Abstract

Haidinger's brushes are an entoptic effect of the human visual system that enables us to detect polarized light. However, individual perceptions of Haidinger's brushes can vary significantly. We find that the birefringence of the cornea influences the rotational motion and the contrast of Haidinger's brushes and may offer an explanation for individual differences. We have devised an experimental setup to simulate various phase shifts of the cornea and found a switching effect in the rotational dynamics of Haidinger's brushes. In addition, age related macular degeneration reduces the polarization effect of the macula and thus also leads to changes in the brush pattern.

© 2007 Optical Society of America

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References

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  1. H. Helmholtz, Treatise on Physiological Optics (Optical Society of America, 1924), Vol. 2, pp. 301-307.
  2. R. A. Bone, "The role of the macular pigment in the detection of polarized light," Vision Res. 20, 213-220 (1980).
    [CrossRef] [PubMed]
  3. R. A. Bone and J. T. Landrum, "Macular pigment in Henle fiber membranes: a model for Haidinger brushes," Vision Res. 24, 103-108 (1984).
    [CrossRef] [PubMed]
  4. G. P. Misson, "Form and behavior of Haidinger's brushes," Ophthalmic Physiol. Opt. 13, 392-396 (1993).
    [CrossRef] [PubMed]
  5. G. P. Misson, "A Mueller matrix model of Haidinger's brushes," Ophthalmic Physiol. Opt. 23, 441-447 (2003).
    [CrossRef] [PubMed]
  6. G. Wald, "Human vision and the spectrum," Science 101, 653-658 (1945).
    [CrossRef] [PubMed]
  7. G. Wald, "The photochemistry of vision," Doc. Ophthalmol. 3, 94-137 (1945).
    [CrossRef]
  8. R. A. Bone, J. T. Landrum, and S. L. Tarsis, "Preliminary identification of the human macular pigment," Vision Res. 25, 1531-1535 (1985).
    [CrossRef] [PubMed]
  9. N. I. Krinsky, J. T. Landrum, and R. A. Bone, "Biologic mechanism of the protective role of lutein and zeaxanthen in the eye," Annu. Rev. Nutr. 23, 171-201 (2003).
    [CrossRef] [PubMed]
  10. C. C. Shute, "Haidinger's brushes and predominant orientation of collagen in corneal stroma," Nature 250, 163-164 (1974).
    [CrossRef] [PubMed]
  11. R. W. Knighton and X. R. Huang, "Linear birefringence of the central human cornea," Invest. Ophthalmol. Visual Sci. 43, 82-86 (2002).
  12. G. Ramachandran and S. Ramaseshan, in Encyclopedia of Physics, S. Flügge, ed. (Springer, 1961), Vol. XXV/1, pp. 1-14.
  13. I. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathematik, 20th ed. (Verlag Nauka and Teubner Verlagsgesellschaft (1981).
  14. R. A. Bone and J. T. Landrum, "Dichroism of lutein: a possible basis for Haidinger's brushes," Appl. Opt. 22, 775-776 (1983).
    [CrossRef] [PubMed]
  15. S. Arjmandi, K. Dholakia, W. Dultz, and H. Schmitzer, "Angular velocity oscillations of birefringent platelets from spin angular momentum transfer of a photon flux," presented at the International Conference of the Sciences, Waikiki, Hawaii, 15-18 January 2004.
  16. G. Boehm, "Ueber maculare (Haidinger'sche) polarisationsbüschel und über einen polarisationsoptischen Fehler der Auges," Acta Ophthalmol. 18, 109-142 (1940).
  17. E. J. Naylor and A. Stanworth, "Retinal pigment and the Haidinger effect," J. Physiol. 124, 543-552 (1954).
    [PubMed]
  18. H. B. K. 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, 49-57 (1988).
    [CrossRef] [PubMed]
  19. R. P. Hemenger, "Dichroism of the macular pigment and Haidinger's brushes," J. Opt. Soc. Am. 72, 734-737 (1982).
    [CrossRef] [PubMed]
  20. A. Stanworth and E. J. Naylor, "Haidinger's brushes and the retinal receptors," Br. J. Ophthamol. 34, 282-291 (1950).
    [CrossRef]
  21. B. F. Hochheimer and H. A. Kues, "Retinal polarization effects," Appl. Opt. 21, 3811-3818 (1982).
    [CrossRef] [PubMed]
  22. D. M. Summers, G. B. Friedman, and R. M. Clements, "Physical model for Haidinger's Brushes," J. Opt. Soc. Am. 60, 271-272 (1970).
    [CrossRef] [PubMed]
  23. Frank Woolley & Co. Inc., 529 Franklin Street, Reading, Pa. 19602. Their polarizers are azimuthally polarizing, which just flips the results by 90°.
  24. E. Myrowitz, "A recent explanation of Haidinger's brushes and their clinical use," Am. J. Optom. Physiol. Opt. 56, 305-308 (1979).
  25. J. R. Griffin, Binocular Anomalies: Procedures for Vision Therapy (Professional Press, 1976).
  26. A. Stanworth and E. J. Naylor, "The measurement and clinical significance of the Haidinger effect," Trans. Ophthalmol. Soc. U.K. 75, 67-79 (1955).
  27. A. Weber, A. E. Elsner, M. Miura, S. Kompa, and M. C. Cheney, "Relationship between foveal birefringence and visual acuity in neovascular age-related macular degeneration," Eye 21, 353-361, doi:10.1038/sj.eye.6702203 (2007).
    [CrossRef]
  28. R. W. Smith and R. A. Weale, "A new method for the determination of the birefringence of the intact human preretinal media," J. Physiol. 246, 37-38 (1975).
  29. Ann E. Elsner, Indiana University School of Optometry (personal communication, 2006).

2007

A. Weber, A. E. Elsner, M. Miura, S. Kompa, and M. C. Cheney, "Relationship between foveal birefringence and visual acuity in neovascular age-related macular degeneration," Eye 21, 353-361, doi:10.1038/sj.eye.6702203 (2007).
[CrossRef]

2003

G. P. Misson, "A Mueller matrix model of Haidinger's brushes," Ophthalmic Physiol. Opt. 23, 441-447 (2003).
[CrossRef] [PubMed]

N. I. Krinsky, J. T. Landrum, and R. A. Bone, "Biologic mechanism of the protective role of lutein and zeaxanthen in the eye," Annu. Rev. Nutr. 23, 171-201 (2003).
[CrossRef] [PubMed]

2002

R. W. Knighton and X. R. Huang, "Linear birefringence of the central human cornea," Invest. Ophthalmol. Visual Sci. 43, 82-86 (2002).

1993

G. P. Misson, "Form and behavior of Haidinger's brushes," Ophthalmic Physiol. Opt. 13, 392-396 (1993).
[CrossRef] [PubMed]

1988

1985

R. A. Bone, J. T. Landrum, and S. L. Tarsis, "Preliminary identification of the human macular pigment," Vision Res. 25, 1531-1535 (1985).
[CrossRef] [PubMed]

1984

R. A. Bone and J. T. Landrum, "Macular pigment in Henle fiber membranes: a model for Haidinger brushes," Vision Res. 24, 103-108 (1984).
[CrossRef] [PubMed]

1983

1982

1980

R. A. Bone, "The role of the macular pigment in the detection of polarized light," Vision Res. 20, 213-220 (1980).
[CrossRef] [PubMed]

1975

R. W. Smith and R. A. Weale, "A new method for the determination of the birefringence of the intact human preretinal media," J. Physiol. 246, 37-38 (1975).

1974

C. C. Shute, "Haidinger's brushes and predominant orientation of collagen in corneal stroma," Nature 250, 163-164 (1974).
[CrossRef] [PubMed]

1970

1955

A. Stanworth and E. J. Naylor, "The measurement and clinical significance of the Haidinger effect," Trans. Ophthalmol. Soc. U.K. 75, 67-79 (1955).

1954

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

1950

A. Stanworth and E. J. Naylor, "Haidinger's brushes and the retinal receptors," Br. J. Ophthamol. 34, 282-291 (1950).
[CrossRef]

1945

G. Wald, "Human vision and the spectrum," Science 101, 653-658 (1945).
[CrossRef] [PubMed]

G. Wald, "The photochemistry of vision," Doc. Ophthalmol. 3, 94-137 (1945).
[CrossRef]

1940

G. Boehm, "Ueber maculare (Haidinger'sche) polarisationsbüschel und über einen polarisationsoptischen Fehler der Auges," Acta Ophthalmol. 18, 109-142 (1940).

Acta Ophthalmol.

G. Boehm, "Ueber maculare (Haidinger'sche) polarisationsbüschel und über einen polarisationsoptischen Fehler der Auges," Acta Ophthalmol. 18, 109-142 (1940).

Annu. Rev. Nutr.

N. I. Krinsky, J. T. Landrum, and R. A. Bone, "Biologic mechanism of the protective role of lutein and zeaxanthen in the eye," Annu. Rev. Nutr. 23, 171-201 (2003).
[CrossRef] [PubMed]

Appl. Opt.

Br. J. Ophthamol.

A. Stanworth and E. J. Naylor, "Haidinger's brushes and the retinal receptors," Br. J. Ophthamol. 34, 282-291 (1950).
[CrossRef]

Doc. Ophthalmol.

G. Wald, "The photochemistry of vision," Doc. Ophthalmol. 3, 94-137 (1945).
[CrossRef]

Eye

A. Weber, A. E. Elsner, M. Miura, S. Kompa, and M. C. Cheney, "Relationship between foveal birefringence and visual acuity in neovascular age-related macular degeneration," Eye 21, 353-361, doi:10.1038/sj.eye.6702203 (2007).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

R. W. Knighton and X. R. Huang, "Linear birefringence of the central human cornea," Invest. Ophthalmol. Visual Sci. 43, 82-86 (2002).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol.

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

R. W. Smith and R. A. Weale, "A new method for the determination of the birefringence of the intact human preretinal media," J. Physiol. 246, 37-38 (1975).

Nature

C. C. Shute, "Haidinger's brushes and predominant orientation of collagen in corneal stroma," Nature 250, 163-164 (1974).
[CrossRef] [PubMed]

Ophthalmic Physiol. Opt.

G. P. Misson, "Form and behavior of Haidinger's brushes," Ophthalmic Physiol. Opt. 13, 392-396 (1993).
[CrossRef] [PubMed]

G. P. Misson, "A Mueller matrix model of Haidinger's brushes," Ophthalmic Physiol. Opt. 23, 441-447 (2003).
[CrossRef] [PubMed]

Science

G. Wald, "Human vision and the spectrum," Science 101, 653-658 (1945).
[CrossRef] [PubMed]

Trans. Ophthalmol. Soc. U.K.

A. Stanworth and E. J. Naylor, "The measurement and clinical significance of the Haidinger effect," Trans. Ophthalmol. Soc. U.K. 75, 67-79 (1955).

Vision Res.

R. A. Bone, "The role of the macular pigment in the detection of polarized light," Vision Res. 20, 213-220 (1980).
[CrossRef] [PubMed]

R. A. Bone and J. T. Landrum, "Macular pigment in Henle fiber membranes: a model for Haidinger brushes," Vision Res. 24, 103-108 (1984).
[CrossRef] [PubMed]

R. A. Bone, J. T. Landrum, and S. L. Tarsis, "Preliminary identification of the human macular pigment," Vision Res. 25, 1531-1535 (1985).
[CrossRef] [PubMed]

Other

H. Helmholtz, Treatise on Physiological Optics (Optical Society of America, 1924), Vol. 2, pp. 301-307.

G. Ramachandran and S. Ramaseshan, in Encyclopedia of Physics, S. Flügge, ed. (Springer, 1961), Vol. XXV/1, pp. 1-14.

I. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathematik, 20th ed. (Verlag Nauka and Teubner Verlagsgesellschaft (1981).

S. Arjmandi, K. Dholakia, W. Dultz, and H. Schmitzer, "Angular velocity oscillations of birefringent platelets from spin angular momentum transfer of a photon flux," presented at the International Conference of the Sciences, Waikiki, Hawaii, 15-18 January 2004.

Ann E. Elsner, Indiana University School of Optometry (personal communication, 2006).

Frank Woolley & Co. Inc., 529 Franklin Street, Reading, Pa. 19602. Their polarizers are azimuthally polarizing, which just flips the results by 90°.

E. Myrowitz, "A recent explanation of Haidinger's brushes and their clinical use," Am. J. Optom. Physiol. Opt. 56, 305-308 (1979).

J. R. Griffin, Binocular Anomalies: Procedures for Vision Therapy (Professional Press, 1976).

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Figures (8)

Fig. 1
Fig. 1

Poincaré sphere. The poles L and R represent left and right circularly polarized light. The bold arrows mark the position of linear polarization at horizontal and vertical orientation. The effect of a birefringent plate with retardation Δ on a light wave P 0 ( 2 δ 0 , 2 θ 0 ) is simple: the exiting polarization P 1 ( 2 δ 1 , 2 θ 1 ) is found by rotating P 0 counterclockwise by the angle Δ around the fast axis F. The dashed arcs 2 δ 1 and 2 θ 1 are the latitude (ellipticity) and longitude (orientation) of the new polarization state P 1 ( 2 δ 1 , 2 θ 1 ) .

Fig. 2
Fig. 2

(Color online) (a) Sequence of experimentally generated photographs and calculated polar intensity patterns show the brush pattern when linearly polarized light enters the eye at orientation angles 90°, 120°, 135°, 150°, and 180° with respect to the fast axis of the cornea. The dark brush is perpendicular to the incoming polarization. Panels progress from top to bottom: the phase shift of the cornea is Δ = 0 λ . The brush rotates uniformly with no loss in contrast. (b) Phase shift is Δ = 0.12 λ . The contrast decreases to 0.7 at 45 °.

Fig. 3
Fig. 3

(Color online) (a) Phase shift is Δ = 0.18 λ . In panels 2 and 4 it can be seen that the maximum of the red brush does not follow the incoming polarization. In panel 2 the incoming polarization is at 120° whereas the maximum is at 108°. In panel 4 the incoming polarization is at 150° whereas the maximum is at 161°. The contrast decreases to 0.4 at 45°. (b) Phase shift is Δ = 0.25 λ . The brush switches between perpendicular orientations and completely loses contrast for an incoming linear polarization at 45°.

Fig. 4
Fig. 4

(Color online) Phase shift is Δ = 0.32 λ . The brush rotates backward with respect to the incoming polarization. The polarization exiting the cornea has the same ellipticity as for Δ = 0.18 λ (but different orientation). Therefore, according to Eq. (5), the loss in contrast is equivalent to the loss in contrast in Fig. 3(a).

Fig. 5
Fig. 5

Calculated polar intensity patterns show how the brush pattern loses contrast if the macula polarizes only partially. The incoming polarization is linear at 0° to the fast axis of the cornea. The waist of the pattern, which indicates the direction of the dark brush, widens with transmission coefficients k A ¯ increasing in steps of 0.1. For k A ¯ = 0.3 (dashed curve) the contrast of the pattern has already decreased to 0.5, which would resemble the brush pattern of Fig. 3(b) at 60°.

Fig. 6
Fig. 6

Experimental setup. A Babinet–Soleil compensator simulated the cornea. An acetate radial analyzer served as macula. The phase shift was varied between 0 λ and λ∕4. For each phase shift we rotated the linear polarization of the incident light in steps of 5° and photographed the resulting intensity pattern behind the radial analyzer.

Fig. 7
Fig. 7

Large birefringence of the cornea leads to a switching of the brush. This nonlinear dynamics is given by the orientation θ 1 of the light that has passed the cornea [Eq. (2)]. Data points of the polarization state were taken with a polarimeter. The solid line and solid curves belong to nearby solid data points, the dashed line and dashed curves belong to hollow data points.

Fig. 8
Fig. 8

Contrast cos ( δ 1 ) [Eq. (6)] of the brush is lower than one half when the corneal birefringence exceeds 0.17λ. The ellipticity δ 1 was measured with a polarimeter. Solid curves belong to nearby solid data points, the dashed line and dashed curves belong to hollow data points.

Equations (8)

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δ 1 = 1 2   arcsin ( sin   Δ   sin   2 θ 0 ) ,
θ 1 = 1 2   arccos ( cos ( 2 θ 0 ) 1 sin 2 Δ sin 2 2 θ 0 ) .
I A ( Φ ) = 1 2 + [ 1 2   cos   2 δ 1   cos   2 ( θ 1 Φ ) ] .
I A ( Φ ) = 1 2 + 1 2 1 sin 2 Δ sin 2 2 θ 0 × cos ( 2 Φ arccos   cos   2 θ 0 1 sin 2 Δ sin 2 2 θ 0 ) .
contrast   I ( Φ max ) I ( Φ min ) I ( Φ max ) + I ( Φ min ) = 1 sin 2 Δ sin 2 2 θ 0 = cos ( δ 1 ) ,
I ( Φ ) = k A I A ( Φ ) + k A ¯ I A ¯ ( Φ ) ,
k A ¯ I A ¯ ( Φ ) = k A ¯ I A ( Φ + π ) .
J z = N ħ 2 ( sin   20 sin   2 δ ) = N ħ 2 ( sin   2 δ ) ,

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