Abstract

A novel technique is presented for obtaining concurrent measurements of the linear and circular birefringence properties of an optical sample by using a rotating-wave-plate Stokes polarimeter to extract the 2×2 central elements of the corresponding Mueller matrix via two linearly polarized probe lights. For a compound sample comprising a half-wave plate in series with a quarter-wave plate, the measured values of the principal angle and retardance of the quarter-wave plate are found to have average normalized errors of 0.56% and 1.16%, respectively, while the measured value of the rotation angle of the half-wave plate has an error of just 0.39%. When analyzing glucose solutions with concentrations ranging from 01.2g/dl positioned in front of a half-wave plate, the average normalized errors in the principal axis angle and retardance measurements of the half-wave plate are 0.69% and 2.65%, respectively, while the error in the rotation angle measurements of the glucose solutions is 2.13%. The correlation coefficient between the measured rotation angle and the concentration of the glucose solution is determined to be 0.99985, while the standard deviation is just 0.0022deg. Overall the experimental results demonstrate the ability of the proposed system to obtain highly accurate measurements of the linear and circular birefringence properties of an optical sample and to decouple the relationship between the principal axis angle and the rotation angle.

© 2008 Optical Society of America

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  1. B. Wang and 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]
  2. Y. L. Lo and P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764-2767 (2002).
    [CrossRef]
  3. J. R. Mackey, E. Salari, and P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179-185 (2002).
    [CrossRef]
  4. B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271-278 (2003).
    [CrossRef]
  5. Y. L. Lo, J. F. Lin, and S. Y. Lee, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013-2022 (2004).
    [CrossRef]
  6. J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
    [CrossRef]
  7. B. D. Cameron and G. L. Cóte, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221-1227 (1997).
    [CrossRef]
  8. C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
    [CrossRef]
  9. Y. L. Lo and T. C. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259, 40-48 (2006).
    [CrossRef]
  10. J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals: principles and construction,” J. Appl. Crystallogr. 16, 204-211 (1983).
    [CrossRef]
  11. I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).
  12. M. Ebisawa, Y. Otani, and N. Umeda, “Microscopic measurement system for birefringence and optical rotation distribution,” Proc. SPIE 6048, 604807-1-604807-6 (2005).
  13. Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
    [CrossRef]
  14. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).
  15. D. C. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).
  16. M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, “Polar decomposition of 3×3 Mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14, 9324-9337 (2006).
    [CrossRef]
  17. B. Wang, “Measurement of circular and linear birefringence in chiral media and optical materials using the photoelastic modulator,” Proc. SPIE 3535, 294-302 (1999).
    [CrossRef]
  18. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physics Sciences (McGraw-Hill, 1992).
  19. Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
    [CrossRef]
  20. L. Giudicotti and M. Brombin, “Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter,” Appl. Opt. 46, 2638-2647 (2007).
    [CrossRef]
  21. S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeter: comparison of performances,” Proc. SPIE 4285, 235-243 (2001).
    [CrossRef]
  22. J. F. Lin, “Simultaneous measurement of optical rotation angle and retardance,” Opt. Commun. 281, 940-947 (2008).
    [CrossRef]
  23. V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
    [CrossRef]
  24. H. Kowa, K. Muraki, and M. Tsukiji, “Simultaneous measurement of linear and circular birefringence with heterodyne interferometer,” Proc. SPIE 2873, 29-32 (1996).
  25. S. T. Tang and H. S. Kowk, “Characteristic parameters of liquid crystal cells and their measurements,” J. Display Technol. 2, 26-31 (2006).
  26. H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincare's equivalence theorem,” J. Mod. Opt. 51, 597-618 (2004).

2008 (1)

J. F. Lin, “Simultaneous measurement of optical rotation angle and retardance,” Opt. Commun. 281, 940-947 (2008).
[CrossRef]

2007 (2)

L. Giudicotti and M. Brombin, “Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter,” Appl. Opt. 46, 2638-2647 (2007).
[CrossRef]

J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
[CrossRef]

2006 (4)

Y. L. Lo and T. C. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259, 40-48 (2006).
[CrossRef]

S. T. Tang and H. S. Kowk, “Characteristic parameters of liquid crystal cells and their measurements,” J. Display Technol. 2, 26-31 (2006).

M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, “Polar decomposition of 3×3 Mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14, 9324-9337 (2006).
[CrossRef]

V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
[CrossRef]

2005 (2)

M. Ebisawa, Y. Otani, and N. Umeda, “Microscopic measurement system for birefringence and optical rotation distribution,” Proc. SPIE 6048, 604807-1-604807-6 (2005).

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

2004 (2)

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincare's equivalence theorem,” J. Mod. Opt. 51, 597-618 (2004).

Y. L. Lo, J. F. Lin, and S. Y. Lee, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013-2022 (2004).
[CrossRef]

2003 (1)

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

2002 (2)

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

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

2001 (1)

S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeter: comparison of performances,” Proc. SPIE 4285, 235-243 (2001).
[CrossRef]

1999 (2)

B. Wang, “Measurement of circular and linear birefringence in chiral media and optical materials using the photoelastic modulator,” Proc. SPIE 3535, 294-302 (1999).
[CrossRef]

B. Wang and 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 (3)

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

B. D. Cameron and G. L. Cóte, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221-1227 (1997).
[CrossRef]

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

1996 (1)

H. Kowa, K. Muraki, and M. Tsukiji, “Simultaneous measurement of linear and circular birefringence with heterodyne interferometer,” Proc. SPIE 2873, 29-32 (1996).

1994 (1)

Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
[CrossRef]

1993 (1)

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

1992 (1)

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physics Sciences (McGraw-Hill, 1992).

1990 (1)

D. C. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

1983 (1)

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals: principles and construction,” J. Appl. Crystallogr. 16, 204-211 (1983).
[CrossRef]

Andruzzi, F.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Benkelfat, B. E.

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

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physics Sciences (McGraw-Hill, 1992).

Brombin, M.

Buddhiwant, P.

Cameron, B. D.

B. D. Cameron and G. L. Cóte, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221-1227 (1997).
[CrossRef]

Chang, M.

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

Chou, C.

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

Cóte, G. L.

B. D. Cameron and G. L. Cóte, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221-1227 (1997).
[CrossRef]

De Angelis, C.

S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeter: comparison of performances,” Proc. SPIE 4285, 235-243 (2001).
[CrossRef]

Duran, V.

V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
[CrossRef]

Ebisawa, M.

M. Ebisawa, Y. Otani, and N. Umeda, “Microscopic measurement system for birefringence and optical rotation distribution,” Proc. SPIE 6048, 604807-1-604807-6 (2005).

Feng, C. M.

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

Ghosh, N.

Giudicotti, L.

Gupta, P. K.

Hammer, H.

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincare's equivalence theorem,” J. Mod. Opt. 51, 597-618 (2004).

Horache, E. H.

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

Hsu, P. F.

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

Huang, Y. C.

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, “Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid,” Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

Hung, Z. J.

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

Hvilsted, S.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Kliger, D. C.

D. C. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Kobayashi, J.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals: principles and construction,” J. Appl. Crystallogr. 16, 204-211 (1983).
[CrossRef]

Kowa, H.

H. Kowa, K. Muraki, and M. Tsukiji, “Simultaneous measurement of linear and circular birefringence with heterodyne interferometer,” Proc. SPIE 2873, 29-32 (1996).

Kowk, H. S.

Lancis, J.

V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
[CrossRef]

Lee, S. Y.

J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
[CrossRef]

Y. L. Lo, J. F. Lin, and S. Y. Lee, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013-2022 (2004).
[CrossRef]

Lewis, J. W.

D. C. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Li, Q. B.

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

Liao, T. T.

J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
[CrossRef]

Lin, J. F.

J. F. Lin, “Simultaneous measurement of optical rotation angle and retardance,” Opt. Commun. 281, 940-947 (2008).
[CrossRef]

J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
[CrossRef]

Y. L. Lo, J. F. Lin, and S. Y. Lee, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013-2022 (2004).
[CrossRef]

Lo, Y. L.

J. F. Lin, T. T. Liao, Y. L. Lo, and S. Y. Lee, “The optical linear birefringence measurement using a Zeeman laser,” Opt. Commun. 274, 153-158 (2007).
[CrossRef]

Y. L. Lo and T. C. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259, 40-48 (2006).
[CrossRef]

Y. L. Lo, J. F. Lin, and S. Y. Lee, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013-2022 (2004).
[CrossRef]

Y. L. Lo and 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, and P. Tin, “Optical material stress measurement system using two orthogonally polarized sinusoidally intensity-modulated semiconductor lasers,” Meas. Sci. Technol. 13, 179-185 (2002).
[CrossRef]

Manhas, S.

Muraki, K.

H. Kowa, K. Muraki, and M. Tsukiji, “Simultaneous measurement of linear and circular birefringence with heterodyne interferometer,” Proc. SPIE 2873, 29-32 (1996).

Naydenova, I.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Nikolova, L.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Oakberg, T. C.

B. Wang and 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]

Otani, Y.

M. Ebisawa, Y. Otani, and N. Umeda, “Microscopic measurement system for birefringence and optical rotation distribution,” Proc. SPIE 6048, 604807-1-604807-6 (2005).

Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
[CrossRef]

Pelizzari, S.

S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeter: comparison of performances,” Proc. SPIE 4285, 235-243 (2001).
[CrossRef]

Ramanujam, P. S.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Randall, C. E.

D. C. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physics Sciences (McGraw-Hill, 1992).

Rovati, L.

S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeter: comparison of performances,” Proc. SPIE 4285, 235-243 (2001).
[CrossRef]

Salari, E.

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

Shi, J. H.

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

Shimada, T.

Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
[CrossRef]

Swami, M. K.

Tajahuerce, E.

V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
[CrossRef]

Tan, Q.

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

Tang, S. T.

Tin, P.

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

Todorov, T.

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Tsukiji, M.

H. Kowa, K. Muraki, and M. Tsukiji, “Simultaneous measurement of linear and circular birefringence with heterodyne interferometer,” Proc. SPIE 2873, 29-32 (1996).

Uesu, Y.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals: principles and construction,” J. Appl. Crystallogr. 16, 204-211 (1983).
[CrossRef]

Umeda, N.

M. Ebisawa, Y. Otani, and N. Umeda, “Microscopic measurement system for birefringence and optical rotation distribution,” Proc. SPIE 6048, 604807-1-604807-6 (2005).

Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
[CrossRef]

Uppal, A.

Vinouze, B.

B. E. Benkelfat, E. H. Horache, Q. Zou, and 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 and 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]

B. Wang, “Measurement of circular and linear birefringence in chiral media and optical materials using the photoelastic modulator,” Proc. SPIE 3535, 294-302 (1999).
[CrossRef]

Wang, Z. P.

Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Hung, and J. H. Shi, “Method to enhance the accuracy of the retardance measurement of quarter-wave plates,” Opt. Las. Eng. 43, 1226-1236 (2005).
[CrossRef]

Yoshozawa, T.

Y. Otani, T. Shimada, T. Yoshozawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
[CrossRef]

Yu, T. C.

Y. L. Lo and T. C. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259, 40-48 (2006).
[CrossRef]

Zou, Q.

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

Appl. Opt. (2)

IEEE Trans. Biomed. Eng. (1)

B. D. Cameron and G. L. Cóte, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221-1227 (1997).
[CrossRef]

J. Appl. Crystallogr. (1)

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals: principles and construction,” J. Appl. Crystallogr. 16, 204-211 (1983).
[CrossRef]

J. Appl. Phys. (1)

V. Duran, J. Lancis, and E. Tajahuerce, “Equivalent retarder-rotator approach to on-state twist nematic liquid crystal display,” J. Appl. Phys. 99, 113101-6 (2006).
[CrossRef]

J. Display Technol. (1)

J. Mod. Opt. (2)

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincare's equivalence theorem,” J. Mod. Opt. 51, 597-618 (2004).

I. Naydenova, L. Nikolova, T. Todorov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarimetric investigation of materials with both linear and circular anisotropy,” J. Mod. Opt. 44, 1643-1650 (1997).

Jpn. J. Appl. Phys. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup for the concurrent measurement of linear and circular birefringence properties of an optical sample.

Fig. 2
Fig. 2

Simulation results of Mueller matrix elements and their differences for the rotation angle value of 0.0263 ° and different linear birefringence (a)  m 23 , (b)  m 32 , (c)  m 23 m 32 , (d)  m 22 , (e)  m 33 , and (f)  m 22 + m 33 .

Fig. 3
Fig. 3

Total uncertainty of the rotation angle regarding glucose solution with a concentration of 0.2 g / dl followed by the linearly birefringent medium of different retardances with the condition that the polarization angle error of the polarizer δ P 0 ° = δ P 45 ° = 0.017 rad ( 1 ° ) (a) retardances are 1 ° , 22.5 ° , 45 ° , 67.5 ° , and (b) retardances are 90 ° , 112.5 ° , 135 ° , 157.5 ° .

Fig. 4
Fig. 4

Variation of the measured principal axis angle and retardance of a quarter-wave plate in a composite sample composed of a half-wave plate positioned in front of a quarter-wave plate.

Fig. 5
Fig. 5

Variation of the measured optical rotation angle of a half-wave plate with the principal axis angle set at 45 ° in a composite sample composed of a half-wave plate positioned in front of a quarter-wave plate.

Fig. 6
Fig. 6

Variation of the principal axis angle and retardance of a half-wave plate with the principal axis angle set at 90 ° in a composite sample composed of glucose solution positioned in front of a half-wave plate.

Fig. 7
Fig. 7

Variation of the rotation angle with glucose concentration in a composite sample composed of a glucose sample positioned in front of a half-wave plate.

Fig. 8
Fig. 8

Repeatability results obtained for linear birefringence properties of a composite sample composed of glucose solution with a concentration of 0.1 g / dl positioned in front of a half-wave plate.

Fig. 9
Fig. 9

Repeatability results obtained for the circular birefringence properties of a composite sample composed of glucose solution with a concentration of 0.1 g / dl positioned in front of a half-wave plate.

Equations (25)

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S = [ S 0 S 1 S 2 S 3 ] = [ I x + I y I x I y I 45 ° I 45 ° I L I R ] ,
S = [ S 0 S 1 S 2 S 3 ] = [ m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ] [ S ^ 0 S ^ 1 S ^ 2 S ^ 3 ] = M S ^ .
M L B = [ 1 0 0 0 0 cos ( 4 α ) sin 2 ( β / 2 ) + cos 2 ( β / 2 ) sin ( 4 α ) sin 2 ( β / 2 ) sin ( 2 α ) sin ( β ) 0 sin ( 4 α ) sin 2 ( β / 2 ) cos ( 4 α ) sin 2 ( β / 2 ) + cos 2 ( β / 2 ) cos ( 2 α ) sin ( β ) 0 sin ( 2 α ) sin ( β ) cos ( 2 α ) sin ( β ) cos ( β ) ] .
M C B = [ 1 0 0 0 0 cos ( 2 γ ) sin ( 2 γ ) 0 0 sin ( 2 γ ) cos ( 2 γ ) 0 0 0 0 1 ] .
S C = [ S 0 S 1 S 2 S 3 ] C = [ M ] L B [ M ] C B S ^ = [ M ] C S ^ = [ 1 0 0 0 0 m 22 m 23 m 24 0 m 32 m 33 m 34 0 m 42 m 43 m 44 ] [ S ^ 0 S ^ 1 S ^ 2 S ^ 3 ] .
m 22 = [ sin ( 2 α ) cos ( 2 α ) ( 1 cos ( β ) ) ] sin ( 2 γ ) + [ cos 2 ( 2 α ) + sin 2 ( 2 α ) cos ( β ) ] cos ( 2 γ ) ,
m 23 = [ cos 2 ( 2 α ) + sin 2 ( 2 α ) cos ( β ) ] sin ( 2 γ ) + [ sin ( 2 α ) cos ( 2 α ) ( 1 cos ( β ) ) ] cos ( 2 γ ) ,
m 32 = [ sin 2 ( 2 α ) + cos 2 ( 2 α ) cos ( β ) ] sin ( 2 γ ) + [ sin ( 2 α ) cos ( 2 α ) ( 1 cos ( β ) ) ] cos ( 2 γ ) ,
m 33 = [ sin ( 2 α ) cos ( 2 α ) ( 1 cos ( β ) ) ] sin ( 2 γ ) + [ sin 2 ( 2 α ) + cos 2 ( 2 α ) cos ( β ) ] cos ( 2 γ ) ,
m 23 m 32 = ( 1 + cos ( β ) ) sin ( 2 γ ) ,
m 22 + m 33 = ( 1 + cos ( β ) ) cos ( 2 γ ) ,
m 22 m 33 = [ sin ( 4 α ) ( 1 cos ( β ) ) ] sin ( 2 γ ) + [ cos ( 4 α ) ( 1 cos ( β ) ) ] cos ( 2 γ ) ,
m 23 + m 32 = [ cos ( 4 α ) ( 1 cos ( β ) ) ] sin ( 2 γ ) + [ sin ( 4 α ) ( 1 cos ( β ) ) ] cos ( 2 γ ) .
β = cos 1 ( ( m 22 + m 33 ) 2 + ( m 23 m 32 ) 2 1 ) ,
γ = 1 2 tan 1 ( m 23 m 32 m 22 + m 33 ) .
4 α + 2 γ = tan 1 ( m 23 + m 32 m 22 m 33 ) .
α = 1 4 [ tan 1 ( m 23 + m 32 m 22 m 33 ) tan 1 ( m 23 m 32 m 22 + m 33 ) ] = 1 4 tan 1 [ 2 ( m 22 m 32 + m 23 m 33 ) ( m 22 2 m 33 2 ) + ( m 23 2 m 32 2 ) ] .
γ α = 0 ,
γ β = 0.
γ P 0 ° = γ V V m 2 m 2 P 0 ° + γ V V m 3 m 3 P 0 ° = ( m 23 2 m 23 m 32 + m 22 m 33 + m 33 2 ) ( m 22 + m 33 ) 2 + ( m 23 m 32 ) 2 ,
γ P 45 ° = γ V V m 2 m 2 P 45 ° + γ V V m 3 m 3 P 45 ° = ( m 22 2 m 23 m 32 + m 22 m 33 + m 32 2 ) ( m 22 + m 33 ) 2 + ( m 23 m 32 ) 2 .
δ γ = ( γ α ) 2 ( α ) 2 + ( γ β ) 2 ( β ) 2 + ( γ P 0 ° ) 2 ( P 0 ° ) 2 + ( γ P 45 ° ) 2 ( P 45 ° ) 2 = ( γ P 0 ° ) 2 ( P 0 ° ) 2 + ( γ P 45 ° ) 2 ( P 45 ° ) 2 = ( m 23 2 m 23 m 32 + m 22 m 33 + m 33 2 ) 2 + ( m 22 2 m 23 m 32 + m 22 m 33 + m 32 2 ) 2 ( 1 + cos ( β ) ) 2 .
γ = γ measured ± δ γ .
ε = | P measured P actual | | P actual | × 100 % .
C = 100 γ L [ γ ] ,

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