Abstract

We have applied Mueller matrix ellipsometry to assess the change in the state of polarization of a light beam that has double passed the ocular media and is scattered at the fundus of the human eye in vivo. At several positions in the pupil plane, which together cover the area of the dilated pupil, Mueller matrices are assessed. From them the magnitude of the retardation and the orientation of the eigenvector are calculated. The properties of the retardation process are surveyed by measuring the retardation along a horizontal meridian as a function of wavelength, density of visual pigment, and location of retinal fixation. Furthermore, photographs are taken from the polarization patterns on the iris with circularly polarized light. We posit that the cornea behaves as a biaxial crystal with its fastest principal axis normal to its surface and its slowest nasally downward. The retardation of light by a model eye with such a cornea is calculated, and the results are compared with the data.

© 1987 Optical Society of America

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References

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  1. G. J. van Blokland, “Ellipsometry of the human retina in vivo: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
    [CrossRef] [PubMed]
  2. G. Boehm, “Ueber maculare (Haidingersche) Polarisations buschel und ueber einen polarizationsoptischen Fehler des Auges,” Acta Ophthalmol. 18, 109–169 (1940).
  3. H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
    [CrossRef]
  4. E. J. Naylor, A. Stanworth, “Retinal pigment and the Haidinger effect,”J. Physiol. 124, 543–552 (1954).
    [PubMed]
  5. A. Stanworth, E. J. Naylor, “The polarization optics of the isolated cornea,” Brit. J. Ophthalmol. 34, 201–211 (1950).
    [CrossRef]
  6. A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,”J. Exp. Biol. 30, 160–169 (1953).
  7. L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
    [CrossRef] [PubMed]
  8. D. G. Cogan, “Some ocular phenomena produced with polarized light,” Arch. Ophthalmol. 25, 391–400 (1941).
    [CrossRef]
  9. W. T. Cope, M. L. Wohlbarsht, B. S. Yamanashi, “The corneal polarization cross,”J. Opt. Soc. Am. 68, 1139–1141 (1978).
    [CrossRef] [PubMed]
  10. R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1973), p. 560.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), p. 705.
  12. R. L. McCally, R. A. Farrell, “Structural implications of small-angle light scattering from cornea,” Exp. Eye Res. 34, 99–113 (1982).
    [CrossRef] [PubMed]
  13. F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
    [CrossRef] [PubMed]
  14. R. A. Weale, “Sex, age and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
    [CrossRef] [PubMed]
  15. B. F. Hochheimer, H. E. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
    [CrossRef] [PubMed]
  16. G. J. van Blokland, “The optics of the human eye studied with respect to polarized light,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1986).
  17. Y. LeGrand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).
  18. H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

1985 (1)

1982 (2)

B. F. Hochheimer, H. E. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
[CrossRef] [PubMed]

R. L. McCally, R. A. Farrell, “Structural implications of small-angle light scattering from cornea,” Exp. Eye Res. 34, 99–113 (1982).
[CrossRef] [PubMed]

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]

1979 (1)

R. A. Weale, “Sex, age and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
[CrossRef] [PubMed]

1978 (1)

1975 (1)

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

1954 (1)

E. J. Naylor, A. Stanworth, “Retinal pigment and the Haidinger effect,”J. Physiol. 124, 543–552 (1954).
[PubMed]

1953 (2)

H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

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]

1941 (1)

D. G. Cogan, “Some ocular phenomena produced with polarized light,” Arch. Ophthalmol. 25, 391–400 (1941).
[CrossRef]

1940 (1)

G. Boehm, “Ueber maculare (Haidingersche) Polarisations buschel und ueber einen polarizationsoptischen Fehler des Auges,” Acta Ophthalmol. 18, 109–169 (1940).

Bettelheim, F. A.

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

Boehm, G.

G. Boehm, “Ueber maculare (Haidingersche) Polarisations buschel und ueber einen polarizationsoptischen Fehler des Auges,” Acta Ophthalmol. 18, 109–169 (1940).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), p. 705.

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]

Cogan, D. G.

D. G. Cogan, “Some ocular phenomena produced with polarized light,” Arch. Ophthalmol. 25, 391–400 (1941).
[CrossRef]

Cope, W. T.

de Vries, H. L.

H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

El Hage, S. G.

Y. LeGrand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

Farrell, R. A.

R. L. McCally, R. A. Farrell, “Structural implications of small-angle light scattering from cornea,” Exp. Eye Res. 34, 99–113 (1982).
[CrossRef] [PubMed]

Hochheimer, B. F.

Jielof, R.

H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Kues, H. E.

LeGrand, Y.

Y. LeGrand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1973), p. 560.

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]

Makino, H.

H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

McCally, R. L.

R. L. McCally, R. A. Farrell, “Structural implications of small-angle light scattering from cornea,” Exp. Eye Res. 34, 99–113 (1982).
[CrossRef] [PubMed]

Nakao, S.

H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

Naylor, E. J.

E. J. Naylor, A. Stanworth, “Retinal pigment and the Haidinger effect,”J. Physiol. 124, 543–552 (1954).
[PubMed]

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]

Ouzato, H.

H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

Saishin, M.

H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

Spoor, A.

H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Stanworth, A.

E. J. Naylor, A. Stanworth, “Retinal pigment and the Haidinger effect,”J. Physiol. 124, 543–552 (1954).
[PubMed]

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 Blokland, G. J.

G. J. van Blokland, “Ellipsometry of the human retina in vivo: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
[CrossRef] [PubMed]

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

Weale, R. A.

R. A. Weale, “Sex, age and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
[CrossRef] [PubMed]

Wohlbarsht, M. L.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), p. 705.

Yamanashi, B. S.

Acta Ophthalmol. (1)

G. Boehm, “Ueber maculare (Haidingersche) Polarisations buschel und ueber einen polarizationsoptischen Fehler des Auges,” Acta Ophthalmol. 18, 109–169 (1940).

Appl. Opt. (1)

Arch. Ophthalmol. (1)

D. G. Cogan, “Some ocular phenomena produced with polarized light,” Arch. Ophthalmol. 25, 391–400 (1941).
[CrossRef]

Brit. J. Ophthalmol. (1)

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

Exp. Eye Res. (3)

R. L. McCally, R. A. Farrell, “Structural implications of small-angle light scattering from cornea,” Exp. Eye Res. 34, 99–113 (1982).
[CrossRef] [PubMed]

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

R. A. Weale, “Sex, age and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
[CrossRef] [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. (1)

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

J. Physiol. (1)

E. J. Naylor, A. Stanworth, “Retinal pigment and the Haidinger effect,”J. Physiol. 124, 543–552 (1954).
[PubMed]

Physica (1)

H. L. de Vries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Vision Res. (1)

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

Other (5)

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

Y. LeGrand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

H. Ouzato, H. Makino, M. Saishin, S. Nakao, “Measurement of visual axis using a laser beam,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983).

R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1973), p. 560.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), p. 705.

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Figures (7)

Fig. 1
Fig. 1

Amount of retardation and orientation of the eigenstates of a double passage through the ocular media and scattering at the fundus. Values are displayed as a function of the position of the exit pupil with a central entry. Each measuring point is represented by a diamond. The orientation and ellipticity of the eigenstate are given by the orientation and ratio of the short to the long axis of the diamond. Its handedness is given by the sign. The lines indicate contours of equal retardation at intervals of 25 deg. Wavelength 514 nm, 100,000 Td, foveal fixation.

Fig. 2
Fig. 2

Polarization patterns of the cornea with circularly polarized light of the same eyes as Fig. 1. Wavelength 530 nm, foveal fixation.

Fig. 3
Fig. 3

Retardation along a horizontal meridian in the pupil. Upper graphs subject GJ, lower graphs subject HK. a, Data with 100,000 Td (90% bleached) and 1000 Td (virtually no bleaching). Right eye, 514 nm, and foveal fixation. b, Data from the right and left eyes. 514 nm, 100,000 Td, foveal fixation. c, Data at wavelengths of 488, 514, and 568 nm. With subject HK 647 nm was also measured. Foveal fixation, right eye, 100,000 Td. d, Data at two additional retinal locations at 5 and 8 deg temporal of subject GJ. Right eye, 514 nm, 100,000 Td.

Fig. 4
Fig. 4

Data of six subjects, right eye, 514 nm, bleached retina, foveal fixation. The orientation of the eigenvector is given in the left-hand graph. Zero deg is vertical. When one looks into the eye, the angle increases clockwise. In the right-hand graph the amount of retardation is given.

Fig. 5
Fig. 5

Retardation along two cross sections of the cornea composed of the data of Fig. 2 extended with data taken from the corneal polarization pictures. Subject BV, left eye. A fourth-order function is fitted through the data points. a, Contour along the line connecting the optical axes. The retardation is assessed with an eigenvector along the connecting line. Therefore at high eccentricities negative values are obtained. b, Contour along a line through the center of the pupil plane, perpendicular to the line connecting the points of zero retardation.

Fig. 6
Fig. 6

Geometry of a light beam when aligned with one of the optical axes of the birefringent cornea.

Fig. 7
Fig. 7

Calculated retardation in a model eye with a biaxial cornea. a, Retardation of a single passage through the cornea. b, Retardation of a double passage and scattering at the fundus with a central position of the entrance pupil.

Equations (5)

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D i = j i j E j             ( i , j = 1 3 ) .
D k = k E k             ( k = x , y , z ) ,
D x 2 / x + D y 2 / y + D z 2 / z = 1.
β = arctan [ ( η y - η x ) / ( η z - η y ) ] 1 / 2 .
δ = ( 2 π ρ / λ ) ( η z - η x ) sin θ 1 sin θ 2 ,

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