Abstract

Characterization of a phase modulator or phase shifter has always been an integral part of phase-modulating or phase-adjusting applications. We propose a simplified approach to characterize a phase modulator by investigating the performance of phase shifts from grabbed interferograms using the phase extraction method. After reviewing some phase analysis techniques, the interframe intensity correlation (IIC) matrix method is introduced to the investigation. The proposed strategy is illustrated by the measurement of a free-space electro-optic modulator (EOM). Placing the modulator in one arm of a Michelson interferometer, the global phase shifts are estimated by the IIC method from the phase-stepped interferograms. Experimental results demonstrate the tested EOM has a phase modulation response of at least 2πrad with a π/20rad modulation precision for λ=1064nm. In addition, our method is applicable to various types of phase modulator or phase shifter calibration, e.g., electro-optic phase modulator, spatial light modulator, or piezoelectric transducer (PZT).

© 2012 Optical Society of America

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References

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    [CrossRef]
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2011 (1)

2008 (1)

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

2007 (2)

H. Yue, X. Su, and Y. Liu, “Fourier transform profilometry based on composite fringe projection,” Opt. Laser Tech. 39, 1170–1175 (2007).
[CrossRef]

C. S. Vikram and H. J. Caulfield, “Interference fringe analysis based on centroid detection,” Appl. Opt. 46, 5137–5141 (2007).
[CrossRef]

2006 (1)

2005 (2)

H. Y. Yun and C. K. Hong, “Interframe intensity correlation matrix for self-calibration in phase-shifting interferometry,” Appl. Opt. 44, 4860–4869 (2005).
[CrossRef]

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

2004 (1)

2003 (2)

2001 (1)

2000 (1)

K. Qian, F. Shu, and X. Wu, “Determination of the best phase step of the Carré algorithm in phase shifting interferometry,” Meas. Sci. Technol. 11, 1220–1223 (2000).
[CrossRef]

1999 (2)

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).
[CrossRef]

H. V. Brug, “Phase-step calibration for phase-stepped interferometry,” Appl. Opt. 38, 3549–3555 (1999).
[CrossRef]

1990 (1)

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

1985 (1)

1981 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Alameh, K.

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

Basaran, C.

Bokor, J.

Brug, H. V.

Cai, D. M.

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

Cai, L. Z.

Cao, Z.

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Caulfield, H. J.

Chen, B.

Chen, M.

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).
[CrossRef]

Cheng, Y. Y.

Chu, X.

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Eng, S.-H.

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

Funnell, W. R. J.

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).

Goldberg, K. A.

Guo, C. S.

He, J. L.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

Hong, C. K.

Hu, L.

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

Jiang, W.

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

Li, D.

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

Li, Y.

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Liu, Q.

Liu, Y.

H. Yue, X. Su, and Y. Liu, “Fourier transform profilometry based on composite fringe projection,” Opt. Laser Tech. 39, 1170–1175 (2007).
[CrossRef]

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

Lu, K.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Lu, X.

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis, 2005).

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

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis, 2005).

Mu, Q

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

Mu, Q.

Qian, K.

K. Qian, F. Shu, and X. Wu, “Determination of the best phase step of the Carré algorithm in phase shifting interferometry,” Meas. Sci. Technol. 11, 1220–1223 (2000).
[CrossRef]

Rong, Z. Y.

Saleh, B. E. A.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis, 2005).

Shu, F.

K. Qian, F. Shu, and X. Wu, “Determination of the best phase step of the Carré algorithm in phase shifting interferometry,” Meas. Sci. Technol. 11, 1220–1223 (2000).
[CrossRef]

Su, X.

H. Yue, X. Su, and Y. Liu, “Fourier transform profilometry based on composite fringe projection,” Opt. Laser Tech. 39, 1170–1175 (2007).
[CrossRef]

Vikram, C. S.

Wang, H. T.

Wang, Y.-R.

Wang, Z.

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).
[CrossRef]

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

Wei, C.

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).
[CrossRef]

Wu, X.

K. Qian, F. Shu, and X. Wu, “Determination of the best phase step of the Carré algorithm in phase shifting interferometry,” Meas. Sci. Technol. 11, 1220–1223 (2000).
[CrossRef]

Wyant, J. C.

Xu, J.

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Xuan, L.

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

Yang, X. L.

Yue, H.

H. Yue, X. Su, and Y. Liu, “Fourier transform profilometry based on composite fringe projection,” Opt. Laser Tech. 39, 1170–1175 (2007).
[CrossRef]

Yun, H. Y.

Zhan, S.

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Zhao, S.

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Zhong, X.

Acta Opt. Sin. (1)

Y. Liu, L. Xuan, L. Hu, Z. Cao, D. Li, Q Mu, and X. Lu, “Investigation on the liquid crystal spatial light modulator with high precision and pure phase,” Acta Opt. Sin. 25, 1682–1686 (2005).
[CrossRef]

Appl. Opt. (9)

Meas. Sci. Technol. (1)

K. Qian, F. Shu, and X. Wu, “Determination of the best phase step of the Carré algorithm in phase shifting interferometry,” Meas. Sci. Technol. 11, 1220–1223 (2000).
[CrossRef]

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Eng. (2)

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).
[CrossRef]

Opt. Express (1)

Opt. Laser Tech. (1)

H. Yue, X. Su, and Y. Liu, “Fourier transform profilometry based on composite fringe projection,” Opt. Laser Tech. 39, 1170–1175 (2007).
[CrossRef]

Opt. Lett. (1)

Optoelectron. Lett. (1)

X. Chu, S. Zhan, S. Zhao, Y. Li, and J. Xu, “Research on phase-detecting method for coherent beam combining of fiber laser array,” Optoelectron. Lett. 3, 455–458 (2008).
[CrossRef]

Other (5)

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).

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

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis, 2005).

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

S.-H. Eng, D. M. Cai, Z. Wang, K. Alameh, and W. Jiang, “Optimization of liquid-crystal spatial light modulator for precise phase generation,” in Proceedings IEEE Conference Optoelectronic and Microelectronic Materials and Devices (IEEE, 2006), pp. 105–108.

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Figures (6)

Fig. 1.
Fig. 1.

Arrangement of the designed free-space LiNbO3 EOM.

Fig. 2.
Fig. 2.

Michelson interferometer used in our experiment. EOM, a free-space LiNbO3 electro-optic phase modulator; CCD, a Nikon D90 digital camera.

Fig. 3.
Fig. 3.

One frame of the captured interferograms: (a) part of the interferogram grabbed by CCD, (b) a small area selected from (a).

Fig. 4.
Fig. 4.

Phase shift estimated by the IIC method. Curve A, results of interferograms shown in Fig. 3(a); curve B, results of interferograms shown in Fig. 3(b).

Fig. 5.
Fig. 5.

Phase modulation precision distribution.

Fig. 6.
Fig. 6.

Phase shift modulated by a commercial high-voltage DC power supply. The response shows the linear electro-optic effect, also known as the Pockels effect.

Equations (8)

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

I(t)=A+B·cos[ϕ+Δϕ(t)]+ΔI(t),
C(1)=1NII+.
C=DC(ns)DT,
D=[1100001001].
CVHV+,
Vk+1=Proj[CVk(Vk+CVk)1Vk+Vk].
Δφ=πλne3γ33VdL,
Vλ/2=λne3γ33·dL.

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