Abstract

A good understanding of the corneal birefringence properties is essential for polarimetric glucose monitoring in the aqueous humor of the eye. Therefore, we have measured complete 16-element Mueller matrices of single-pass transitions through nine porcine corneas in-vitro, spectrally resolved in the range 300…1000 nm. These ellipsometric measurements have been performed at several angles of incidence at the apex and partially at the periphery of the corneas. The Mueller matrices have been decomposed into linear birefringence, circular birefringence (i.e. optical rotation), depolarization, and diattenuation. We found considerable circular birefringence, strongly increasing with decreasing wavelength, for most corneas. Furthermore, the decomposition revealed significant dependence of the linear retardance (in nm) on the wavelength below 500 nm. These findings suggest that uniaxial and biaxial crystals are insufficient models for a general description of the corneal birefringence, especially in the blue and in the UV spectral range. The implications on spectral-polarimetric approaches for glucose monitoring in the eye (for diabetics) are discussed.

© 2016 Optical Society of America

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References

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  1. B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
    [Crossref] [PubMed]
  2. D. Brewster, “Experiments on the depolarization of light as exhibited by various mineral, animal and vegetable bodies, with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. Lond. 105(0), 29–53 (1815).
    [Crossref]
  3. W. His, Beiträge zur normalen und pathologischen Histologie der Cornea (Schweighauser'sche Sortimentsbuchhandlung, 1856).
  4. O. Wiener, Die Theorie des Mischkörpers für das Feld der stationären Strömung. Erste Abhandlung: Die Mittelwertsätze für Kraft, Polarisation und Energie (BG Teubner, 1912).
  5. D. M. Maurice, “The structure and transparency of the cornea,” J. Physiol. 136(2), 263–286 (1957).
    [Crossref] [PubMed]
  6. L. J. Bour, “Polarized light and the eye,” in Vision Optics and Instrumentation, W. N. Charman, ed. (CRC, 1991), pp. 310–325.
  7. G. P. Misson, “Birefringent properties of the human cornea in vivo: towards a new model of corneal structure,” PhD thesis, University of Warwick (2012).
  8. E. Reusch, “Untersuchung über Glimmercombinationen,” Ann. Phys. 214(12), 628–638 (1869).
    [Crossref]
  9. D. J. Donohue, B. J. Stoyanov, R. L. McCally, and R. A. Farrell, “Numerical modeling of the cornea’s lamellar structure and birefringence properties,” J. Opt. Soc. Am. A 12(7), 1425–1438 (1995).
    [Crossref] [PubMed]
  10. T. J. Wang and F. A. Bettelheim, “Comparative birefringence of cornea,” Comp. Biochem. Physiol. A 51(11A), 89–94 (1975).
    [Crossref] [PubMed]
  11. A. Stanworth and E. J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” J. Exp. Biol. 30(2), 160–163 (1953).
  12. L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981).
    [Crossref] [PubMed]
  13. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987).
    [Crossref] [PubMed]
  14. V. Louis-Dorr, K. Naoun, P. Allé, A.-M. Benoit, and A. Raspiller, “Linear dichroism of the cornea,” Appl. Opt. 43(7), 1515–1521 (2004).
    [Crossref] [PubMed]
  15. R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16(18), 13738–13751 (2008).
    [Crossref] [PubMed]
  16. R. A. Bone and G. Draper, “Optical anisotropy of the human cornea determined with a polarizing microscope,” Appl. Opt. 46(34), 8351–8357 (2007).
    [Crossref] [PubMed]
  17. G. P. Misson, “Circular polarization biomicroscopy: a method for determining human corneal stromal lamellar organization in vivo,” Ophthalmic Physiol. Opt. 27(3), 256–264 (2007).
    [Crossref] [PubMed]
  18. G. P. Misson, “The theory and implications of the biaxial model of corneal birefringence,” Ophthalmic Physiol. Opt. 30(6), 834–846 (2010).
    [Crossref] [PubMed]
  19. E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
    [Crossref] [PubMed]
  20. F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
    [Crossref] [PubMed]
  21. R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
    [PubMed]
  22. H. B. Brink and G. J. van Blokland, “Birefringence of the human foveal area assessed in vivo with Mueller-matrix ellipsometry,” J. Opt. Soc. Am. A 5(1), 49–57 (1988).
    [Crossref] [PubMed]
  23. K. Irsch, B. Gramatikov, Y.-K. Wu, and D. Guyton, “Modeling and minimizing interference from corneal birefringence in retinal birefringence scanning for foveal fixation detection,” Biomed. Opt. Express 2(7), 1955–1968 (2011).
    [Crossref] [PubMed]
  24. B. K. Pierscionek and R. A. Weale, “Investigation of the polarization optics of the living human cornea and lens with Purkinje images,” Appl. Opt. 37(28), 6845–6851 (1998).
    [Crossref] [PubMed]
  25. J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21(5), 384–392 (2001).
    [Crossref] [PubMed]
  26. J. M. Bueno and F. Vargas-Martín, “Measurements of the corneal birefringence with a liquid-crystal imaging polariscope,” Appl. Opt. 41(1), 116–124 (2002).
    [Crossref] [PubMed]
  27. R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).
  28. J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
    [Crossref] [PubMed]
  29. C. A. Browne and F. W. Zerban, “Physical and chemical methods of sugar analysis: a practical and descriptive treatise for use in research, technical, and control laboratories,” 3rd ed., New York: J. Wiley & sons, inc., London: Chapman & Hall, 263–273 (1941).
  30. R. Engbert and K. Mergenthaler, “Microsaccades are triggered by low retinal image slip,” Proc. Natl. Acad. Sci. U.S.A. 103(18), 7192–7197 (2006).
    [Crossref] [PubMed]
  31. G. Purvinis, B. D. Cameron, and D. M. Altrogge, “Noninvasive polarimetric-based glucose monitoring: an in vivo study,” J. Diabetes Sci. Technol. 5(2), 380–387 (2011).
    [Crossref] [PubMed]
  32. C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
    [Crossref] [PubMed]
  33. B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
    [Crossref] [PubMed]
  34. H. Fujiwara, Spectroscopic ellipsometry: principles and applications (John Wiley & Sons., 2007).
  35. S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” in 33rd Annual Technical Symposium, (International Society for Optics and Photonics, 1990), pp. 177–187.
  36. S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13(5), 1106–1113 (1996).
    [Crossref]
  37. D. S. Greenfield and R. W. Knighton, “Stability of corneal polarization axis measurements for scanning laser polarimetry,” Ophthalmology 108(6), 1065–1069 (2001).
    [Crossref] [PubMed]
  38. K. Irsch and A. A. Shah, “Birefringence of the central cornea in children assessed with scanning laser polarimetry,” J. Biomed. Opt. 17(8), 086001 (2012).
    [Crossref] [PubMed]
  39. R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
    [Crossref] [PubMed]
  40. J. Humlicek, “Polarized Light and Ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, ed. (William Andrew, 2005).
  41. M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
    [Crossref] [PubMed]
  42. W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
    [Crossref] [PubMed]
  43. G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
    [PubMed]
  44. B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
    [Crossref] [PubMed]

2013 (1)

B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
[Crossref] [PubMed]

2012 (2)

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

K. Irsch and A. A. Shah, “Birefringence of the central cornea in children assessed with scanning laser polarimetry,” J. Biomed. Opt. 17(8), 086001 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (3)

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

G. P. Misson, “The theory and implications of the biaxial model of corneal birefringence,” Ophthalmic Physiol. Opt. 30(6), 834–846 (2010).
[Crossref] [PubMed]

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

2008 (1)

2007 (2)

R. A. Bone and G. Draper, “Optical anisotropy of the human cornea determined with a polarizing microscope,” Appl. Opt. 46(34), 8351–8357 (2007).
[Crossref] [PubMed]

G. P. Misson, “Circular polarization biomicroscopy: a method for determining human corneal stromal lamellar organization in vivo,” Ophthalmic Physiol. Opt. 27(3), 256–264 (2007).
[Crossref] [PubMed]

2006 (1)

R. Engbert and K. Mergenthaler, “Microsaccades are triggered by low retinal image slip,” Proc. Natl. Acad. Sci. U.S.A. 103(18), 7192–7197 (2006).
[Crossref] [PubMed]

2004 (3)

V. Louis-Dorr, K. Naoun, P. Allé, A.-M. Benoit, and A. Raspiller, “Linear dichroism of the cornea,” Appl. Opt. 43(7), 1515–1521 (2004).
[Crossref] [PubMed]

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[Crossref] [PubMed]

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

2002 (4)

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

J. M. Bueno and F. Vargas-Martín, “Measurements of the corneal birefringence with a liquid-crystal imaging polariscope,” Appl. Opt. 41(1), 116–124 (2002).
[Crossref] [PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

2001 (3)

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21(5), 384–392 (2001).
[Crossref] [PubMed]

D. S. Greenfield and R. W. Knighton, “Stability of corneal polarization axis measurements for scanning laser polarimetry,” Ophthalmology 108(6), 1065–1069 (2001).
[Crossref] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
[Crossref] [PubMed]

1998 (1)

1997 (1)

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

1996 (1)

1995 (1)

1988 (1)

1987 (1)

1982 (2)

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
[Crossref] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
[Crossref] [PubMed]

1981 (1)

L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981).
[Crossref] [PubMed]

1975 (1)

T. J. Wang and F. A. Bettelheim, “Comparative birefringence of cornea,” Comp. Biochem. Physiol. A 51(11A), 89–94 (1975).
[Crossref] [PubMed]

1957 (1)

D. M. Maurice, “The structure and transparency of the cornea,” J. Physiol. 136(2), 263–286 (1957).
[Crossref] [PubMed]

1953 (1)

A. Stanworth and E. J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” J. Exp. Biol. 30(2), 160–163 (1953).

1869 (1)

E. Reusch, “Untersuchung über Glimmercombinationen,” Ann. Phys. 214(12), 628–638 (1869).
[Crossref]

1815 (1)

D. Brewster, “Experiments on the depolarization of light as exhibited by various mineral, animal and vegetable bodies, with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. Lond. 105(0), 29–53 (1815).
[Crossref]

Adams, R. L.

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
[Crossref] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
[Crossref] [PubMed]

Allé, P.

Altrogge, D. M.

G. Purvinis, B. D. Cameron, and D. M. Altrogge, “Noninvasive polarimetric-based glucose monitoring: an in vivo study,” J. Diabetes Sci. Technol. 5(2), 380–387 (2011).
[Crossref] [PubMed]

Ansari, R. R.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[Crossref] [PubMed]

Arce-Diego, J. L.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

Aycan, K.

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Baba, J. S.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
[Crossref] [PubMed]

Baumann, B.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

Benoit, A.-M.

Bettelheim, F. A.

T. J. Wang and F. A. Bettelheim, “Comparative birefringence of cornea,” Comp. Biochem. Physiol. A 51(11A), 89–94 (1975).
[Crossref] [PubMed]

Bhattacharya, S. K.

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

Böckle, S.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[Crossref] [PubMed]

Bone, R. A.

Bour, L. J.

L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981).
[Crossref] [PubMed]

Bozkir, G.

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Bozkir, M.

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Brewster, D.

D. Brewster, “Experiments on the depolarization of light as exhibited by various mineral, animal and vegetable bodies, with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. Lond. 105(0), 29–53 (1815).
[Crossref]

Brink, H. B.

Bueno, J. M.

J. M. Bueno and F. Vargas-Martín, “Measurements of the corneal birefringence with a liquid-crystal imaging polariscope,” Appl. Opt. 41(1), 116–124 (2002).
[Crossref] [PubMed]

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21(5), 384–392 (2001).
[Crossref] [PubMed]

Cameron, B. D.

G. Purvinis, B. D. Cameron, and D. M. Altrogge, “Noninvasive polarimetric-based glucose monitoring: an in vivo study,” J. Diabetes Sci. Technol. 5(2), 380–387 (2011).
[Crossref] [PubMed]

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
[Crossref] [PubMed]

Cavuoto, L. A.

Chipman, R. A.

Cloude, S. R.

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” in 33rd Annual Technical Symposium, (International Society for Optics and Photonics, 1990), pp. 177–187.

Coté, G. L.

B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
[Crossref] [PubMed]

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
[Crossref] [PubMed]

Dogan, H.

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Donohue, D. J.

Draper, G.

Engbert, R.

R. Engbert and K. Mergenthaler, “Microsaccades are triggered by low retinal image slip,” Proc. Natl. Acad. Sci. U.S.A. 103(18), 7192–7197 (2006).
[Crossref] [PubMed]

Fanjul-Vélez, F.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

Farrell, R. A.

Fercher, A. F.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

Goel, M.

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

Götzinger, E.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

Gramatikov, B.

Greenfield, D. S.

D. S. Greenfield and R. W. Knighton, “Stability of corneal polarization axis measurements for scanning laser polarimetry,” Ophthalmology 108(6), 1065–1069 (2001).
[Crossref] [PubMed]

Gresham, V. C.

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

Güler, B.

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Guyton, D.

Hitzenberger, C. K.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

Huang, X. R.

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16(18), 13738–13751 (2008).
[Crossref] [PubMed]

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

Irsch, K.

Jaronski, J.

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21(5), 384–392 (2001).
[Crossref] [PubMed]

Knighton, R. W.

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16(18), 13738–13751 (2008).
[Crossref] [PubMed]

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

D. S. Greenfield and R. W. Knighton, “Stability of corneal polarization axis measurements for scanning laser polarimetry,” Ophthalmology 108(6), 1065–1069 (2001).
[Crossref] [PubMed]

Lee, R. K.

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

Lopes Cardozo, N. J.

L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981).
[Crossref] [PubMed]

Louis-Dorr, V.

Lu, S.-Y.

Malik, B. H.

B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
[Crossref] [PubMed]

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

March, W. F.

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
[Crossref] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
[Crossref] [PubMed]

Maurice, D. M.

D. M. Maurice, “The structure and transparency of the cornea,” J. Physiol. 136(2), 263–286 (1957).
[Crossref] [PubMed]

McCally, R. L.

Mergenthaler, K.

R. Engbert and K. Mergenthaler, “Microsaccades are triggered by low retinal image slip,” Proc. Natl. Acad. Sci. U.S.A. 103(18), 7192–7197 (2006).
[Crossref] [PubMed]

Misson, G. P.

G. P. Misson, “The theory and implications of the biaxial model of corneal birefringence,” Ophthalmic Physiol. Opt. 30(6), 834–846 (2010).
[Crossref] [PubMed]

G. P. Misson, “Circular polarization biomicroscopy: a method for determining human corneal stromal lamellar organization in vivo,” Ophthalmic Physiol. Opt. 27(3), 256–264 (2007).
[Crossref] [PubMed]

Naoun, K.

Naylor, E. J.

A. Stanworth and E. J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” J. Exp. Biol. 30(2), 160–163 (1953).

Picciani, R. G.

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

Pierscionek, B. K.

Pircher, M.

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

Pirnstill, C. W.

B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
[Crossref] [PubMed]

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

Purvinis, G.

G. Purvinis, B. D. Cameron, and D. M. Altrogge, “Noninvasive polarimetric-based glucose monitoring: an in vivo study,” J. Diabetes Sci. Technol. 5(2), 380–387 (2011).
[Crossref] [PubMed]

Rabinovitch, B.

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
[Crossref] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
[Crossref] [PubMed]

Raspiller, A.

Reusch, E.

E. Reusch, “Untersuchung über Glimmercombinationen,” Ann. Phys. 214(12), 628–638 (1869).
[Crossref]

Rovati, L.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[Crossref] [PubMed]

Shah, A. A.

K. Irsch and A. A. Shah, “Birefringence of the central cornea in children assessed with scanning laser polarimetry,” J. Biomed. Opt. 17(8), 086001 (2012).
[Crossref] [PubMed]

Stanworth, A.

A. Stanworth and E. J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” J. Exp. Biol. 30(2), 160–163 (1953).

Sticker, M.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

Stoyanov, B. J.

Theru, S.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

van Blokland, G. J.

Vargas-Martín, F.

Verhelst, S. C.

Wang, T. J.

T. J. Wang and F. A. Bettelheim, “Comparative birefringence of cornea,” Comp. Biochem. Physiol. A 51(11A), 89–94 (1975).
[Crossref] [PubMed]

Weale, R. A.

Wu, Y.-K.

Acta Med. Okayama (1)

G. Bozkir, M. Bozkir, H. Dogan, K. Aycan, and B. Güler, “Measurements of axial length and radius of corneal curvature in the rabbit eye,” Acta Med. Okayama 51(1), 9–11 (1997).
[PubMed]

Ann. Phys. (1)

E. Reusch, “Untersuchung über Glimmercombinationen,” Ann. Phys. 214(12), 628–638 (1869).
[Crossref]

Appl. Opt. (4)

Biomed. Opt. Express (1)

Comp. Biochem. Physiol. A (1)

T. J. Wang and F. A. Bettelheim, “Comparative birefringence of cornea,” Comp. Biochem. Physiol. A 51(11A), 89–94 (1975).
[Crossref] [PubMed]

Diabetes Care (2)

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurement of very small optical rotations,” Diabetes Care 5(3), 254–258 (1982).
[Crossref] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diabetes Care 5(3), 259–265 (1982).
[Crossref] [PubMed]

Diabetes Technol. Ther. (2)

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3(2), 201–207 (2001).
[Crossref] [PubMed]

C. W. Pirnstill, B. H. Malik, V. C. Gresham, and G. L. Coté, “In Vivo Glucose Monitoring Using Dual-Wavelength Polarimetry to Overcome Corneal Birefringence in the Presence of Motion,” Diabetes Technol. Ther. 14(9), 819–827 (2012).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

J. Biomed. Opt. (6)

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7(3), 321–328 (2002).
[Crossref] [PubMed]

B. H. Malik, C. W. Pirnstill, and G. L. Coté, “Dual-wavelength polarimetric glucose sensing in the presence of birefringence and motion artifact using anterior chamber of the eye phantoms,” J. Biomed. Opt. 18(1), 017007 (2013).
[Crossref] [PubMed]

E. Götzinger, M. Pircher, M. Sticker, A. F. Fercher, and C. K. Hitzenberger, “Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9(1), 94–102 (2004).
[Crossref] [PubMed]

F. Fanjul-Vélez, M. Pircher, B. Baumann, E. Götzinger, C. K. Hitzenberger, and J. L. Arce-Diego, “Polarimetric analysis of the human cornea measured by polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(5), 056004 (2010).
[Crossref] [PubMed]

K. Irsch and A. A. Shah, “Birefringence of the central cornea in children assessed with scanning laser polarimetry,” J. Biomed. Opt. 17(8), 086001 (2012).
[Crossref] [PubMed]

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[Crossref] [PubMed]

J. Diabetes Sci. Technol. (1)

G. Purvinis, B. D. Cameron, and D. M. Altrogge, “Noninvasive polarimetric-based glucose monitoring: an in vivo study,” J. Diabetes Sci. Technol. 5(2), 380–387 (2011).
[Crossref] [PubMed]

J. Exp. Biol. (1)

A. Stanworth and E. J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” J. Exp. Biol. 30(2), 160–163 (1953).

J. Opt. Soc. Am. A (4)

J. Physiol. (1)

D. M. Maurice, “The structure and transparency of the cornea,” J. Physiol. 136(2), 263–286 (1957).
[Crossref] [PubMed]

Open Ophthalmol. J. (1)

M. Goel, R. G. Picciani, R. K. Lee, and S. K. Bhattacharya, “Aqueous humor dynamics: a review,” Open Ophthalmol. J. 4(1), 52–59 (2010).
[Crossref] [PubMed]

Ophthalmic Physiol. Opt. (3)

G. P. Misson, “Circular polarization biomicroscopy: a method for determining human corneal stromal lamellar organization in vivo,” Ophthalmic Physiol. Opt. 27(3), 256–264 (2007).
[Crossref] [PubMed]

G. P. Misson, “The theory and implications of the biaxial model of corneal birefringence,” Ophthalmic Physiol. Opt. 30(6), 834–846 (2010).
[Crossref] [PubMed]

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21(5), 384–392 (2001).
[Crossref] [PubMed]

Ophthalmology (1)

D. S. Greenfield and R. W. Knighton, “Stability of corneal polarization axis measurements for scanning laser polarimetry,” Ophthalmology 108(6), 1065–1069 (2001).
[Crossref] [PubMed]

Opt. Express (1)

Philos. Trans. R. Soc. Lond. (1)

D. Brewster, “Experiments on the depolarization of light as exhibited by various mineral, animal and vegetable bodies, with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. Lond. 105(0), 29–53 (1815).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

R. Engbert and K. Mergenthaler, “Microsaccades are triggered by low retinal image slip,” Proc. Natl. Acad. Sci. U.S.A. 103(18), 7192–7197 (2006).
[Crossref] [PubMed]

Vision Res. (1)

L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981).
[Crossref] [PubMed]

Other (8)

W. His, Beiträge zur normalen und pathologischen Histologie der Cornea (Schweighauser'sche Sortimentsbuchhandlung, 1856).

O. Wiener, Die Theorie des Mischkörpers für das Feld der stationären Strömung. Erste Abhandlung: Die Mittelwertsätze für Kraft, Polarisation und Energie (BG Teubner, 1912).

L. J. Bour, “Polarized light and the eye,” in Vision Optics and Instrumentation, W. N. Charman, ed. (CRC, 1991), pp. 310–325.

G. P. Misson, “Birefringent properties of the human cornea in vivo: towards a new model of corneal structure,” PhD thesis, University of Warwick (2012).

C. A. Browne and F. W. Zerban, “Physical and chemical methods of sugar analysis: a practical and descriptive treatise for use in research, technical, and control laboratories,” 3rd ed., New York: J. Wiley & sons, inc., London: Chapman & Hall, 263–273 (1941).

H. Fujiwara, Spectroscopic ellipsometry: principles and applications (John Wiley & Sons., 2007).

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” in 33rd Annual Technical Symposium, (International Society for Optics and Photonics, 1990), pp. 177–187.

J. Humlicek, “Polarized Light and Ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, ed. (William Andrew, 2005).

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Figures (9)

Fig. 1
Fig. 1 Cornea holder with two spherically shaped fused silica elements (Suprasil Q1, Schott AG). The cornea is placed between the glasses. The distance between the glasses can be adjusted according to the cornea thickness. Illumination light in the ellipsometer is incident from the direction opposite to the z-direction. For variation of the angle of incidence the holder can be rotated around the y-axis. The radii of the glass surfaces in contact with the cornea are 6.63 mm for the left glass and 7.61 mm for the right glass. The left glass has a thickness of 1.49 mm, the right glass of 1.58 mm.
Fig. 2
Fig. 2 Mueller matrix elements of cornea no. 2 as a typical example for results of a spectrally resolved ellipsometric measurement in transmission mode. The element M11 is normalized to 1 and hence not displayed. M44 is drawn bold because it is a direct measure for the linear retardance.
Fig. 3
Fig. 3 Birefringence parameters deduced from Mueller matrix measurements of nine porcine corneas in dependence on the wavelength. These measurements were taken at the apex of the corneas for a perpendicular angle of incidence. The three parameters (linear retardance, orientation of the fast axis, and optical rotation) are given in degrees [°].
Fig. 4
Fig. 4 Linear retardance (here given in nanometers) of the nine porcine corneas, measured at the apex (x = 0 mm) for a perpendicular angle of incidence. For wavelengths below 500 nm the corneal retardance exhibits a significant spectral dependency.
Fig. 5
Fig. 5 Degree of polarization and diattenuation of the nine porcine corneas, measured at the apex (x = 0 mm) for a perpendicular angle of incidence. For wavelengths above 500 nm the degree of polarization is typically > 95%. Below 400 nm a strong decrease of the degree of polarization is observed. The degree of polarization was averaged for several polarization states of the incident beam. Compared to the other polarimetric properties of the corneas diattenuation is a negligible effect.
Fig. 6
Fig. 6 Linear retardance and optical rotation of cornea no. 2, measured at the apex (x = 0 mm) for several angles of rotation around the y-axis. For a perpendicular angle of incidence (0°) the light beam is irradiated from the direction opposite to the z-axis. Increasing angles of rotation correspond to a clockwise rotation of the cornea holder around the y-axis.
Fig. 7
Fig. 7 Linear retardance and optical rotation of cornea no. 2, measured at the periphery (x = 3 mm) for several angles of rotation around the y-axis. For these measurements the cornea holder was shifted by 3 mm in x-direction relative to the ellipsometer light beam. Increasing angles of rotation correspond to a clockwise rotation of the cornea holder around the y-axis.
Fig. 8
Fig. 8 Optical Rotatory Dispersion (ORD) of glucose for a concentration of 100 mg/dl and an interaction length of 10 mm. The ORD curve can be described adequately by a polynomial fit of 6th-degree. The polynomial function and the coefficients are given in the text.
Fig. 9
Fig. 9 Simulated net rotation due to optical activity of glucose in the aqueous humor and eye lens reflectivity in dependence on the angle of incidence to the eye lens, for different incident (linear) polarizations. The exemplary curves are calculated at 400 nm wavelength for 100 mg/dl glucose concentration. The interaction length of the light with the aqueous humor is assumed to be 3.5 mm before and after reflection. At the Brewster angle (46.46°) the net rotation is half of the rotation expected for 90° angle of incidence since only the optical activity after reflection contributes to the net rotation in this case. A high portion of p-polarized light may yield high net rotation but also low reflectivity.

Equations (10)

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M M Measure =M M Depolarisation M M Retardance M M Diattenuation
M M Retardance = M M LinRet M M Rot
M M LinRet ( θ,δ )=[ 1 0 0 0 0 cos 2 ( 2θ )+ sin 2 ( 2θ )cosδ sin( 2θ )cos( 2θ )(1-cosδ) -sin( 2θ )sinδ 0 sin( 2θ )cos( 2θ )(1-cosδ) sin 2 ( 2θ )+ cos 2 ( 2θ )cosδ cos( 2θ )sinδ 0 sin( 2θ )sinδ -cos( 2θ )sinδ cosδ ]
M M Rot ( ψ )=[ 1 0 0 0 0 cos( 2ψ ) sin( 2ψ ) 0 0 sin( 2ψ ) cos( 2ψ ) 0 0 0 0 1 ]
M M Retardance ( θ,δ,ψ )=M M LinRet ( θ,δ )M M Rot ( ψ )
M11=1 M12=M13=M14=M21=M31=M41=0 M22=[ cosδ1 ]cos( 2θ )sin( 2θ )sin( 2ψ )+[ cos 2 ( 2θ )+cosδ sin 2 ( 2θ ) ]cos( 2ψ ) M23=[ 1cosδ ]cos( 2θ )sin( 2θ )sin( 2ψ )+[ cos 2 ( 2θ )+cosδ sin 2 ( 2θ ) ]sin( 2ψ ) M24=sinδsin( 2θ ) M32= [ 1cosδ ]cos( 2θ )sin( 2θ )cos( 2ψ )[ cosδ cos 2 ( 2θ )+ sin 2 ( 2θ ) ]sin( 2ψ ) M33=[ 1cosδ ]cos( 2θ )sin( 2θ )sin( 2ψ )+[ cosδ cos 2 ( 2θ )+ sin 2 ( 2θ ) ]cos( 2ψ ) M34=sinδcos( 2θ ) M42=sinδsin( 2θ+2ψ ) M43=sinδcos( 2θ+2ψ ) M44=cosδ
δ=arccos( M44 ) θ= 1 2 arccos( M34 sinδ ) ψ= 1 2 arcsin( M23M32 1+cosδ )=arctan( M23M32 trace( M M Retardance ) )
S OUT =M M Measure S IN
P= S 1 2 + S 2 2 + S 3 2 S 0        with       S OUT =( S 0 S 1 S 2 S 3 ) ,           0P1 
ORD (λ) Glucose [°]= p 6 λ 6 + p 5 λ 5 + p 4 λ 4 + p 3 λ 3 + p 2 λ 2 + p 1 λ+ p 0 with λ in [ nm ]

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