Abstract

What we believe to be a new technique for the measurement of two-dimensional retardation distributions of a wave plate (WP) is presented. Phase-shifting interferometry has been applied for determining the relative retardation distribution using a Nomarski prism (NP) as a phase shifter. Absolute retardation distribution is obtained by accurately determining the position of zero retardation in the interference field using white light interference fringes and adjusting the phase distribution with respect to the zero retardation position. The measured absolute retardation distribution of the NP is subtracted from that obtained for the combination of the WP and NP, to get the desired retardation distributions for the WP. The technique is suitable for the measurement of phase retardation of both single and multiple order WPs, as the actual phase retardation distributions are obtained. Results obtained for WPs are presented.

© 2008 Optical Society of America

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References

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  1. J. M. Bennett and H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, 1978), Chap. 10, pp. 129-140.
  2. N. N. Nagib, “Phase retardometer: a proposed device for measuring phase retardance,” Appl. Opt. 39, 2078-2080 (2000).
    [CrossRef]
  3. P. Kurzynowski and W. A. Wozniak, “Phase retardation measurement in single and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51-53 (2002).
  4. S. Nakadate, “High precision retardation measurement using phase detection of Young's fringes,” Appl. Opt. 29, 242-246(1990).
    [CrossRef] [PubMed]
  5. C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two wave plate compensator method for full field retardation measurements,” Appl. Opt. 45, 271-280(2006).
    [CrossRef] [PubMed]
  6. S. Y. Berezhna, I. V. Berezhnyy, and M. Takashi, “Dynamic photometric imaging polarizer-sample-analyzer polarimeter: instrument for mapping birefringence and optical rotation,” J. Opt. Soc. Am. A. 18, 666-672 (2001).
    [CrossRef]
  7. S. Drobczynski and H. Kasprzak, “Application of space periodic variation of light polarization in imaging polarimetry,” Appl. Opt. 44, 3160-3166 (2005).
    [CrossRef] [PubMed]
  8. S. Drobczynski, J. M. Bueno, P. Artal, and H. Kasprzak, “Transmission imaging polarimeter for a linear birefringent medium using a carrier fringe method,” Appl. Opt. 45, 5489-5496 (2006).
    [CrossRef] [PubMed]
  9. J. W. Jaronski and H. T. Kasprzak, “Generalised algorithm for photoelastic measurements based on phase stepping imaging polarimetry,” Appl. Opt. 38, 7018-7025 (1999).
    [CrossRef]
  10. Y. Otani, T. Shimada, T. Yushizawa, and N. Umeda, “Two dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604-1609 (1994).
    [CrossRef]
  11. B. Laude-Boulesteix, A. D. Martino, B. Drevillon, and L. Schwartz, “Muller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824-2832 (2004).
    [CrossRef] [PubMed]
  12. S. D. Chidester, J. W. Harvey, and R. P. Hubbard, “Measurement of crystal retarders,” Appl. Opt. 30, 12-14 (1991).
    [CrossRef] [PubMed]
  13. Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. 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]
  14. Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
    [CrossRef]
  15. M. H. Chiu, C. D. Chen, and D. C. Su, “Method for determining the fast axis and phase retardation of a wave plate,” J. Opt. Soc. Am. A 13, 1924-1929 (1996).
    [CrossRef]
  16. K. B. Rochford and C. M. Wang, “Accurate interferometric retardance measurememt,” Appl. Opt. 36, 6473-6479(1997).
    [CrossRef]
  17. Y. Zhang, S. Zhang, Y. Han, Y. Li, and X. Xu, “Method for the measurement of retardation of wave plates based on laser frequency splitting technology,” Opt. Eng. 40, 1071-1075(2001).
    [CrossRef]
  18. C. C. Montarou, T. K. Gaylord, R. A. Villalaz, and E. A. Glytsis, “Colorimetry based retardation measurement method with white light interference,” Appl. Opt. 41, 5290-5297 (2002).
    [CrossRef] [PubMed]
  19. M. Borwinska, A. Masajada, and P. Kurzynowski, “Measurements of birefringent media properties using optical vortex birefringence compensator,” Appl. Opt. 46, 6419-6426(2007).
    [CrossRef] [PubMed]
  20. S. Chatterjee, “Design considerations and fabrication technique of Nomarski reflection microscope,” Opt. Eng. 42, 2202-2213 (2003).
    [CrossRef]
  21. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 28, pp. 349-393.
    [CrossRef]
  22. P. Hariharan, “Phase shifting interferometery: minimization of systematic errors,” Opt. Eng. 39, 967-969 (2000).
    [CrossRef]
  23. K. Creath, “Comparison of phase measurement algorithm,” Proc. SPIE 680, 19-28 (1986).
  24. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase shifting interferometery: a simple error compensating phase calculation algorithm,” Appl. Opt. 26, 2504-2505 (1987).
    [CrossRef] [PubMed]
  25. D. Malacara, S. Malacara, and Z. Malacara, Interferogram Analysis for Optical Testing, 1st ed. (Marcel Dekker, 1998), pp. 248-255.
  26. J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A Pure Appl. Opt. 2, 216-222 (2000).
    [CrossRef]
  27. E. A. West and M. H. Smith, “Polarization errors associated with birefringence wave plates,” Opt. Eng. 34, 1574-1580(1995).
    [CrossRef]

2007

2006

2005

2004

2003

S. Chatterjee, “Design considerations and fabrication technique of Nomarski reflection microscope,” Opt. Eng. 42, 2202-2213 (2003).
[CrossRef]

2002

P. Kurzynowski and W. A. Wozniak, “Phase retardation measurement in single and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51-53 (2002).

C. C. Montarou, T. K. Gaylord, R. A. Villalaz, and E. A. Glytsis, “Colorimetry based retardation measurement method with white light interference,” Appl. Opt. 41, 5290-5297 (2002).
[CrossRef] [PubMed]

2001

Y. Zhang, S. Zhang, Y. Han, Y. Li, and X. Xu, “Method for the measurement of retardation of wave plates based on laser frequency splitting technology,” Opt. Eng. 40, 1071-1075(2001).
[CrossRef]

S. Y. Berezhna, I. V. Berezhnyy, and M. Takashi, “Dynamic photometric imaging polarizer-sample-analyzer polarimeter: instrument for mapping birefringence and optical rotation,” J. Opt. Soc. Am. A. 18, 666-672 (2001).
[CrossRef]

2000

N. N. Nagib, “Phase retardometer: a proposed device for measuring phase retardance,” Appl. Opt. 39, 2078-2080 (2000).
[CrossRef]

P. Hariharan, “Phase shifting interferometery: minimization of systematic errors,” Opt. Eng. 39, 967-969 (2000).
[CrossRef]

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

1999

1997

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

K. B. Rochford and C. M. Wang, “Accurate interferometric retardance measurememt,” Appl. Opt. 36, 6473-6479(1997).
[CrossRef]

1996

1995

E. A. West and M. H. Smith, “Polarization errors associated with birefringence wave plates,” Opt. Eng. 34, 1574-1580(1995).
[CrossRef]

1994

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

1991

1990

1987

1986

K. Creath, “Comparison of phase measurement algorithm,” Proc. SPIE 680, 19-28 (1986).

Appl. Opt.

N. N. Nagib, “Phase retardometer: a proposed device for measuring phase retardance,” Appl. Opt. 39, 2078-2080 (2000).
[CrossRef]

S. Nakadate, “High precision retardation measurement using phase detection of Young's fringes,” Appl. Opt. 29, 242-246(1990).
[CrossRef] [PubMed]

C. C. Montarou, T. K. Gaylord, B. L. Bachim, A. I. Dachevski, and A. Agarwal, “Two wave plate compensator method for full field retardation measurements,” Appl. Opt. 45, 271-280(2006).
[CrossRef] [PubMed]

S. Drobczynski and H. Kasprzak, “Application of space periodic variation of light polarization in imaging polarimetry,” Appl. Opt. 44, 3160-3166 (2005).
[CrossRef] [PubMed]

S. Drobczynski, J. M. Bueno, P. Artal, and H. Kasprzak, “Transmission imaging polarimeter for a linear birefringent medium using a carrier fringe method,” Appl. Opt. 45, 5489-5496 (2006).
[CrossRef] [PubMed]

J. W. Jaronski and H. T. Kasprzak, “Generalised algorithm for photoelastic measurements based on phase stepping imaging polarimetry,” Appl. Opt. 38, 7018-7025 (1999).
[CrossRef]

B. Laude-Boulesteix, A. D. Martino, B. Drevillon, and L. Schwartz, “Muller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824-2832 (2004).
[CrossRef] [PubMed]

S. D. Chidester, J. W. Harvey, and R. P. Hubbard, “Measurement of crystal retarders,” Appl. Opt. 30, 12-14 (1991).
[CrossRef] [PubMed]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. 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]

K. B. Rochford and C. M. Wang, “Accurate interferometric retardance measurememt,” Appl. Opt. 36, 6473-6479(1997).
[CrossRef]

C. C. Montarou, T. K. Gaylord, R. A. Villalaz, and E. A. Glytsis, “Colorimetry based retardation measurement method with white light interference,” Appl. Opt. 41, 5290-5297 (2002).
[CrossRef] [PubMed]

M. Borwinska, A. Masajada, and P. Kurzynowski, “Measurements of birefringent media properties using optical vortex birefringence compensator,” Appl. Opt. 46, 6419-6426(2007).
[CrossRef] [PubMed]

P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase shifting interferometery: a simple error compensating phase calculation algorithm,” Appl. Opt. 26, 2504-2505 (1987).
[CrossRef] [PubMed]

J. Opt. A Pure Appl. Opt.

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

S. Y. Berezhna, I. V. Berezhnyy, and M. Takashi, “Dynamic photometric imaging polarizer-sample-analyzer polarimeter: instrument for mapping birefringence and optical rotation,” J. Opt. Soc. Am. A. 18, 666-672 (2001).
[CrossRef]

Opt. Commun.

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

Opt. Eng.

Y. Zhang, S. Zhang, Y. Han, Y. Li, and X. Xu, “Method for the measurement of retardation of wave plates based on laser frequency splitting technology,” Opt. Eng. 40, 1071-1075(2001).
[CrossRef]

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

E. A. West and M. H. Smith, “Polarization errors associated with birefringence wave plates,” Opt. Eng. 34, 1574-1580(1995).
[CrossRef]

P. Hariharan, “Phase shifting interferometery: minimization of systematic errors,” Opt. Eng. 39, 967-969 (2000).
[CrossRef]

S. Chatterjee, “Design considerations and fabrication technique of Nomarski reflection microscope,” Opt. Eng. 42, 2202-2213 (2003).
[CrossRef]

Optik (Jena)

P. Kurzynowski and W. A. Wozniak, “Phase retardation measurement in single and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51-53 (2002).

Proc. SPIE

K. Creath, “Comparison of phase measurement algorithm,” Proc. SPIE 680, 19-28 (1986).

Other

D. Malacara, S. Malacara, and Z. Malacara, Interferogram Analysis for Optical Testing, 1st ed. (Marcel Dekker, 1998), pp. 248-255.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 28, pp. 349-393.
[CrossRef]

J. M. Bennett and H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, 1978), Chap. 10, pp. 129-140.

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Figures (15)

Fig. 1
Fig. 1

Optical schematic of the experimental setup for measurement of two-dimensional retardation distribution of a WP.

Fig. 2
Fig. 2

Ray paths in an NP.

Fig. 3
Fig. 3

Variation of single pass OPD with position of the point of incidence ( d 1 ) from one end of the NP with design parameters as λ = 633 nm , n o = 1.544 , and n e = 1.553 , thickness of individual component of the NP ( l 1 ) = 0.5 mm , ω = 0.8 ° .

Fig. 4
Fig. 4

Fizeau type white light fringes (grabbed with a monochrome CCD) with zero order fringe due to the NP.

Fig. 5
Fig. 5

Intensity variation (gray levels) along a central section of the Fizeau type white light interference pattern shown in Fig. 4.

Fig. 6
Fig. 6

Fizeau type white light fringes with a shifted zero order fringe compared to that shown in Fig. 4 due to the combination of the NP and a WP.

Fig. 7
Fig. 7

Intensity variation (gray levels) along a central section of the Fizeau type white light interference pattern shown in Fig. 6.

Fig. 8
Fig. 8

Fizeau type fringes obtained with the NP for λ = 633 nm .

Fig. 9
Fig. 9

Fizeau type fringes obtained with a combination of the NP and a WP for λ = 633 nm .

Fig. 10
Fig. 10

Variation of phase retardation (wrapped) along a line in the central section of the NP.

Fig. 11
Fig. 11

Variation of phase retardation (wrapped) along a line in the central section for the combination of the NP and WP.

Fig. 12
Fig. 12

Variation of OPD (unwrapped) along a line in the central section for (B) the NP and (C) combination of the NP and WP.

Fig. 13
Fig. 13

Variation of retardation along a section of the WP.

Fig. 14
Fig. 14

Two-dimensional linear optical retardation distribution obtained for a good quality QWP with mean retardation— 158.18 nm and standard deviation 1.09 nm ; (A) in gray levels and (B) as three-dimensional height variations.

Fig. 15
Fig. 15

Retardation profiles obtained for a particular section of the WP (A) for ten different measurements and (B) corresponding average profile with average error bars ( ε av 0.30 nm ), respectively.

Equations (4)

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I ( x , y ) = I 0 ( x , y ) { 1 + V ( x , y ) cos [ ϕ ( x , y ) + α j ] } ,
ϕ = arctan [ 2 ( I 4 I 2 ) / ( I 1 + I 5 2 I 3 ) ] .
Δ ϕ = ( ε 2 / 4 ) sin 2 ϕ ,
δ = ( λ / 2 π ) ϕ ,

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