S. T. Wu, “Two-coefficient Cauchy model for low birefringence liquid crystals,” Appl. Phys. 96, 170–174 (2004).

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

S. T. Wu, “A semiempirical model for liquid‐crystal refractive index dispersions,” J. Appl. Phys. 69, 2080–2087 (1991).
[CrossRef]

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[CrossRef]

S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23, 3911–3915 (1984).
[CrossRef]

S. T. Wu and D. K. Yang, Reflective LC Displays (Wiley, 2001).

Wu, T.

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

Yang, D. K.

S. T. Wu and D. K. Yang, Reflective LC Displays (Wiley, 2001).

Yu, C. J.

Zaki, A. A.

A. A. Zaki, “Optical measurement of mixture thermotropic liquid crystals,” Opt. Lasers Eng. 48, 538–542 (2010).
[CrossRef]

Zhao, Q.

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

Zhou, J.

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys.

J. Li and S. T. Wu, “Two-coefficient Cauchy model for low birefringence liquid crystals,” Appl. Phys. 96, 170–174 (2004).

Appl. Phys. Lett.

Q. Zhao, L. Kang, B. Li, and J. Zhou, “Tunable negative refraction in nematic liquid crystals,” Appl. Phys. Lett. 89, 221918 (2006).
[CrossRef]

J. Appl. Phys.

S. T. Wu, “A semiempirical model for liquid‐crystal refractive index dispersions,” J. Appl. Phys. 69, 2080–2087 (1991).
[CrossRef]

J. Opt. Soc. Am.

Mol. Cryst. Liq. Cryst.

H. Wang, X. Nie, T. Wu, and S. Wu, “Cell gap on the dynamics of liquid crystal phase modulators,” Mol. Cryst. Liq. Cryst. 454, 285–295 (2006).
[CrossRef]

Opt. Commun.

M. Inam, G. Singh, V. Srivastava, J. Prakash, T. Joshi, A. M. Biradar, and D. S. Mehta, “Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique,” Opt. Commun. 284, 5448–5452 (2011).
[CrossRef]

Opt. Eng.

S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, “Refractive index dispersion of liquid crystals,” Opt. Eng. 32, 1775–1780 (1993).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

A. A. Zaki, “Optical measurement of mixture thermotropic liquid crystals,” Opt. Lasers Eng. 48, 538–542 (2010).
[CrossRef]

Opt. Spektrosk.

M. F. Vuks, “Determination of optical anisotropy of aromatic molecules from double refraction of crystal,” Opt. Spektrosk. 20, 644–651 (1966).

Phys. Rev. A

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[CrossRef]

Proc. IEEE

I. C. Khoo, M. Shih, M. V. Wood, B. D. Guenther, P. H. Chen, F. Simoni, S. S. Slussarenko, O. Francescangeli, and L. Lucchetti, “Dye-doped photorefractive liquid crystals for dynamic and storage holographic grating formation and spatial light modulation,” Proc. IEEE 87, 1897–1911 (1999).

SID Symp. Digest Tech. Papers

J. Gandhi and J. E. Anderson, “P-96: experimental measurement of Cauchy values for Δn of nematic liquid crystals,” SID Symp. Digest Tech. Papers 96, 582–586 (2002).
[CrossRef]

Other

S. T. Wu and D. K. Yang, Reflective LC Displays (Wiley, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram illustrating the nearly common-path MZI setup.

Fig. 2.
Fig. 2.

Recorded interferograms using an MZI using red, green, and blue lasers at 0 V applied to an LC cell in (a), (b), and (c), respectively, and in (d), (e), and (f) for red, green, and blue lasers at 16.5 V, respectively.

Fig. 3.
Fig. 3.

Phase maps corresponding to the maximum shift in interference fringe at 16.5 V for blue, green, and red lasers in (a), (b), and (c), respectively.

Tables (1)

Tables Icon

Table 1. Phase Difference Measured by FT Fringe Analysis and Birefringence Calculated for Red, Green, and Blue Colors

Equations (10)

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

1neff2(V,λ)=cos2θ(V)ne2(λ)+sin2θ(V)no2(λ).
I(x,y)=IR(x,y)+IO(x,y)+2IR(x,y)·IO(x,y)cos(ϕ0(x,y)+Δϕt(x,y,V)),
g(x,y)=a(x,y)+b(x,y)cos[2πf(x,y)+ϕ(x,y)],
g(x,y)=a(x,y)+c(x,y)exp(2πifx)+c(x,y)exp*(2πifx).
c(x,y)=12b(x,y)exp[iϕ(x,y)],
G(fx,y)=A(y,fx)+C(y,fxfo)+C*[y,(fx+fo)],
F1[C(fxfo,y)]=b(x,y)2exp[i(fo×ϕ(x,y))].
ϕ(x,y)=tan1Im[C(x,y)]Re[C(x,y)].
Δϕ(λi=R,G,B,V)=2πλi=R,G,BOPD=2πλi=R,G,BΔn(λi=R,G,B,V)·d(x,y),
Δn(λi=R,G,B,V)=(2πd(x,y))*λi=R,G,B*Δϕ(λi=R,G,B,V).

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