Abstract

A novel polariscope with electro-optic modulation that is capable of simultaneous measurement of the principal axis and the phase retardation of an optical linear birefringent medium by means of two phase-locked extractions is described. A phase compensator is used to suppress the transmission phase-retardation effect of the beam splitter, thereby enhancing the precision of the measuring performance. The validity of the proposed design is demonstrated by measurement of the principal axis and phase retardation of a quarter-wave plate sample. There are absolute errors of 0.25° on average and 0.58° at maximum in the principal-axis measurement and of 0.75° (0.83%) on average and 3.11° at maximum in the phase-retardation measurement. Meanwhile, the retardation error lies within a 5% uncertainty range of a commercial wave plate. The root-mean-square resolutions for the principal-axis angle and phase-retardation measurements are 0.042° and 0.081°, respectively. Finally, the dynamic ranges of the principal-axis angle measurement and the phase-retardation measurement extend as far as 180°.

© 2004 Optical Society of America

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References

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  1. H. B. Serreze, R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
    [CrossRef]
  2. Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).
  3. Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt. 13, 553–555 (1988).
  4. P. Kurzynowski, W. A. Wozniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53 (2002).
    [CrossRef]
  5. Y. L. Lo, P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
    [CrossRef]
  6. B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
    [CrossRef]
  7. L. H. Shyu, C. L. Chen, D. C. Su, “Method for measuring the retardation of a wave plate,” Appl. Opt. 32, 4228–4230 (1993).
    [CrossRef] [PubMed]
  8. J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
    [CrossRef]
  9. B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
    [CrossRef]
  10. S. Ohkubo, N. Umeda, “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. Mater. 13, 433–443 (2001).
  11. Y. L. Lo, C. H. Lai, J. F. Lin, P. F. Hsu, “Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
    [CrossRef] [PubMed]
  12. S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
    [CrossRef]
  13. W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962).
  14. H. Z. Hu, “Polarization heterodyne interferometry using a simple rotating analyzer. 1. Theory and error analysis,” Appl. Opt. 22, 2052–2056 (1983).
    [CrossRef]
  15. Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
    [CrossRef]
  16. K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

2004

S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
[CrossRef]

Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, P. F. Hsu, “Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
[CrossRef] [PubMed]

2003

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

2002

J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
[CrossRef]

P. Kurzynowski, W. A. Wozniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53 (2002).
[CrossRef]

Y. L. Lo, P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
[CrossRef]

2001

S. Ohkubo, N. Umeda, “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. Mater. 13, 433–443 (2001).

1999

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

1997

K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

1993

1988

Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt. 13, 553–555 (1988).

1983

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

H. Z. Hu, “Polarization heterodyne interferometry using a simple rotating analyzer. 1. Theory and error analysis,” Appl. Opt. 22, 2052–2056 (1983).
[CrossRef]

1974

H. B. Serreze, R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

Benkelfat, B. E.

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

Chen, C. L.

Goldner, R. B.

H. B. Serreze, R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

Hanabusa, H.

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Horache, E. H.

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

Hsu, P. F.

Hu, H. Z.

Kurzynowski, P.

P. Kurzynowski, W. A. Wozniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53 (2002).
[CrossRef]

Lai, C. H.

Lee, S. Y.

Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
[CrossRef]

S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
[CrossRef]

Lin, J. F.

S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
[CrossRef]

Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, P. F. Hsu, “Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
[CrossRef] [PubMed]

Lin, Y.

Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt. 13, 553–555 (1988).

Lo, Y. L.

S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, P. F. Hsu, “Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
[CrossRef] [PubMed]

Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
[CrossRef]

Y. L. Lo, P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
[CrossRef]

Mackey, J. R.

J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
[CrossRef]

Oakberg, T. C.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Ohkubo, S.

S. Ohkubo, N. Umeda, “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. Mater. 13, 433–443 (2001).

Rochford, K. B.

K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

Rose, A. H.

K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

Salari, E.

J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
[CrossRef]

Serreze, H. B.

H. B. Serreze, R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

Shindo, Y.

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962).

Shyu, L. H.

Su, D. C.

Tin, P.

J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
[CrossRef]

Umeda, N.

S. Ohkubo, N. Umeda, “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. Mater. 13, 433–443 (2001).

Vinouze, B.

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

Wang, B.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Wang, C. M.

K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

Wang, R.

Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt. 13, 553–555 (1988).

Wozniak, W. A.

P. Kurzynowski, W. A. Wozniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53 (2002).
[CrossRef]

Zhou, Z.

Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Appl. Opt. 13, 553–555 (1988).

Zou, Q.

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

Appl. Opt.

Laser Focus World

K. B. Rochford, A. H. Rose, C. M. Wang, “NIST study investigates retardance uncertainty,” Laser Focus World 33(5), 223–227 (1997).

Meas. Sci. Technol.

S. Y. Lee, J. F. Lin, Y. L. Lo, “A compact circular heterodyne interferometer for the simultaneous measurement of variation in the magnitude of phase retardation and the principal angle,” Meas. Sci. Technol. 15, 978–982 (2004).
[CrossRef]

J. R. Mackey, E. Salari, P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179–185 (2002).
[CrossRef]

Opt. Commun.

B. E. Benkelfat, E. H. Horache, Q. Zou, B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278 (2003).
[CrossRef]

Y. L. Lo, S. Y. Lee, J. F. Lin, “The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties,” Opt. Commun. 237, 267–273 (2004).
[CrossRef]

Opt. Eng.

Y. L. Lo, P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
[CrossRef]

Optik

P. Kurzynowski, W. A. Wozniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53 (2002).
[CrossRef]

Polym. Commun.

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Rev. Sci. Instrum.

H. B. Serreze, R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Sens. Mater.

S. Ohkubo, N. Umeda, “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. Mater. 13, 433–443 (2001).

Other

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962).

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Figures (5)

Fig. 1
Fig. 1

Proposed polariscope optical setup for two phase-locked extractions.

Fig. 2
Fig. 2

Simulation results for principal axis angle and phase retardation.

Fig. 3
Fig. 3

Experimental results for λ/4 plate sample.

Fig. 4
Fig. 4

System repeatability results.

Fig. 5
Fig. 5

System stability results.

Equations (10)

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

E1=A10°Q2-45°Sα, βQ145°EO90°, ωtP45°Ein=10001-i2-1-i2-1-i21-i2cosβ2+i cos 2α sinβ2i sin 2α sinβ2i sin 2α sinβ2cosβ2-i cos 2α sinβ21-i21+i21+i21-i2×expi ωt200exp-i ωt2121212120E0expiω0t,
E2=A245°Q2-45°Sα, βQ145°EO90°, ωtP45°Ein=121212121-i2-1-i2-1-i21-i2cosβ2+i cos 2α sinβ2i sin 2α sinβ2i sin 2α sinβ2cosβ2-i cos 2α sinβ21-i21+i21+i21-i2×expi ωt200exp-i ωt2121212120E0expiω0t,
I1=Idc1+sin β sinωt-π2+2α=Idc+R1 sinωt+θ1,
I2=Idc1+121+cos β-cos 4α1-cos β2+sin 4α1-cos β21/2 sinωt+tan-11+cos β-cos 4α1-cos βsin 4α1-cos β =Idc+R2 sinωt+θ2,
tan-11+cos β-cos 4α1-cos βsin 4α1-cos β.
α=θ12+π4,
β=cos-1-1+cos 2θ1+sin 2θ1 tan θ21-cos 2θ1-sin 2θ1 tan θ2.
BSR=exp-i ϕBSR200expi ϕBSR2,
BST=exp-i ϕBST200expi ϕBST2,
I2,BST=Idc+R2 sinωt+tan-11+cos βcos ϕBST-1-cos βcos4α+ϕBST1+cos βsin ϕBST+1-cos βsin4α+ϕBST.

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