Abstract

We studied aspects of the birefringence in the human crystalline lens. With the use of Mueller-matrix ellipsometry in vivo on both accommodated and unaccommodated eyes, we found no difference between the associated retardations. We calculated form birefringence of the lens by interpreting the membranes of the lens fiber cells as Wiener bodies. The resulting retardation for a light beam that passes the lens as in the experiments exceeds by far the measured total retardation. We conclude that form and intrinsic birefringence of the lens cancel out.

© 1991 Optical Society of America

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References

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  1. D. Brewster, “On the structure of the crystalline lens in fishes and quadrupeds, as ascertained by its action on polarized light,” Philos. Trans. R. Soc. London Ser. B 106, 311–317 (1816).
    [CrossRef]
  2. G. Valentin, “Neue Untersuchungen Über die Polarisations-Erscheinungen der Krystalllinsen des Menschen und der Thiere,” Arch. Ophthalmol. 4, 227–268 (1859).
  3. F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
    [CrossRef] [PubMed]
  4. R. A. Weale, “Sex, age and the birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
    [CrossRef] [PubMed]
  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. 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]
  7. H. B. klein Brink, G. J. van Blokland, “Birefringence of the human foveal area assessed in vivowith Mueller-matrix ellipsometry” J. Opt. Soc. Am. A 5, 49–57 (1988).
    [CrossRef]
  8. Both retarders are quarter-wave plates for 514 nm. We used the same retarders at 488 and 568 nm for which the phase shifts deviate considerably from 90 deg, so corrections had to be made during the data processing. Mueller-matrix ellipsometry meets this demand by including wavelength-dependent deficiency parameters in the conversion from the Fourier amplitudes to the matrix elements.9Likewise, any possible inexactitude in the phase shifts for 514 nm is eliminated.
  9. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
    [CrossRef]
  10. Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).
  11. B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
    [CrossRef] [PubMed]
  12. G. B. Benedek, “Theory of transparency of the eye,” Appl. Opt. 10, 459–473 (1971).
    [CrossRef] [PubMed]
  13. F. A. Bettelheim, “Physical basis of lens transparency” in The Ocular Lens, Structure, Function and Pathology, H. Maisel, ed. (Academic, New York, 1985).
  14. As the terminology might be confusing, we emphasize the distinction between optical axis (central line of the exit optics) and optic axis (each of both specific directions in the biaxially double-refracting cornea; a light beam traveling along an optic axis undergoes no retardation).
  15. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).
  16. A. Stanworth, E. J. Naylor, “Polarized light studies of the cornea,” J. Exp. Biol. 30, 160–169 (1953).

1988

1987

1985

1979

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

1978

1975

B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
[CrossRef] [PubMed]

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

1971

1953

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

1859

G. Valentin, “Neue Untersuchungen Über die Polarisations-Erscheinungen der Krystalllinsen des Menschen und der Thiere,” Arch. Ophthalmol. 4, 227–268 (1859).

1816

D. Brewster, “On the structure of the crystalline lens in fishes and quadrupeds, as ascertained by its action on polarized light,” Philos. Trans. R. Soc. London Ser. B 106, 311–317 (1816).
[CrossRef]

Balazs, E. A.

B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
[CrossRef] [PubMed]

Benedek, G. B.

Bettelheim, F. A.

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

F. A. Bettelheim, “Physical basis of lens transparency” in The Ocular Lens, Structure, Function and Pathology, H. Maisel, ed. (Academic, New York, 1985).

Brewster, D.

D. Brewster, “On the structure of the crystalline lens in fishes and quadrupeds, as ascertained by its action on polarized light,” Philos. Trans. R. Soc. London Ser. B 106, 311–317 (1816).
[CrossRef]

El Hage, S. G.

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

Hanninen, L.

B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
[CrossRef] [PubMed]

Hauge, P. S.

klein Brink, H. B.

Le Grand, Y.

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

Naylor, E. J.

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

Philipson, B. T.

B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
[CrossRef] [PubMed]

Stanworth, A.

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

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Valentin, G.

G. Valentin, “Neue Untersuchungen Über die Polarisations-Erscheinungen der Krystalllinsen des Menschen und der Thiere,” Arch. Ophthalmol. 4, 227–268 (1859).

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]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Appl. Opt.

Arch. Ophthalmol.

G. Valentin, “Neue Untersuchungen Über die Polarisations-Erscheinungen der Krystalllinsen des Menschen und der Thiere,” Arch. Ophthalmol. 4, 227–268 (1859).

Exp. Eye Res.

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 the birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1979).
[CrossRef] [PubMed]

B. T. Philipson, L. Hanninen, E. A. Balazs, “Cell contacts in human and bovine lenses,” Exp. Eye Res. 21, 205–219 (1975).
[CrossRef] [PubMed]

J. Exp. Biol.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Philos. Trans. R. Soc. London Ser. B

D. Brewster, “On the structure of the crystalline lens in fishes and quadrupeds, as ascertained by its action on polarized light,” Philos. Trans. R. Soc. London Ser. B 106, 311–317 (1816).
[CrossRef]

Other

F. A. Bettelheim, “Physical basis of lens transparency” in The Ocular Lens, Structure, Function and Pathology, H. Maisel, ed. (Academic, New York, 1985).

As the terminology might be confusing, we emphasize the distinction between optical axis (central line of the exit optics) and optic axis (each of both specific directions in the biaxially double-refracting cornea; a light beam traveling along an optic axis undergoes no retardation).

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Both retarders are quarter-wave plates for 514 nm. We used the same retarders at 488 and 568 nm for which the phase shifts deviate considerably from 90 deg, so corrections had to be made during the data processing. Mueller-matrix ellipsometry meets this demand by including wavelength-dependent deficiency parameters in the conversion from the Fourier amplitudes to the matrix elements.9Likewise, any possible inexactitude in the phase shifts for 514 nm is eliminated.

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

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Figures (2)

Fig. 1
Fig. 1

Schematic view of the setup. In the entrance optics the polarization-state generator (PSG) consists of an Ar–Kr laser, a linear polarizer (LP), and a retardation platelet (RP). Another combination RP and LP, in reversed order, and a photomultiplier (PM) constitute the polarization-state detector (PSD). The field stop (FS) and the aperture stop (AS) together with the imaging lenses are between the PSG and the PSD.

Fig. 2
Fig. 2

Configuration of exit position in the cornea (E), relevant planes and reference xyz frame valid for the right eye. (a)–(c) Front views of the flattened corneal surface. (d) Features of plane l. (e) Features of plane p. (f) This constructed coordinate system aids in the calculation of the retardation-determining angle ϕ. Symbols are defined in Appendix A.

Tables (2)

Tables Icon

Table 1 Retardations (φ) and Eigenvectors (Ψ,χ) for Total Eye Passages for the Unaccommodated State (0 Diopters) and the Accommodated State (5 Diopters)

Tables Icon

Table 2 Averaged Differences

Equations (13)

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arctan ( ± 0.75 mm / 1.80 mm ) = ± 22.5 deg ,
( sin β , 0 , cos β ) , ( sin β , 0 , cos β ) , ( cos α * sin θ , sin α * sin θ , cos θ ) .
arcsin ( 1.8 mm / 7.8 m ) = 13.3 deg
13.3 deg + arctan ( 1.8 mm / 0.2 m ) = 13.8 deg
δ = ( 360 * l / λ ) * ( n z n x ) * sin ( ϕ 1 ) * sin ( ϕ 2 )
ϕ 1 = arccos ( 0.981 ) = 11.3 deg , ϕ 2 = arccos ( 0.900 ) = 25.8 deg .
δ ( 0 diopter ) = 45.4 deg .
ϕ 1 = arccos ( 0.990 ) = 8.1 deg , ϕ 2 = arccos ( 0.891 ) = 27.0 deg .
δ ( 0 diopter ) = 34.0 deg .
ϕ 1 = arccos ( 0.981 ) = 11.1 deg , ϕ 2 = arccos ( 0.897 ) = 26.2 deg .
δ ( 5 diopter ) = 45.3 deg .
ϕ 1 = arccos ( 0.991 ) = 7.7 deg , ϕ 2 = arccos ( 0.888 ) = 27.4 deg .
δ ( 5 diopter ) = 32.9 deg .

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