Abstract

We have assessed retinal birefringence in the foveal and parafoveal regions by applying Mueller matrix ellipsometry on the human eye in vivo. Basically, a light beam passed the ocular media twice and was scattered at the fundus intermediately. Keeping the entry and exit positions on the cornea constant and varying the retinal location along a circle around the foveal center enabled us to separate the corneal and retinal components of the measured retardation. We conclude that the retina within the outer margin of the parafovea behaves as a uniaxial crystal, with its slow axis radially oriented from the fovea and a retardation of about 16 deg (to 70 deg in the corneal center). We believe that Henle’s fiber layer causes retardation in this specific configuration of entrance and exit beams. The outer segments of the photoreceptors, although birefringent, have their optic axes aligned with these beams.

© 1988 Optical Society of America

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References

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  1. G. J. van Blokland, 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] [PubMed]
  2. B. F. Hochheimer, H. E. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
    [CrossRef] [PubMed]
  3. F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).
  4. R. A. Weale, “On the birefringence of rods and cones,” Pfluegers Arch. 329, 244–257 (1971).
    [CrossRef]
  5. 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]
  6. 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]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.
  8. F. I. Hárosi, “Microspectrophotometry and optical phenomena: birefringence, dichroism, and anomalous dispersion,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds. (Springer-Verlag, Berlin, 1981).
    [CrossRef]
  9. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
    [CrossRef]
  10. B. F. Hochheimer, “Polarized light retinal photography of a monkey eye,” Vision Res. 18, 19–23 (1978).
    [CrossRef] [PubMed]
  11. R. A. Weale, “Sex, age and the birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979),
    [CrossRef] [PubMed]
  12. F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
    [CrossRef] [PubMed]
  13. R. P. Hemenger, “Dichroism of the macular pigment and Haidinger’s brushes,” J. Opt. Soc. Am. 72, 734–737 (1982).
    [CrossRef] [PubMed]
  14. B. S. Fine, M. Yanoff, Ocular Histology (Harper and Row, Hagerstown, Pa., 1979).
  15. G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
    [CrossRef] [PubMed]

1987 (1)

1986 (1)

G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef] [PubMed]

1985 (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 (2)

1979 (2)

F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).

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

1978 (2)

B. F. Hochheimer, “Polarized light retinal photography of a monkey eye,” Vision Res. 18, 19–23 (1978).
[CrossRef] [PubMed]

P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
[CrossRef]

1975 (1)

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

1971 (1)

R. A. Weale, “On the birefringence of rods and cones,” Pfluegers Arch. 329, 244–257 (1971).
[CrossRef]

Bettelheim, F. A.

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

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, London, 1980), Chap. 14.

Delori, F. C.

F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).

Fine, B. S.

B. S. Fine, M. Yanoff, Ocular Histology (Harper and Row, Hagerstown, Pa., 1979).

Hárosi, F. I.

F. I. Hárosi, “Microspectrophotometry and optical phenomena: birefringence, dichroism, and anomalous dispersion,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds. (Springer-Verlag, Berlin, 1981).
[CrossRef]

Hauge, P. S.

Hemenger, R. P.

Hochheimer, B. F.

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

B. F. Hochheimer, “Polarized light retinal photography of a monkey eye,” Vision Res. 18, 19–23 (1978).
[CrossRef] [PubMed]

Kues, H. E.

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]

Parker, J. S.

F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).

van Blokland, G. J.

Verhelst, S. C.

Weale, R. A.

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

R. A. Weale, “On the birefringence of rods and cones,” Pfluegers Arch. 329, 244–257 (1971).
[CrossRef]

Webb, R. H.

F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.

Yanoff, M.

B. S. Fine, M. Yanoff, Ocular Histology (Harper and Row, Hagerstown, Pa., 1979).

Appl. Opt. (1)

Exp. Eye Res. (2)

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

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

Invest. Ophthalmol. Vis. Sci. Suppl. (1)

F. C. Delori, R. H. Webb, J. S. Parker, “Macular birefringence,” Invest. Ophthalmol. Vis. Sci. Suppl. 19, 53 (1979).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Pfluegers Arch. (1)

R. A. Weale, “On the birefringence of rods and cones,” Pfluegers Arch. 329, 244–257 (1971).
[CrossRef]

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]

B. F. Hochheimer, “Polarized light retinal photography of a monkey eye,” Vision Res. 18, 19–23 (1978).
[CrossRef] [PubMed]

G. J. van Blokland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef] [PubMed]

Other (3)

B. S. Fine, M. Yanoff, Ocular Histology (Harper and Row, Hagerstown, Pa., 1979).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.

F. I. Hárosi, “Microspectrophotometry and optical phenomena: birefringence, dichroism, and anomalous dispersion,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds. (Springer-Verlag, Berlin, 1981).
[CrossRef]

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Figures (6)

Fig 1
Fig 1

Scheme of the optical system for measuring the polarization properties of the fundus, incorporating a Mueller-matrix ellipsometer. The entrance light path consists of the following elements: LA, ion laser; BE, beam expander and Gaussian spatial filter; S, shutter; Drf, diaphragm defining the size of the illuminated field on the retina (2.5 deg); P, polarizer; C1, rotating compensator; Lin, entrance lens focusing the laser beam just beyond the cornea; M, mirror covering the lower half of the pupil plane in order to separate the entrance and exit light paths. The exit light path consists of the following elements: Lout, exit lens with its back focus in the pupil plane; Dmf, diaphragm selecting the measured field on the retina (1.5 deg); Dpup, laterally adjustable diaphragm selecting the position of the exit pupil (imaged in the pupil plane, 1.0 mm × 0.8 mm); C2, rotating compensator; A, analyzer parallel to P; PMT, photomultiplier tube. The inset shows the pupil plane. In our measurements the exit position was selected over the entrance position at a distance of 1.5 mm.

Fig. 2
Fig. 2

Calculated retardations as a function of the azimuth in the retinal plane for the two subjects, (a) GJ and (b) HK. In both cases the wavelength is 514 nm, the annular radius is 2.90 degrees, and the retinal illumination is 5 log Td. Note the differences in the mean values and the ranges. The drawn curve is a best-fitting Fourier synthesis.

Fig. 3
Fig. 3

Simplified geometry of the light beams in the conical surface of either the entrance or the exit. The apex of the cone lies both in the corneal surface and in the principal section; the latter is defined by the two optic axes of the cornea. The four dots (e’s) indicate the directrices, i.e., the light beams, with alternately minimum and maximum total retardations. Whether the principal section contains minima or maxima depends on the orientation of the retinal slow axes.

Fig. 4
Fig. 4

Declination in the absence of inclination. The cone axis bisects the angle between the pair of optic axes. (a) Minimum retardation (view of principal section). (b) Maximum retardation (three-dimensional picture).

Fig. 5
Fig. 5

Configuration of the axes of the entrance and exit cones. The eccentricities of the two apices (0.75 mm) involve inclinations ψ because of the curvature of the cornea (radius 7.80 mm).

Fig. 6
Fig. 6

Different types of inclination. The cone axis is tilted with respect to the normal on the cornea. (a) Parallel inclination (view of principal section). (b) Perpendicular inclination (three-dimensional picture).

Tables (3)

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Table 1 Mean Amplitudesa

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Table 3 Corrected Values for the Retinal Retardationa

Equations (10)

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R ( φ ) = R 0 + R 1 sin ( φ 1 ) + R 2 sin [ 2 ( φ 2 ) ] .
R = Δ n [ 2 l / λ ) ] ( 360 deg ) .
ρ = ρ 0 sin ( θ 1 ) sin ( θ 2 ) ,
ρ = ρ 0 sin 2 ( β ) .
ρ min = ρ 0 sin ( β + χ ) sin ( β χ ) = ρ 0 [ cos 2 ( χ ) cos 2 ( β ) ] .
cos ( θ 1 ) = cos ( θ 2 ) = cos ( β ) cos ( χ ) ;
ρ max = ρ 0 sin 2 ( θ 1 ) = ρ 0 [ 1 cos 2 ( β ) cos 2 ( χ ) ] .
ρ 2 = ½ ( ρ max ρ min ) = ρ 0 sin 2 ( χ ) ½ [ 1 + cos 2 ( β ) ] .
ρ c = ρ 0 [ 1 cos 2 ( β ) cos 2 ( ψ ) ] .
R 2 c = 2 ρ c ( 0.0046 ) for χ = 1.25 deg = 2 ρ c ( 0.0247 ) for χ = 1.90 deg ,

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