Abstract

A method for simultaneous measurement of the retardance and the fast axis angle of quarter-wave plate using one photoelastic modulator is presented. A laser beam passes through a polarizer, a photoelastic modulator, the quarter-wave plate to be measured, and an analyzer to be detected. Before and after the quarter-wave plate is rotated 45° at any initial fast axis direction, two detection signals are obtained to resolve simultaneously the retardance and the fast axis angle. In experiments, a quarter-wave plate was measured with fast axis angles from 89° to 90°. The average and the standard deviation of the retardances at different fast axis directions are respectively 89.50° and 0.17°. The maximum measurement deviation of the fast axis angle is 0.5°. The usefulness of the method is verified.

© 2011 Optical Society of America

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References

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  1. P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating polarizer polarimeter for accurate retardation measurement,” Appl. Opt. 36, 6466–6472 (1997).
    [CrossRef]
  2. S. Pelizzari, L. Rovati, and C. D. Angelis, “Rotating polarizer and rotating retarder plate polarimeters: comparison of performances,” Proc. SPIE 4285, 235–243 (2001).
    [CrossRef]
  3. L. Giudicotti and M. Brombin, “Data analysis for a rotating quarter-wave, far- infrared Stokes polarimeter,” Appl. Opt. 46, 2638–2647 (2007).
    [CrossRef] [PubMed]
  4. J. Lin and Y. Lo, “Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights,” Opt. Lasers Eng. 47, 948–955 (2009).
    [CrossRef]
  5. Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
    [CrossRef]
  6. X. Chen, L. Yan, and X. S. Yao, “Waveplate analyzer using binary magneto-optic rotators,” Opt. Express 15, 12989–12994(2007).
    [CrossRef] [PubMed]
  7. P. Kurzynowski and W. A. Woźniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik 113, 51–53(2002).
    [CrossRef]
  8. C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator method for single-point retardation measurements,” Appl. Opt. 43, 6580–6595 (2004).
    [CrossRef]
  9. Y. Zhang, F. Song, H. Li, and X. Yang, “Precise measurement of optical phase retardation of a wave plate using modulated-polarized light,” Appl. Opt. 49, 5837–5843 (2010).
    [CrossRef] [PubMed]
  10. B. D. Cameron and G. L. Cote, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
    [CrossRef] [PubMed]
  11. C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
    [CrossRef]
  12. W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
    [CrossRef]
  13. B. E. Benkelfata, E. H. Horachea, Q. Zoua, and B. Vinouze, “An electro-optic modulation technique for direct and accurate measurement of birefringence,” Opt. Commun. 221, 271–278(2003).
    [CrossRef]
  14. S. Lee, J. Lin, and Y. 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]
  15. Y. Lo, C. Lai, J. Lin, and P. Hsu, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
    [CrossRef] [PubMed]
  16. T. C. Oakberg, “Measurement of waveplate retardation using a photoelastic modulator,” Proc. SPIE 3121, 19–22(1997).
    [CrossRef]
  17. B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
    [CrossRef]
  18. B. Wang, “Linear birefringence measurement instrument using two photoelastic modulators,” Opt. Eng. 41, 981–987(2002).
    [CrossRef]
  19. B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
    [CrossRef]
  20. S. M. Wilson, V. Vats, and P. H. Vaccaro, “Time-domain method for characterizing retardation plates with high sensitivity and resolution,” J. Opt. Soc. Am. B 24, 2500–2508 (2007).
    [CrossRef]
  21. B. Wang and J. List, “Basic optical properties of the photoelastic modulator: part I. Useful aperture and acceptance angle,” Proc. SPIE 5888, 58881I (2005).
    [CrossRef]
  22. B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
    [CrossRef]
  23. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 2003).

2010 (1)

2009 (2)

J. Lin and Y. Lo, “Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights,” Opt. Lasers Eng. 47, 948–955 (2009).
[CrossRef]

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

2007 (3)

2006 (1)

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

2005 (2)

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

B. Wang and J. List, “Basic optical properties of the photoelastic modulator: part I. Useful aperture and acceptance angle,” Proc. SPIE 5888, 58881I (2005).
[CrossRef]

2004 (4)

B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
[CrossRef]

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

C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator method for single-point retardation measurements,” Appl. Opt. 43, 6580–6595 (2004).
[CrossRef]

2003 (2)

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

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 2003).

2002 (2)

B. Wang, “Linear birefringence measurement instrument using two photoelastic modulators,” Opt. Eng. 41, 981–987(2002).
[CrossRef]

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

2001 (1)

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

1999 (1)

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

1997 (4)

T. C. Oakberg, “Measurement of waveplate retardation using a photoelastic modulator,” Proc. SPIE 3121, 19–22(1997).
[CrossRef]

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

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating polarizer polarimeter for accurate retardation measurement,” Appl. Opt. 36, 6466–6472 (1997).
[CrossRef]

Angelis, C. D.

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

Benkelfata, B. E.

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

Brombin, M.

Cameron, B. D.

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

Chang, J.

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Chang, M.

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Chen, X.

Chou, C.

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 2003).

Cote, G. L.

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

Feng, C.

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Gaylord, T. K.

Giudicotti, L.

Hinds, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Horachea, E. H.

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

Hsu, P.

Huang, Y.

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Huang, Z.

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Jan, G.

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

Krivoy, E.

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

Kuo, W.

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

Kurzynowski, P.

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

Lai, C.

Leadbetter, A.

B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
[CrossRef]

Lee, S.

S. Lee, J. Lin, and Y. 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]

Li, H.

Li, Q.

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Liao, K.

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

Lin, J.

J. Lin and Y. Lo, “Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights,” Opt. Lasers Eng. 47, 948–955 (2009).
[CrossRef]

Y. Lo, C. Lai, J. Lin, and P. Hsu, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
[CrossRef] [PubMed]

S. Lee, J. Lin, and Y. 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]

List, J.

B. Wang and J. List, “Basic optical properties of the photoelastic modulator: part I. Useful aperture and acceptance angle,” Proc. SPIE 5888, 58881I (2005).
[CrossRef]

Lo, Y.

J. Lin and Y. Lo, “Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights,” Opt. Lasers Eng. 47, 948–955 (2009).
[CrossRef]

Y. Lo, C. Lai, J. Lin, and P. Hsu, “Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer,” Appl. Opt. 43, 2013–2022 (2004).
[CrossRef] [PubMed]

S. Lee, J. Lin, and Y. 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]

Montarou, C. C.

Oakberg, T. C.

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

T. C. Oakberg, “Measurement of waveplate retardation using a photoelastic modulator,” Proc. SPIE 3121, 19–22(1997).
[CrossRef]

Pelizzari, S.

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

Rockwell, R. R.

B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
[CrossRef]

Rose, A. H.

Rovati, L.

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

Shi, J.

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Song, F.

Tan, Q.

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Teng, H.

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

Vaccaro, P. H.

Vats, V.

Vinouze, B.

B. E. Benkelfata, E. H. Horachea, Q. Zoua, 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, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

B. Wang and J. List, “Basic optical properties of the photoelastic modulator: part I. Useful aperture and acceptance angle,” Proc. SPIE 5888, 58881I (2005).
[CrossRef]

B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
[CrossRef]

B. Wang, “Linear birefringence measurement instrument using two photoelastic modulators,” Opt. Eng. 41, 981–987(2002).
[CrossRef]

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

Wang, C. M.

Wang, Z.

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Williams, P. A.

Wilson, S. M.

Wozniak, W. A.

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

Yan, L.

Yang, X.

Yao, X. S.

Zhang, Y.

Zoua, Q.

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

Appl. Opt. (5)

IEEE Trans. Biomed. Eng. (1)

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

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

W. Kuo, K. Liao, G. Jan, H. Teng, and C. Chou, “Simultaneous measurement of phase retardation and fast-axis angle of phase retardation plate,” Jpn. J. Appl. Phys. 44, 1095–1100(2005).
[CrossRef]

Meas. Sci. Technol. (1)

S. Lee, J. Lin, and Y. 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]

Measurement (1)

Z. Wang, Q. Li, Q. Tan, Z. Huang, and J. Shi, “Method of measuring the practical retardance and judging the fast or slow axis of a quarter-wave plate,” Measurement 39, 729–735(2006).
[CrossRef]

Opt. Commun. (2)

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

C. Feng, Y. Huang, J. Chang, M. Chang, and C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Opt. Eng. (1)

B. Wang, “Linear birefringence measurement instrument using two photoelastic modulators,” Opt. Eng. 41, 981–987(2002).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

J. Lin and Y. Lo, “Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights,” Opt. Lasers Eng. 47, 948–955 (2009).
[CrossRef]

Optik (1)

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

Proc. SPIE (5)

B. Wang and J. List, “Basic optical properties of the photoelastic modulator: part I. Useful aperture and acceptance angle,” Proc. SPIE 5888, 58881I (2005).
[CrossRef]

B. Wang, E. Hinds, and E. Krivoy, “Basic optical properties of the photoelastic modulator: part II. Residual birefringence in the optical element,” Proc. SPIE 7461, 746110 (2009).
[CrossRef]

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

T. C. Oakberg, “Measurement of waveplate retardation using a photoelastic modulator,” Proc. SPIE 3121, 19–22(1997).
[CrossRef]

B. Wang, R. R. Rockwell, and A. Leadbetter, “A polarimeter using two photoelastic modulators,” Proc. SPIE 5531, 367–374(2004).
[CrossRef]

Rev. Sci. Instrum. (1)

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

Other (1)

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 2003).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram for simultaneous measurement of retardance and fast axis angle of quarter-wave plate.

Fig. 2
Fig. 2

Measurement results of retardance of quarter-wave plate.

Fig. 3
Fig. 3

Measurement results of fast axis angle of quarter-wave plate.

Fig. 4
Fig. 4

Measurement results of retardance of eighth-wave plate.

Equations (27)

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

S I = I 0 [ 1 0 1 0 ] ,
M PEM = [ 1 0 0 0 0 1 0 0 0 0 cos ( δ PEM ) sin ( δ PEM ) 0 0 sin ( δ PEM ) cos ( δ PEM ) ] , δ PEM = a 0 sin ω t ,
M QWP = [ 1 0 0 0 0 cos 2 ( 2 θ ) + cos ( δ ) sin 2 ( 2 θ ) ( 1 cos ( δ ) ) cos ( 2 θ ) sin ( 2 θ ) sin ( δ ) sin ( 2 θ ) 0 ( 1 cos ( δ ) ) cos ( 2 θ ) sin ( 2 θ ) sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) sin ( δ ) cos ( 2 θ ) 0 sin ( δ ) sin ( 2 θ ) sin ( δ ) cos ( 2 θ ) cos ( δ ) ] ,
M A = 1 2 [ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ] ,
S A = M A M QWP M PEM S P = I 0 2 [ S 0 S 1 S 2 S 3 ] ,
S 0 = 1 cos ( δ PEM ) [ sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ] + sin ( δ PEM ) sin ( δ ) cos ( 2 θ ) .
I = I 0 2 { 1 cos ( δ PEM ) [ sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ] + sin ( δ PEM ) sin ( δ ) cos ( 2 θ ) } .
sin δ PEM = sin ( a 0 sin ω t ) = 2 k + 1 2 J 2 k + 1 ( a 0 ) sin [ ( 2 k + 1 ) ω t ] ,
cos δ PEM = cos ( a 0 sin ω t ) = J 0 ( a 0 ) + 2 k 2 J 2 k ( a 0 ) cos [ ( 2 k ) ω t ] ,
V = K I = K I 0 2 { 1 J 0 ( a 0 ) ( sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ) + 2 J 1 ( a 0 ) cos ( ω t ) sin ( δ ) cos ( 2 θ ) 2 J 2 ( a 0 ) cos ( 2 ω t ) ( sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ) + } ,
V DC ( δ | θ ) = k 1 K I 0 2 { 1 J 0 ( a 0 ) ( sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ) } ,
V f ( δ | θ ) = k 2 K I 0 J 1 ( a 0 ) sin ( δ ) cos ( 2 θ ) ,
V 2 f ( δ | θ ) = k 3 K I 0 J 2 ( a 0 ) ( sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ) ,
V DC ( δ | θ ) = k 1 K I 0 2 .
V f ( δ | θ ) V DC ( δ | θ ) = 2 k 2 k 1 J 1 ( 2.405 ) sin ( δ ) cos ( 2 θ ) ,
V 2 f ( δ | θ ) V DC ( δ | θ ) = 2 k 3 k 1 J 2 ( 2.405 ) ( sin 2 ( 2 θ ) + cos ( δ ) cos 2 ( 2 θ ) ) .
V f ( δ | θ + 45 ) V DC ( δ | θ + 45 ) = 2 k 2 k 1 J 1 ( 2.405 ) sin ( δ ) sin ( 2 θ ) ,
V 2 f ( δ | θ + 45 ° ) V DC ( δ | θ + 45 ) = 2 k 3 k 1 J 2 ( 2.405 ) ( cos 2 ( 2 θ ) + cos ( δ ) sin 2 ( 2 θ ) ) .
V 2 f ( δ | θ ) V DC ( δ | θ ) + V 2 f ( δ | θ + 45 ) V DC ( δ | θ + 45 ) = 2 k 3 k 1 J 2 ( 2.405 ) ( 1 + cos ( δ ) ) ,
V f ( δ | θ + 45 ° ) V DC ( δ | θ + 45 ) / V f ( δ | θ ) V DC ( δ | θ ) = tan ( 2 θ ) ,
V f ( δ | θ ) V DC ( δ | θ ) / V f ( δ | θ + 45 ° ) V DC ( δ | θ + 45 ° ) = cot ( 2 θ ) .
V 2 f ( δ = 0 ) V DC ( δ = 0 ) = 2 k 3 k 1 J 2 ( 2.405 ) .
δ = arccos ( V 2 f ( δ | θ ) V DC ( δ | θ ) + V 2 f ( δ | θ + 45 ) V DC ( δ | θ + 45 ) V 2 f ( δ = 0 ) V DC ( δ = 0 ) 1 ) .
θ = 1 2 arctan ( V f ( δ | θ + 45 ° ) V DC ( δ | θ + 45 ° ) / V f ( δ | θ ) V DC ( δ | θ ) )
θ = 1 2 arccot ( V f ( δ | θ ) V DC ( δ | θ ) / V f ( δ | θ + 45 ° ) V DC ( δ | θ + 45 ° ) ) .
θ = { θ cos ( 2 θ ) > 0 θ 90 cos ( 2 θ ) < 0 & θ > 0 θ + 90 cos ( 2 θ ) < 0 & θ < 0 ,
θ = { θ 90 sin ( 2 θ ) < 0 θ else .

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