Abstract

A technique is proposed for measuring the linear birefringence and linear diattenuation of an optical sample using a polarimeter. In the proposed approach, the principal axis angle (α), phase retardance (β), diattenuation axis angle (θd), and diattenuation (D) are derived using an analytical model based on the Mueller matrix formulation and the Stokes parameters. The dynamic measurement ranges of the four parameters are shown to be α = 0~180°, β = 0~180°, θd = 0~180°, and D = 0~1, respectively. Thus, full-range measurements are possible for all parameters other than β. In this study, the proposed methodology does not require the principal birefringence axes and diattenuation axes to be aligned. In addition, the linear birefringence and linear diattenuation properties are decoupled within the analytical model, and thus the birefringence properties of the sample can be solved directly without any prior knowledge of the diattenuation parameters. Also, the characteristic parameters in the baked polarizer with linear birefringence are successfully extracted from an optically equivalent model and proved by the respective simulation and experiment introduced in this study.

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References

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  1. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  2. J. P. McGuire, Jr., “Image formation and analysis in optical systems with polarization aberrations,” Ph.D. thesis, University of Alabama in Huntsville, (1990).
  3. R. A. Chipman, Handbook of Optics (McGraw-Hill, 1995), Vol. 2, Chap. 22.
  4. D. B. Chenault and R. A. Chipman, ““Linear diattenuation and retardation measurements in an ir-spectropolarimeter,” Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray 1317, 263–278 (1990).
  5. D. B. Chenault and R. A. Chipman, “Infrared birefringence spectra for cadmium-sulfide and cadmium selenide,” Opt. Lett. 17, 4223–4227 (1992).
  6. D. B. Chenault and R. A. Chipman, “Measurements of linear diattenuation and linear retardation spectra with a rotating sample spectropolarimeter,” Appl. Opt. 32(19), 3513–3519 (1993).
    [CrossRef] [PubMed]
  7. J. M. Bueno and P. Artal, “Diattenuation of the human eye at the fovea,” Invest. Ophthalmol. Vis. Sci. 46, ••• (2005).
  8. J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55(4), 849–859 (2008).
    [CrossRef]
  9. M. Todorović, S. L. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
    [CrossRef] [PubMed]
  10. X. R. Huang and R. W. Knighton, “Diattenuation and polarization preservation of retinal nerve fiber layer reflectance,” Appl. Opt. 42(28), 5737–5743 (2003).
    [CrossRef] [PubMed]
  11. D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
    [CrossRef]
  12. A. L. Campillo and J. W. P. Hsu, “Near-field scanning optical microscope studies of the anisotropic stress variations in patterned SiN membranes,” J. Appl. Phys. 91(2), 646–651 (2002).
    [CrossRef]
  13. M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
    [CrossRef] [PubMed]
  14. L. S. Goldner, M. J. Fasolka, S. Nougier, H. P. Nguyen, G. W. Bryant, J. Hwang, K. D. Weston, K. L. Beers, A. Urbas, and E. L. Thomas, “Fourier analysis near-field polarimetry for measurement of local optical properties of thin films,” Appl. Opt. 42(19), 3864–3881 (2003).
    [CrossRef] [PubMed]
  15. L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
    [CrossRef]
  16. L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
    [CrossRef]
  17. L. S. Srinath and A. V. S. S. S. R. Sarma, “Determination of the optically equivalent model in three-dimensional photoelasticity,” Exp. Mech. 14(3), 118–122 (1974).
    [CrossRef]
  18. R. A. Tomlinson and E. A. Patterson, “The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity,” Exp. Mech. 42(1), 43–50 (2002).
    [CrossRef]
  19. H. Hurwitz and R. C. Jones, “A new calculus for the treatment of optical systems-II: proof of three general equivalent theorems,” J. Opt. Soc. Am. 31, 493–499 (1941).
  20. S. T. Tang and H. S. Kwok, “Characteristic parameters of liquid crystal cells and their measurements,” J. Disp. Techno. 2(1), 26–31 (2006).
    [CrossRef]
  21. http://www.meadowlark.com
  22. I. C. Khoo, and F. Simoni, Physics of Liquid Crystalline Materials (Gorden and Breach Science Publishers, 1991), Chap. 13.
  23. H. Dong, Y. D. Gong, V. Paulose, P. Shum, and M. Olivo, “Effect of input states of polarization on the measurement error of Mueller matrix in a system having small polarization-dependent loss or gain,” Opt. Express 17(15), 13017–13028 (2009).
    [CrossRef] [PubMed]
  24. L. Giudicotti and M. Brombin, “Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter,” Appl. Opt. 46(14), 2638–2648 (2007).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55(4), 849–859 (2008).
[CrossRef]

2007 (1)

2006 (1)

S. T. Tang and H. S. Kwok, “Characteristic parameters of liquid crystal cells and their measurements,” J. Disp. Techno. 2(1), 26–31 (2006).
[CrossRef]

2005 (2)

J. M. Bueno and P. Artal, “Diattenuation of the human eye at the fovea,” Invest. Ophthalmol. Vis. Sci. 46, ••• (2005).

L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
[CrossRef]

2004 (2)

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

M. Todorović, S. L. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

2003 (3)

2002 (2)

R. A. Tomlinson and E. A. Patterson, “The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity,” Exp. Mech. 42(1), 43–50 (2002).
[CrossRef]

A. L. Campillo and J. W. P. Hsu, “Near-field scanning optical microscope studies of the anisotropic stress variations in patterned SiN membranes,” J. Appl. Phys. 91(2), 646–651 (2002).
[CrossRef]

1996 (1)

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

1993 (1)

1992 (1)

D. B. Chenault and R. A. Chipman, “Infrared birefringence spectra for cadmium-sulfide and cadmium selenide,” Opt. Lett. 17, 4223–4227 (1992).

1990 (1)

D. B. Chenault and R. A. Chipman, ““Linear diattenuation and retardation measurements in an ir-spectropolarimeter,” Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray 1317, 263–278 (1990).

1989 (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

1974 (1)

L. S. Srinath and A. V. S. S. S. R. Sarma, “Determination of the optically equivalent model in three-dimensional photoelasticity,” Exp. Mech. 14(3), 118–122 (1974).
[CrossRef]

1941 (1)

Artal, P.

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55(4), 849–859 (2008).
[CrossRef]

J. M. Bueno and P. Artal, “Diattenuation of the human eye at the fovea,” Invest. Ophthalmol. Vis. Sci. 46, ••• (2005).

Barbara, P. F.

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

Beers, K. L.

Brombin, M.

Bryant, G. W.

Bueno, J. M.

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55(4), 849–859 (2008).
[CrossRef]

J. M. Bueno and P. Artal, “Diattenuation of the human eye at the fovea,” Invest. Ophthalmol. Vis. Sci. 46, ••• (2005).

Campillo, A. L.

A. L. Campillo and J. W. P. Hsu, “Near-field scanning optical microscope studies of the anisotropic stress variations in patterned SiN membranes,” J. Appl. Phys. 91(2), 646–651 (2002).
[CrossRef]

Chenault, D. B.

D. B. Chenault and R. A. Chipman, “Measurements of linear diattenuation and linear retardation spectra with a rotating sample spectropolarimeter,” Appl. Opt. 32(19), 3513–3519 (1993).
[CrossRef] [PubMed]

D. B. Chenault and R. A. Chipman, “Infrared birefringence spectra for cadmium-sulfide and cadmium selenide,” Opt. Lett. 17, 4223–4227 (1992).

D. B. Chenault and R. A. Chipman, ““Linear diattenuation and retardation measurements in an ir-spectropolarimeter,” Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray 1317, 263–278 (1990).

Chipman, R. A.

D. B. Chenault and R. A. Chipman, “Measurements of linear diattenuation and linear retardation spectra with a rotating sample spectropolarimeter,” Appl. Opt. 32(19), 3513–3519 (1993).
[CrossRef] [PubMed]

D. B. Chenault and R. A. Chipman, “Infrared birefringence spectra for cadmium-sulfide and cadmium selenide,” Opt. Lett. 17, 4223–4227 (1992).

D. B. Chenault and R. A. Chipman, ““Linear diattenuation and retardation measurements in an ir-spectropolarimeter,” Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray 1317, 263–278 (1990).

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

DeRege, P.

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

Dong, H.

Douglas, J. F.

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

Fasolka, M. J.

L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
[CrossRef]

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

L. S. Goldner, M. J. Fasolka, S. Nougier, H. P. Nguyen, G. W. Bryant, J. Hwang, K. D. Weston, K. L. Beers, A. Urbas, and E. L. Thomas, “Fourier analysis near-field polarimetry for measurement of local optical properties of thin films,” Appl. Opt. 42(19), 3864–3881 (2003).
[CrossRef] [PubMed]

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

Giudicotti, L.

Goldie, S. N.

L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
[CrossRef]

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

Goldner, L. S.

L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
[CrossRef]

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

L. S. Goldner, M. J. Fasolka, S. Nougier, H. P. Nguyen, G. W. Bryant, J. Hwang, K. D. Weston, K. L. Beers, A. Urbas, and E. L. Thomas, “Fourier analysis near-field polarimetry for measurement of local optical properties of thin films,” Appl. Opt. 42(19), 3864–3881 (2003).
[CrossRef] [PubMed]

Gong, Y. D.

Higgins, D. A.

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

Hsu, J. W. P.

A. L. Campillo and J. W. P. Hsu, “Near-field scanning optical microscope studies of the anisotropic stress variations in patterned SiN membranes,” J. Appl. Phys. 91(2), 646–651 (2002).
[CrossRef]

Huang, X. R.

Hurwitz, H.

Hwang, J.

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

L. S. Goldner, M. J. Fasolka, S. Nougier, H. P. Nguyen, G. W. Bryant, J. Hwang, K. D. Weston, K. L. Beers, A. Urbas, and E. L. Thomas, “Fourier analysis near-field polarimetry for measurement of local optical properties of thin films,” Appl. Opt. 42(19), 3864–3881 (2003).
[CrossRef] [PubMed]

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

Jiao, S. L.

Jones, R. C.

Kerimo, J.

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

Knighton, R. W.

Kwok, H. S.

S. T. Tang and H. S. Kwok, “Characteristic parameters of liquid crystal cells and their measurements,” J. Disp. Techno. 2(1), 26–31 (2006).
[CrossRef]

Nguyen, H. P.

Nougier, S.

Olivo, M.

Patterson, E. A.

R. A. Tomlinson and E. A. Patterson, “The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity,” Exp. Mech. 42(1), 43–50 (2002).
[CrossRef]

Paulose, V.

Renaldo, F.

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

Sarma, A. V. S. S. S. R.

L. S. Srinath and A. V. S. S. S. R. Sarma, “Determination of the optically equivalent model in three-dimensional photoelasticity,” Exp. Mech. 14(3), 118–122 (1974).
[CrossRef]

Shum, P.

Srinath, L. S.

L. S. Srinath and A. V. S. S. S. R. Sarma, “Determination of the optically equivalent model in three-dimensional photoelasticity,” Exp. Mech. 14(3), 118–122 (1974).
[CrossRef]

Stoica, G.

Swager, T.

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

Tang, S. T.

S. T. Tang and H. S. Kwok, “Characteristic parameters of liquid crystal cells and their measurements,” J. Disp. Techno. 2(1), 26–31 (2006).
[CrossRef]

Thomas, E. L.

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

L. S. Goldner, M. J. Fasolka, S. Nougier, H. P. Nguyen, G. W. Bryant, J. Hwang, K. D. Weston, K. L. Beers, A. Urbas, and E. L. Thomas, “Fourier analysis near-field polarimetry for measurement of local optical properties of thin films,” Appl. Opt. 42(19), 3864–3881 (2003).
[CrossRef] [PubMed]

Todorovic, M.

Tomlinson, R. A.

R. A. Tomlinson and E. A. Patterson, “The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity,” Exp. Mech. 42(1), 43–50 (2002).
[CrossRef]

Urbas, A.

Urbas, A. M.

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

VandenBout, D. A.

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

Wang, L. V.

Weston, K. D.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

L. S. Goldner, S. N. Goldie, M. J. Fasolka, F. Renaldo, J. Hwang, and J. F. Douglas, “Near-field polarimetric characterization of polymer crystallites,” Appl. Phys. Lett. 85(8), 1338–1340 (2004).
[CrossRef]

Applications of Scanned Probe Microscopy to Polymers (1)

L. S. Goldner, M. J. Fasolka, and S. N. Goldie, “Measurement of the local diattenuation and retardance of thin polymer films using near-field polarimetry,” Applications of Scanned Probe Microscopy to Polymers 897, 65–84 (2005).
[CrossRef]

Exp. Mech. (2)

L. S. Srinath and A. V. S. S. S. R. Sarma, “Determination of the optically equivalent model in three-dimensional photoelasticity,” Exp. Mech. 14(3), 118–122 (1974).
[CrossRef]

R. A. Tomlinson and E. A. Patterson, “The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity,” Exp. Mech. 42(1), 43–50 (2002).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (1)

J. M. Bueno and P. Artal, “Diattenuation of the human eye at the fovea,” Invest. Ophthalmol. Vis. Sci. 46, ••• (2005).

J. Appl. Phys. (1)

A. L. Campillo and J. W. P. Hsu, “Near-field scanning optical microscope studies of the anisotropic stress variations in patterned SiN membranes,” J. Appl. Phys. 91(2), 646–651 (2002).
[CrossRef]

J. Disp. Techno. (1)

S. T. Tang and H. S. Kwok, “Characteristic parameters of liquid crystal cells and their measurements,” J. Disp. Techno. 2(1), 26–31 (2006).
[CrossRef]

J. Mod. Opt. (1)

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55(4), 849–859 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

D. A. Higgins, D. A. VandenBout, J. Kerimo, and P. F. Barbara, “Polarization-modulation near-field scanning optical microscopy of mesostructured materials,” J. Phys. Chem. 100(32), 13794–13803 (1996).
[CrossRef]

Opt. Eng. (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. J. Fasolka, L. S. Goldner, J. Hwang, A. M. Urbas, P. DeRege, T. Swager, and E. L. Thomas, “Measuring local optical properties: near-field polarimetry of photonic block copolymer morphology,” Phys. Rev. Lett. 90(1), 016107 (2003).
[CrossRef] [PubMed]

Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray (1)

D. B. Chenault and R. A. Chipman, ““Linear diattenuation and retardation measurements in an ir-spectropolarimeter,” Polarimetry: Radar, Infrared, Visible, Ultraviolet, And X-Ray 1317, 263–278 (1990).

Other (4)

J. P. McGuire, Jr., “Image formation and analysis in optical systems with polarization aberrations,” Ph.D. thesis, University of Alabama in Huntsville, (1990).

R. A. Chipman, Handbook of Optics (McGraw-Hill, 1995), Vol. 2, Chap. 22.

http://www.meadowlark.com

I. C. Khoo, and F. Simoni, Physics of Liquid Crystalline Materials (Gorden and Breach Science Publishers, 1991), Chap. 13.

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Figures (16)

Fig. 1
Fig. 1

Correlation between input value of principal axis angle (α) and extracted value of principal axis angle (α’).

Fig. 2
Fig. 2

Correlation between input value of phase retardance (β) and extracted value of phase retardance (β’).

Fig. 3
Fig. 3

Correlation between input value of diattenuation axis angle (θ d ) and extracted value of diattenuation axis angle (θ d ’).

Fig. 4
Fig. 4

Correlation between input value of diattenuation (D) and extracted value of diattenuation (D’).

Fig. 5
Fig. 5

(a) Correlation between α and α’. (b) Correlation between β and β’. (c) Correlation between θ d and θ d ’. (d) Correlation between D and D’.

Fig. 6
Fig. 6

(a) Correlation between α and α’. (b) Correlation between β and β’. (c) Correlation between θ d and θ d ’. (d) Correlation between D and D’.

Fig. 7
Fig. 7

(a) Correlation between α and α’. (b) Correlation between β and β’. (c) Correlation between θ d and θ d ’. (d) Correlation between D and D’.

Fig. 8
Fig. 8

Schematic illustration of experimental measurement system.

Fig. 9
Fig. 9

Experimental results for birefringence properties of quarter-wave plate.

Fig. 10
Fig. 10

Experimental results for diattenuation properties of quarter-wave plate.

Fig. 11
Fig. 11

Experimental results obtained for birefringence properties of polarizer.

Fig. 12
Fig. 12

Experimental results obtained for diattenuation of polarizer.

Fig. 13
Fig. 13

Experimental results obtained for effective birefringence of baked polarizer.

Fig. 14
Fig. 14

Experimental results obtained for the effective diattenuation of baked polarizer.

Fig. 15
Fig. 15

The relation of measured S1n-S3n and simulated S1n-S3n when baked polarization’s diattenuation axis placed at 120 degrees (a) measured S1n and simulated S1n. (b) measured S2n and simulated S2n. (c) measured S3n and simulated S3n.

Fig. 16
Fig. 16

The relation of measured S1n-S3n and simulated S1n-S3n when baked polarization’s diattenuation axis placed at 150 degrees (a) measured S1n and simulated S1n. (b) measured S2n and simulated S2n. (c) measured S3n and simulated S3n.

Tables (5)

Tables Icon

Table 1 Experimental data obtained for the effective birefringence and diattenuation of baked polarizer.

Tables Icon

Table 2 The measurement and simulation of nine sets of normalized Stokes parameters when baked polarization’s diattenuation axis placed at 120 degrees.

Tables Icon

Table 3 The measurement and simulation of nine sets of normalized Stokes parameters when baked polarization’s diattenuation axis placed at 150 degrees.

Tables Icon

Table 4 Experimental results obtained for various optical samples with a composite sample in the first case.

Tables Icon

Table 5 Experimental results obtained for various optical samples with a composite sample in the second case.

Equations (37)

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S=[S0S1S2S3]=[Ix+IyIxIyI45oI45oIrcpIlcp]
S=[S0S1S2S3]=(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44)(S^0S^1S^2S^3)=MS^
Mlb=(10000cos(4α)sin2(β/2)+cos2(β/2)sin(4α)sin2(β/2)sin(2α)sin(β)0sin(4α)sin2(β/2)cos(4α)sin2(β/2)+cos2(β/2)cos(2α)sin(β)0sin(2α)sin(β)cos(2α)sin(β)cos(β))
Mld=((u+v)2cos(2θd)(uv)2sin(2θd)(uv)20cos(2θd)(uv)2(u+v)24+cos(4θd)(uv)24sin(4θd)(uv)240sin(2θd)(uv)2sin(4θd)(uv)24(u+v)24cos(4θd)(uv)240000uv)
D=uvu+v
Sc=[S0S1S2S3]c=[Mld][Mlb]S^c=(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44)(S^0S^1S^2S^3)c
m11=(u+v)2
m12=(cos(2θd)(uv)2)(cos(4α)sin2(β/2)+cos2(β/2))+(sin(2θd)(uv)2)(sin(4α)sin2(β/2))
m13=(cos(2θd)(uv)2)(sin(4α)sin2(β/2))+(sin(2θd)(uv)2)(cos(4α)sin2(β/2)+cos2(β/2))
m14=(cos(2θd)(uv)2)(sin(2α)sin(β))+(sin(2θd)(uv)2)(cos(2α)sin(β))
m21=cos(2θd)(uv)2
m22=((u+v)24+cos(4θd)(uv)24)(cos(4α)sin2(β/2)+cos2(β/2))+(sin(4θd)(uv)24)(sin(4α)sin2(β/2))
m23=((u+v)24+cos(4θd)(uv)24)(sin(4α)sin2(β/2))+(sin(4θd)(uv)24)(cos(4α)sin2(β/2)+cos2(β/2))
m24=((u+v)24+cos(4θd)(uv)24)(sin(2α)sin(β))+(sin(4θd)(uv)24)(cos(2α)sin(β))
m31=sin(2θd)(uv)2
m32=(sin(4θd)(uv)24)(cos(4α)sin2(β/2)+cos2(β/2))+((u+v)24cos(4θd)(uv)24)(sin(4α)sin2(β/2))
m33=(sin(4θd)(uv)24)(sin(4α)sin2(β/2))+((u+v)24cos(4θd)(uv)24)(cos(4α)sin2(β/2)+cos2(β/2))
m34=(sin(4θd)(uv)24)(sin(2α)sin(β))+((u+v)24cos(4θd)(uv)24)(cos(2α)sin(β))
m41=0
m42=uvsin(2α)sin(β)
m43=uvcos(2α)sin(β)
m44=uvcos(β)
S0=[m11+m12,m21+m22,m31+m32,m41+m42]
S45=[m11+m13,m21+m23,m31+m33,m41+m43]
SRHC=[m11+m14,m21+m24,m31+m34,m41+m44]
S0(S3)S45(S3)=m42m43=uvsin(2α)sin(β)uvcos(2α)sin(β)
2α=tan1(S0(S3)S45(S3))
S45(S3)SRHC(S3)=m43m44=uvcos(2α)sin(β)uvcos(β)
β=tan1(S45(S3)cos(2α)SRHC(S3))
S90=[m11m12,m21m22,m31m32,m41m42]
S135=[m11m13,m21m23,m31m33,m41m43]
S0(S0)+S90(S0)=2m11=(u+v)
S0(S1)+S90(S1)=2m21=cos(2θd)(uv)
S45(S2)+S135(S2)=2m31=sin(2θd)(uv)
2θd=tan1(S45(S2)+S135(S2)S0(S1)+S90(S1))
D=uvu+v=S0(S1)+S90(S1)cos(2θd)[S0(S0)+S90(S0)]
D=uvu+v=S45(S2)+S135(S2)sin(2θd)[S0(S0)+S90(S0)]

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