Abstract

We present an imaging polarimeter in transmission mode that is based on a carrier frequency method and allows a spatially resolved polarimetric description of nondichroic linear birefringent media. The apparatus incorporates a generator of polarization states in the incoming pathway and a Wollaston prism and a linear polarizer as the analyzer unit. A series of two fringe pattern images of the birefringent sample under study, corresponding to two independent polarization states of the generator unit, were recorded. From these images and by using Fourier analysis, the 2D distribution of azimuth angle and retardation were calculated. Two alternative generator units were used: (i) a linear polarizer combined with a rotatory quarter-wave plate and (ii) a liquid-crystal variable retarder. A uniform quarter-wave plate at different orientations was measured with both generator units to demonstrate the effectiveness and the accuracy of the method. The mean absolute deviations were 1.8° and 4.1° for the azimuth and the retardation, respectively, with the first generator unit, and 2.9° and 4.4° for the second one. Moreover, some nonuniform birefringent samples presenting wider ranges of azimuth and retardation were also tested.

© 2006 Optical Society of America

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    [CrossRef]
  3. J. Jaronski and H. Kasprzak, "Generalized algorithm for photoelastic measurements based on phase-stepping imaging polarimetry," Appl. Opt. 38, 7018-7025 (1999).
    [CrossRef]
  4. R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, "Mueller polarimetric imaging system with liquid crystals," Appl. Opt. 43, 2824-2832 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Lett. 24, 64-66 (1999).
    [CrossRef]
  11. J. M. Bueno, "Measurement of parameters of polarization in the living human eye using imaging polarimetry," Vision Res. 40, 3791-3799 (2000).
    [CrossRef] [PubMed]
  12. J. Bueno and F. Vargas-Martín, "Measurements of the corneal birefringence with a liquid-crystal imaging polariscope," Appl. Opt. 41, 116-124 (2002).
    [CrossRef] [PubMed]
  13. J. M. Bueno and M. C. W. Campbell, "Confocal scanning laser ophthalmoscopy improvement by use of Mueller-matrix polarimetry," Opt. Lett. 27, 830-832 (2002).
    [CrossRef]
  14. B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).
  15. D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
    [CrossRef] [PubMed]
  16. Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Visual Sci. 43, 2221-2228 (2002).
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    [CrossRef]
  19. J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A Pure Appl. Opt. 2, 216-222 (2000).
    [CrossRef]
  20. F. Delplancke, "Automated high-speed Mueller matrix scatterometer," Appl. Opt. 36, 5388-5395 (1997).
    [CrossRef] [PubMed]
  21. R. C. Thompson, J. R. Bottinger, and E. S. Fry, "Measurement of polarized light interactions via the Mueller matrix," Appl. Opt. 19, 1323-1332 (1980).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  26. Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, "Two-dimensional birefringence measurement using the phase shifting technique," Opt. Eng. 33, 1604-1609 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  29. J. E. Roth, J. A. Kozak, S. Yazdanfar, A. M. Rollinsm, and J. A. Izatt, "Simplified method for polarization-sensitive optical coherence tomography," Opt. Lett. 26, 1069-1071 (2001).
    [CrossRef]
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    [CrossRef]
  33. F. A. Modine, R. W. Major, and E. Sonder, "High frequency polarization modulation method for measuring birefringence," Appl. Opt. 14, 757-760 (1975).
    [CrossRef] [PubMed]
  34. C. F. Wong, "Birefringence measurement using a photoelastic modulator," Appl. Opt. 18, 3996-3999 (1979).
    [CrossRef] [PubMed]
  35. B. L. Wang, "Linear birefringence measurement instrument using two photoelastic modulators," Opt. Eng. 41, 981-987 (2002).
    [CrossRef]
  36. J. A. Quiroga and A. González-Cano, "Phase measuring algorithm for extraction of isochromatics of photoelastic fringe patterns," Appl. Opt. 36, 8397-8402 (1997).
    [CrossRef]

2005 (1)

2004 (1)

2003 (1)

2002 (7)

2001 (2)

2000 (3)

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

J. M. Bueno, "Measurement of parameters of polarization in the living human eye using imaging polarimetry," Vision Res. 40, 3791-3799 (2000).
[CrossRef] [PubMed]

D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (3)

1995 (1)

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

1994 (1)

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

1993 (1)

C. Quan, P. Bryanston-Cross, and T. Judge, "Photoelasticity stress analysis using carrier fringe and FFT techniques," Opt. Lasers Eng. 18, 79-108 (1993).
[CrossRef]

1985 (1)

1982 (1)

1981 (1)

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

1980 (1)

1979 (1)

1978 (1)

1975 (1)

1965 (1)

W. L. Bond, "Measurement of the refractive indices of several crystals," J. Appl. Phys. 36, 1674-1677 (1965).
[CrossRef]

Artal, P.

Azzam, R. M. A.

Baba, J. S.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992).

Bigio, I. J.

Bille, J. F.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Bond, W. L.

W. L. Bond, "Measurement of the refractive indices of several crystals," J. Appl. Phys. 36, 1674-1677 (1965).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Bottinger, J. R.

Bryanston-Cross, P.

C. Quan, P. Bryanston-Cross, and T. Judge, "Photoelasticity stress analysis using carrier fringe and FFT techniques," Opt. Lasers Eng. 18, 79-108 (1993).
[CrossRef]

Bueno, J.

Bueno, J. M.

J. M. Bueno and M. C. W. Campbell, "Confocal scanning laser ophthalmoscopy improvement by use of Mueller-matrix polarimetry," Opt. Lett. 27, 830-832 (2002).
[CrossRef]

J. M. Bueno, "Measurement of parameters of polarization in the living human eye using imaging polarimetry," Vision Res. 40, 3791-3799 (2000).
[CrossRef] [PubMed]

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

J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Lett. 24, 64-66 (1999).
[CrossRef]

Burk, R. O. W.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Cameron, B. D.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Campbell, M. C. W.

Chipman, R. A.

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

R. A. Chipman, "Polarimetry," in Handbook of Optics, 2nd ed. M.Bass, ed. (McGraw-Hill, 1995) Vol. 2, Chap. 22.

Chung, J.-R.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Coté, G. L.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

De Martino, A.

DeLaughter, A. H.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Delplancke, F.

Drevillon, B.

Drobczynski, S.

Eick, A. A.

Fercher, A. F.

Fischer, J. P.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Freyer, J. P.

Fry, E. S.

Goelz, S.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Gomes, J. F. S.

J. F. S. Gomes, "Photoelasticity" in Optical Metrology, O.D. D.Soares, ed. (Martinus Nijhoff, 1987).

González-Cano, A.

Götzinger, E.

Greenfield, D. S.

D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
[CrossRef] [PubMed]

Griffiths, C. O.

Hielscher, A. H.

Hitzenberger, C. K.

Holcomb, D. E.

Huang, X.-R.

D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
[CrossRef] [PubMed]

Ina, H.

Izatt, J. A.

Jaronski, J.

Jellison, G. E.

Jiao, S.

Judge, T.

C. Quan, P. Bryanston-Cross, and T. Judge, "Photoelasticity stress analysis using carrier fringe and FFT techniques," Opt. Lasers Eng. 18, 79-108 (1993).
[CrossRef]

Kaneko, T.

Kasprzak, H.

Knighton, R. W.

D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
[CrossRef] [PubMed]

Kobayashi, S.

Kozak, J. A.

Laude-Boulesteix, B.

Major, R. W.

Modine, F. A.

Mourant, J. R.

Oka, K.

Otani, Y.

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

Pelz, B.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

Pircher, M.

Quan, C.

C. Quan, P. Bryanston-Cross, and T. Judge, "Photoelasticity stress analysis using carrier fringe and FFT techniques," Opt. Lasers Eng. 18, 79-108 (1993).
[CrossRef]

Quiroga, J. A.

Rollinsm, A. M.

Roth, J. E.

Rouleau, C. M.

Schwartz, L.

Shen, D.

Shimada, T.

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

Sonder, E.

Sticker, M.

Takeda, M.

Thompson, R. C.

Umeda, N.

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

van Blokland, G. J.

Vargas-Martín, F.

Walraven, R.

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

Wang, B. L.

B. L. Wang, "Linear birefringence measurement instrument using two photoelastic modulators," Opt. Eng. 41, 981-987 (2002).
[CrossRef]

Wang, L. V.

Weinreb, R. N.

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Visual Sci. 43, 2221-2228 (2002).

Weschenmoser, C.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Wong, C. F.

Yazdanfar, S.

Yoshizawa, T.

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

Zhou, Q.

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Visual Sci. 43, 2221-2228 (2002).

Am. J. Ophthalmol. (1)

D. S. Greenfield, R. W. Knighton, and X.-R. Huang, "Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry," Am. J. Ophthalmol. 129, 715-722 (2000).
[CrossRef] [PubMed]

Appl. Opt. (10)

F. A. Modine, R. W. Major, and E. Sonder, "High frequency polarization modulation method for measuring birefringence," Appl. Opt. 14, 757-760 (1975).
[CrossRef] [PubMed]

C. F. Wong, "Birefringence measurement using a photoelastic modulator," Appl. Opt. 18, 3996-3999 (1979).
[CrossRef] [PubMed]

R. C. Thompson, J. R. Bottinger, and E. S. Fry, "Measurement of polarized light interactions via the Mueller matrix," Appl. Opt. 19, 1323-1332 (1980).
[CrossRef] [PubMed]

J. A. Quiroga and A. González-Cano, "Phase measuring algorithm for extraction of isochromatics of photoelastic fringe patterns," Appl. Opt. 36, 8397-8402 (1997).
[CrossRef]

F. Delplancke, "Automated high-speed Mueller matrix scatterometer," Appl. Opt. 36, 5388-5395 (1997).
[CrossRef] [PubMed]

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

J. Bueno and F. Vargas-Martín, "Measurements of the corneal birefringence with a liquid-crystal imaging polariscope," Appl. Opt. 41, 116-124 (2002).
[CrossRef] [PubMed]

G. E. Jellison, Jr., C. O. Griffiths, D. E. Holcomb, and C. M. Rouleau, "Transmission two-modulator generalized ellipsometry measurements," Appl. Opt. 41, 6555-6566 (2002).
[CrossRef] [PubMed]

B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, "Mueller polarimetric imaging system with liquid crystals," Appl. Opt. 43, 2824-2832 (2004).
[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]

Invest. Ophthalmol. Visual Sci. (1)

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Visual Sci. 43, 2221-2228 (2002).

J. Appl. Phys. (1)

W. L. Bond, "Measurement of the refractive indices of several crystals," J. Appl. Phys. 36, 1674-1677 (1965).
[CrossRef]

J. Biomed. Opt. (1)

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

J. Opt. A (1)

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. (1)

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

Opt. Eng. (4)

B. L. Wang, "Linear birefringence measurement instrument using two photoelastic modulators," Opt. Eng. 41, 981-987 (2002).
[CrossRef]

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

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

C. Quan, P. Bryanston-Cross, and T. Judge, "Photoelasticity stress analysis using carrier fringe and FFT techniques," Opt. Lasers Eng. 18, 79-108 (1993).
[CrossRef]

Opt. Lett. (5)

Vision Res. (1)

J. M. Bueno, "Measurement of parameters of polarization in the living human eye using imaging polarimetry," Vision Res. 40, 3791-3799 (2000).
[CrossRef] [PubMed]

Other (5)

J. F. S. Gomes, "Photoelasticity" in Optical Metrology, O.D. D.Soares, ed. (Martinus Nijhoff, 1987).

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, "In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer," in Lasers in Ophthalmology IV, R.Birngruber, A.F.Fercher, and P.Sourdille, eds., Proc. SPIE 2930,92-101 (1996).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

R. A. Chipman, "Polarimetry," in Handbook of Optics, 2nd ed. M.Bass, ed. (McGraw-Hill, 1995) Vol. 2, Chap. 22.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the optical system. [PSG], polarization state generator; [OB], examined object; [W], Wollaston prism; [A], analyzer; [P], polarizer; [QWP], quarter-wave plate; [LC], LC cell; LCVR, liquid-crystal variable retarder.

Fig. 2
Fig. 2

Images corresponding to the two independent polarization states (left, linear; right, circular) produced by PSG-1 without an object in the system. Size is 1.5   mm × 1.5   mm and gray level ranges from 0 (black) to 255 (white).

Fig. 3
Fig. 3

Intensity signal registered during the calibration of the LCVR. Solid and dashed curves correspond to crossed and parallel linear polarizers, respectively.

Fig. 4
Fig. 4

Polarimetric fringe images for a sample consisting of a QWP with azimuth at 30 ° , registered with the experimental configuration PSG-1. Left, linear polarization; right, circular polarization. Size and gray levels are the same as in Fig. 2.

Fig. 5
Fig. 5

Distribution of azimuth (left) and retardation (right) computed from images in Fig. 4. The size of each image is also 1.5   mm × 1.5   mm . The gray scales are shown on the right. Units are degrees.

Fig. 6
Fig. 6

Measured versus nominal azimuth using PSG-1 for a QWP used as a test object. Standard deviations are within the symbols.

Fig. 7
Fig. 7

Averaged values of azimuth (black symbols) and retardation (white symbols) for a QWP using PSG-1. Solid lines represent the nominal values.

Fig. 8
Fig. 8

Fringe images of a QWP test at 20° for linear (left) and circular (right) incoming polarizations produced by PSG-2. Gray levels and size are the same as those in Fig. 2.

Fig. 9
Fig. 9

Maps of of azimuth (left) and retardation (right) obtained from fringe images in Fig. 8. Units are degrees. The gray scales are shown on the right for each map.

Fig. 10
Fig. 10

Measured retardation (white symbols) and azimuth (black symbols) versus nominal azimuth for a QWP using PSG-2. Each symbol is an averaged value computed from three different series. For a better comparison, lines indicate the expected values. Some data are missing due to technical problems.

Fig. 11
Fig. 11

Maps of azimuth (left panel) and retardation (right panel) for a LC cell. Mean values for these maps were 43.96 ° ± 2.6 ° for the azimuth, and 19.6 ° ± 1.2 ° for the retardation.

Fig. 12
Fig. 12

Distribution of azimuth (left panels) and retardation (right panels) for a photoelastic sample (upper panels) and an in vitro porcine cornea (lower panels). Configuration PSG-1 was used to produce the two required polarization states.

Equations (12)

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[ S CCD ] = [ A ] [ W ] [ OB ] [ S PSG ] ,
I 1 = T { 1 + sin 2 α cos 2 α ( 1 cos δ ) cos [ 2 π ƒ 0 ( x + k ) ] + sin 2 α sin δ sin [ 2 π ƒ 0 ( x + k ) ] } ,
I 2 = T { 1 + cos 2 α sin δ cos [ 2 π ƒ 0 ( x + k ) ] + cos δ sin [ 2 π ƒ 0 ( x + k ) ] } .
Im ( c 1 ) = T [ sin ( 2 π ƒ 0 k ) sin 4 α sin 2 ( δ / 2 ) cos ( 2 π ƒ 0 k ) sin 2 α sin δ ] ,
Re ( c 1 ) = T [ sin ( 2 π ƒ 0 k ) sin 2 α sin δ + cos ( 2 π ƒ 0 k ) sin 4 α sin 2 ( δ / 2 ) ] ,
Im ( c 2 ) = T [ sin ( 2 π ƒ 0 k ) cos 2 α sin δ cos ( 2 π ƒ 0 k ) cos δ ] ,
Re ( c 2 ) = T [ sin ( 2 π ƒ 0 k ) cos δ + cos ( 2 π ƒ 0 k ) cos 2 α sin δ ] .
α = 1 2 arctan [ Im ( c 1 ) Re ( c 2 ) ] ,
δ = arctan [ Re ( c 2 ) Im ( c 2 ) cos 2 α ] .
δ = arctan [ Im ( c 1 ) Im ( c 2 ) sin 2 α ] .
I ( δ LC ) = I p ( 1 sin 2 δ LC 2 ) ,
I ( δ LC ) = I p sin 2 δ LC 2 .

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