Abstract

The dichroic properties of in vitro sheep corneas were studied with a spectrophotometer in transmission mode for several angles of incidence of light beams. Several models of corneal anisotropy have been presented in the literature. The results presented here allow us to believe that the cornea behaves as a dichroic biaxial crystal. Furthermore, this dichroism is weak when the angle of incidence on the corneal surface stays small. The mathematical model that describes these optical properties of the cornea uses Mueller matrices.

© 2004 Optical Society of America

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References

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  1. R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
    [CrossRef] [PubMed]
  2. N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
    [CrossRef] [PubMed]
  3. J. M. Bueno, F. Vargas-Martin, “Measurement of the corneal birefringence with a liquid crystal imaging polariscope,” Appl. Opt. 41, 116–124 (2002).
    [CrossRef] [PubMed]
  4. D. S. Greenfield, R. W. Knighton, “Correction for corneal polarization axis improves the discriminating power of scanning laser polarimetry,” Am. J. Ophthalmol. 134, 27–33 (2002).
    [CrossRef] [PubMed]
  5. R. W. Knighton, X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43, 82–86 (2002).
    [PubMed]
  6. J. M. Bueno, “Measurement of parameters of the polarization in the living human eye using imaging polarimetry,” Vision Res. 40, 3791–3799 (2000).
    [CrossRef]
  7. D. S. Greenfield, R. W. Knighton, “Effect of corneal polarization axis on the assessment of the retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
    [CrossRef] [PubMed]
  8. A. M. Benoit, K. Naoun, V. Louis-Dorr, L. Mala, A. Raspiller, “Linear dichroism of the retinal nerve fiber layer expressed with Mueller matrices,” Appl. Opt. 40, 565–569 (2001).
    [CrossRef]
  9. G. J. Van Blockland, “The optics of the human eye studied with respect to polarized light,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1986).
  10. J. M. Bueno, J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthalmic Physiol. Opt. 21, 384–392 (2001).
    [CrossRef] [PubMed]
  11. L. J. Bour, “Polarized light and eye,” in Visual Optics and Instrumentation (CRC Press, Boca Raton, Fla., 1991), Vol. 1.
  12. A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).
  13. A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
    [CrossRef]
  14. L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
    [CrossRef] [PubMed]
  15. G. J. Van Blockland, S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4, 82–90 (1987).
    [CrossRef]
  16. E. E. Wahlstrom, Optical Crystallography (Wiley, New York, 1949).
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).
  18. R. P. Hemenger, “Dichroism of the macula pigment and Haidinger’s brushes,” J. Opt. Soc. Am. 72, 734–737 (1982).
    [CrossRef] [PubMed]
  19. R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
    [CrossRef]
  20. H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661 (1948).
  21. D. M. Maurice, “The structure and transparency of the cornea,” J. Physiol. 136, 263–286 (1957).
    [PubMed]

2003 (2)

R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
[CrossRef] [PubMed]

N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
[CrossRef] [PubMed]

2002 (3)

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

D. S. Greenfield, R. W. Knighton, “Correction for corneal polarization axis improves the discriminating power of scanning laser polarimetry,” Am. J. Ophthalmol. 134, 27–33 (2002).
[CrossRef] [PubMed]

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

2001 (2)

A. M. Benoit, K. Naoun, V. Louis-Dorr, L. Mala, A. Raspiller, “Linear dichroism of the retinal nerve fiber layer expressed with Mueller matrices,” Appl. Opt. 40, 565–569 (2001).
[CrossRef]

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

2000 (2)

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

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

1987 (1)

1984 (1)

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

1982 (1)

1981 (1)

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

1957 (1)

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

1953 (1)

A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).

1950 (1)

A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
[CrossRef]

1948 (1)

H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661 (1948).

Benoit, A. M.

Bone, R. A.

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Bour, L. J.

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

L. J. Bour, “Polarized light and eye,” in Visual Optics and Instrumentation (CRC Press, Boca Raton, Fla., 1991), Vol. 1.

Bowd, C.

R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
[CrossRef] [PubMed]

Bueno, J. M.

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

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

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

Choplin, N. T.

N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
[CrossRef] [PubMed]

Greenfield, D. S.

D. S. Greenfield, R. W. Knighton, “Correction for corneal polarization axis improves the discriminating power of scanning laser polarimetry,” Am. J. Ophthalmol. 134, 27–33 (2002).
[CrossRef] [PubMed]

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

Hemenger, R. P.

Huang, X. R.

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

Jaronski, J.

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

Knighton, R. W.

N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
[CrossRef] [PubMed]

D. S. Greenfield, R. W. Knighton, “Correction for corneal polarization axis improves the discriminating power of scanning laser polarimetry,” Am. J. Ophthalmol. 134, 27–33 (2002).
[CrossRef] [PubMed]

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

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

Landrum, J. T.

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

Lopes Cardozo, N. J.

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

Louis-Dorr, V.

Mala, L.

Maurice, D. M.

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

Mueller, H.

H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661 (1948).

Naoun, K.

Naylor, E. J.

A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).

A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
[CrossRef]

Raspiller, A.

Stanworth, A.

A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).

A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
[CrossRef]

Van Blockland, G. J.

G. J. Van Blockland, S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4, 82–90 (1987).
[CrossRef]

G. J. Van Blockland, “The optics of the human eye studied with respect to polarized light,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1986).

Vargas-Martin, F.

Verhelst, S. C.

Wahlstrom, E. E.

E. E. Wahlstrom, Optical Crystallography (Wiley, New York, 1949).

Weinreb, R. N.

R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Zangwill, L. M.

R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
[CrossRef] [PubMed]

Zhou, Q.

N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
[CrossRef] [PubMed]

Am. J. Ophthalmol. (2)

D. S. Greenfield, R. W. Knighton, “Correction for corneal polarization axis improves the discriminating power of scanning laser polarimetry,” Am. J. Ophthalmol. 134, 27–33 (2002).
[CrossRef] [PubMed]

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

Appl. Opt. (2)

Arch. Ophthalmol. (1)

R. N. Weinreb, C. Bowd, L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121, 218–224 (2003).
[CrossRef] [PubMed]

Brit. J. Ophthalmol. (1)

A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (1)

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

J. Exp. Biol. (1)

A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).

J. Opt. Soc. Am. (2)

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

J. Physiol. (1)

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

Ophthalmic Physiol. Opt. (1)

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

Ophthalmology (1)

N. T. Choplin, Q. Zhou, R. W. Knighton, “Effect of individualized compensation for anterior segment birefringence on retinal nerve fiber layer assessments as determined by scanning laser polarimetry,” Ophthalmology 110, 719–725 (2003).
[CrossRef] [PubMed]

Vision Res. (3)

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

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

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

Other (4)

G. J. Van Blockland, “The optics of the human eye studied with respect to polarized light,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1986).

L. J. Bour, “Polarized light and eye,” in Visual Optics and Instrumentation (CRC Press, Boca Raton, Fla., 1991), Vol. 1.

E. E. Wahlstrom, Optical Crystallography (Wiley, New York, 1949).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

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Figures (10)

Fig. 1
Fig. 1

Optical triaxial ellipsoid of a biaxial crystal.

Fig. 2
Fig. 2

Surfaces of the indices in three dimensions for a biaxial crystal.

Fig. 3
Fig. 3

Surfaces of the absorption coefficients for a dichroic biaxial crystal.

Fig. 4
Fig. 4

Schematic of the optical setup of the spectrophotometer: De, deuterium light; W, tungsten light; M1–M7, ellipsoidal mirrors; F1, F2, slits; L1, L2, lenses; D1, D2, rectangular diaphragms; P, polarizer; CS, sample; values of I defined in text.

Fig. 5
Fig. 5

Geometry of a light beam passing through the cornea: IC, corneal revolution axis; α o , angle of incidence; d, distance between the incident beam and the corneal revolution axis; D1, D2, retangular diaphragms; R, radius of curvature of the cornea; z, direction of the normal to the corneal surface.

Fig. 6
Fig. 6

Variation of the transmission coefficients of vibration amplitudes at refraction on the air-cornea boundary relative to angle of incidence α o [calculated from Eqs. (7) and (8)]. Diamonds, t H = A t,H /A 0; squares, t V = A t,V /A 0.

Fig. 7
Fig. 7

(a) Transmittances T %(T H , polarizer P horizontally; T V , polarizer P vertically) without the cornea (T H,0 %, lighter solid curve; T V,0 %, darker solid curve) and with the centered cornea (T H,C %, lighter dashed curve; T V,C %, darker dashed curve. (b) LD without the cornea (LD0, darker curve) and with the centered cornea (LDC, lighter curve).

Fig. 8
Fig. 8

LD curves for three corneas (1, darker solid curve; 2, lighter solid curve; and 3, darker dashed curve) centered on the incident beam and for cornea 4, lighter dashed curve, with incidence angle α o ≈ 25°.

Fig. 9
Fig. 9

(a), (b) LD curves of sheep corneas 5 and 6, respectively, with different incidences on the corneal surface (d along the major axis); (c), (d) LD curves of sheep corneas 5 and 6, respectively, with different incidences on the corneal surface (d along the minor axis). (a), (b), (d) Darker solid curves, centered; lighter solid curves, 5° < α o < 15°; darker dotted curves, 15° < α o < 20°; lighter dotted curves, 20° < α o < 25°. (c) Same values for curves from top to bottom, respectively.

Fig. 10
Fig. 10

LD curves with normal incidence for three isolated sheep cornea (1, darker solid curve; 2, lighter solid curve; and 6, darker dashed curve) and for one eye with a cornea and a retina, lighter dashed shoes.

Equations (9)

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tan V=nz/nxny2-nx2/nz2-ny21/2.
LD=IGA-IPA/IGA+IPA.
ST=MC×S0, ST=S0,TS1,TS2,TS3,T =exp-2κsl×cosh 2κdlsinh 2κdl00sinh 2κdlcosh 2κdl0000cos φ-sin φ00sin φcos φ ×I01cos 2θsin 2θ0,
φ=2π/λn-nl,κd=½κ-κ,κs=½κ+κ,
ITθ=S0,T=I0 exp-2κslcosh 2κdl+cos 2θ sinh 2κdl, ITθ=I0exp-2κlsin2 θ+exp-2κlcos2 θ.
LD=IGA-IPAIGA+IPA=TGA%-TPA%TGA%+TPA%,
LD=tanhκ-κl.
At,H=At,GA=2 cos αo sin αicosαo-αisinαo+αi Ao, At,V=At,PA=2 cos αo sin αisinαo+αi Ao,
At,H=At,V=2n+1 Ao.

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