Abstract

Haidinger’s brushes (HB) are entoptic phenomena resulting from differential absorption of linear polarized light by the human macula. Computational models have assisted in understanding the behavior of these subjective phenomena but have been limited in their application. This study presents a revised computational model that incorporates known determinants of the form and behavior of HB. The model generates both static and animated simulations of HB that can be quantified by their density, contrast, and radial/circumferential extent. Measured physiological parameters are used to demonstrate the dependency of HB on macular pigment (MP) density, MP distribution, and ocular retardation. Physiological variations in these parameters explain the reported variations in the perception of HB.

© 2018 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Haidinger’s brushes elicited at varying degrees of polarization rapidly and easily assesses total macular pigmentation

Shelby E. Temple, Nicholas W. Roberts, and Gary P. Misson
J. Opt. Soc. Am. A 36(4) B123-B131 (2019)

Nonlinearity in the rotational dynamics of Haidinger's brushes

Mark Rothmayer, Wolfgang Dultz, Erna Frins, Qiwen Zhan, Dennis Tierney, and Heidrun Schmitzer
Appl. Opt. 46(29) 7244-7251 (2007)

Retinal polarization effects

B. F. Hochheimer and Henry A. Kues
Appl. Opt. 21(21) 3811-3818 (1982)

References

  • View by:
  • |
  • |
  • |

  1. W. Haidinger, “Ueber das directe Erkennen des polarisirten Lights und der Lage der Polarisationsebene,” Ann. Phys. Berlin 139, 29–39 (1844).
    [Crossref]
  2. J. McGregor, S. E. Temple, and G. Horváth, “Human polarization sensitivity,” in Polarized Light and Polarization Vision in Animal Sciences, G. Horváth, ed., 2nd ed. (Springer, 2014), pp. 303–315.
  3. W. Haidinger, “Ueber complementäre Farbeneindrücke bei Beobachtung der Lichtpolarisationsbüschel,” Ann. Phys. Berlin 143, 435–437 (1846).
    [Crossref]
  4. H. de Vries, A. Spoor, and R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
    [Crossref]
  5. E. J. Naylor and A. Stanworth, “Retinal pigment and the Haidinger effect,” J. Physiol. 124, 543–552 (1954).
    [Crossref]
  6. W. Haidinger, “Dauer des Eindruckes der Polarisationsbüschel auf die Netzhaut,” Ann. Phys. 169, 318–320 (1854).
    [Crossref]
  7. G. Boehm, “Über maculare (Haidinger’sche) Polarizationsbüschel und über eine polarizationsoptischen Fehler der Auges,” Acta Ophthalmol. 18, 109–142 (1940).
    [Crossref]
  8. C. C. Shute, “Haidinger’s brushes and predominant orientation of collagen in corneal stroma,” Nature 250, 163–164 (1974).
    [Crossref]
  9. W. Haidinger, “Beobachtung der Licht-Polarisations-Büschel auf Flächen, welche das Licht in zwei senkrecht auf einander stehenden Richtungen polarisiren,” Ann. Phys. Berlin 144, 305–319 (1846).
    [Crossref]
  10. J. C. Maxwell, “Manuscript on experiments on the cause of Haidinger’s brushes,” in The Scientific Letters and Papers of James Clerk Maxwell (Taylor and Francis, 1850), pp. 199–204.
  11. H. Helmholtz, Treatise on Physiological Optics, 3rd German ed. (Optical Society of America, 1924), Vol. 2, pp. 304–308.
  12. M. Goldschmidt, “A new test for function of the macula lutea,” Arch. Ophthalmol. 44, 129–135 (1950).
    [Crossref]
  13. H. W. Forster, “The clinical use of the Haidinger’s brushes phenomenon,” Am. J. Ophthalmol. 38, 661–665 (1954).
    [Crossref]
  14. A. Stanworth and E. J. Naylor, “The measurement and clinical significance of the Haidinger effect,” Trans. Ophth. Soc. U.K. 75, 67–79 (1955).
  15. R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–220 (1980).
    [Crossref]
  16. R. A. Bone and J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
    [Crossref]
  17. P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
    [Crossref]
  18. G. P. Misson, “Form and behaviour of Haidinger’s brushes,” Ophthal. Physiol. Opt. 13, 392–396 (1993).
    [Crossref]
  19. G. P. Misson, “A Mueller matrix model of Haidinger’s brushes,” Ophthal. Physiol. Opt. 23, 441–447 (2003).
    [Crossref]
  20. M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
    [Crossref]
  21. L. J. Bour, “Polarized light and the eye,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, 1991), pp. 310–325.
  22. D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2010).
  23. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).
  24. W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, 1962).
  25. R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43, 82–86 (2002).
  26. J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55, 849–859 (2008).
    [Crossref]
  27. 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]
  28. M. F. Land and D. E. Nilsson, Animal Eyes, Oxford Animal Biology Series (Oxford University, 2002).
  29. J. B. R. Hammond, B. R. Wooten, and D. M. Snodderly, “Individual variations in the spatial profile of human macular pigment,” J. Opt. Soc. Am. A 14, 1187–1196 (1997).
    [Crossref]
  30. P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
    [Crossref]
  31. M. Sharifzadeh, P. S. Bernstein, and W. Gellermann, “Nonmydriatic fluorescence-based quantitative imaging of human macular pigment distributions,” J. Opt. Soc. Am. A 23, 2373–2387 (2006).
    [Crossref]
  32. T. T. Berendschot and D. van Norren, “Macular pigment shows ringlike structures,” Invest. Ophthalmol. Vis. Sci. 47, 709–714 (2006).
    [Crossref]
  33. A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
    [Crossref]
  34. R. A. Bone and J. T. Landrum, “Distribution of macular pigment components, zeaxanthin and lutein, in human retina,” Methods Enzymol. 213, 360–366 (1992).
    [Crossref]
  35. R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
    [Crossref]
  36. S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
    [Crossref]
  37. R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16, 13738–13751 (2008).
    [Crossref]
  38. M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
    [Crossref]
  39. B. J. Hammond and K. Fuld, “Interocular differences in macular pigment density,” Invest. Ophthalmol. Vis. Sci. 33, 350–355 (1992).
  40. B. F. Hochheimer, “Polarized light retinal photography of a monkey eye,” Vision Res. 18, 19–23 (1978).
    [Crossref]
  41. B. F. Hochheimer and H. A. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
    [Crossref]
  42. A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
    [Crossref]

2016 (1)

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

2015 (1)

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

2010 (1)

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

2008 (3)

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55, 849–859 (2008).
[Crossref]

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16, 13738–13751 (2008).
[Crossref]

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

2007 (2)

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

M. Rothmayer, W. Dultz, E. Frins, Q. Zhan, D. Tierney, and H. Schmitzer, “Nonlinearity in the rotational dynamics of Haidinger’s brushes,” Appl. Opt. 46, 7244–7251 (2007).
[Crossref]

2006 (2)

2003 (2)

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

G. P. Misson, “A Mueller matrix model of Haidinger’s brushes,” Ophthal. Physiol. Opt. 23, 441–447 (2003).
[Crossref]

2002 (2)

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

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

1997 (1)

1993 (1)

G. P. Misson, “Form and behaviour of Haidinger’s brushes,” Ophthal. Physiol. Opt. 13, 392–396 (1993).
[Crossref]

1992 (2)

B. J. Hammond and K. Fuld, “Interocular differences in macular pigment density,” Invest. Ophthalmol. Vis. Sci. 33, 350–355 (1992).

R. A. Bone and J. T. Landrum, “Distribution of macular pigment components, zeaxanthin and lutein, in human retina,” Methods Enzymol. 213, 360–366 (1992).
[Crossref]

1988 (1)

1984 (1)

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

1982 (1)

1980 (1)

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–220 (1980).
[Crossref]

1978 (1)

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

1974 (1)

C. C. Shute, “Haidinger’s brushes and predominant orientation of collagen in corneal stroma,” Nature 250, 163–164 (1974).
[Crossref]

1955 (1)

A. Stanworth and E. J. Naylor, “The measurement and clinical significance of the Haidinger effect,” Trans. Ophth. Soc. U.K. 75, 67–79 (1955).

1954 (2)

H. W. Forster, “The clinical use of the Haidinger’s brushes phenomenon,” Am. J. Ophthalmol. 38, 661–665 (1954).
[Crossref]

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

1953 (1)

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

1950 (1)

M. Goldschmidt, “A new test for function of the macula lutea,” Arch. Ophthalmol. 44, 129–135 (1950).
[Crossref]

1940 (1)

G. Boehm, “Über maculare (Haidinger’sche) Polarizationsbüschel und über eine polarizationsoptischen Fehler der Auges,” Acta Ophthalmol. 18, 109–142 (1940).
[Crossref]

1854 (1)

W. Haidinger, “Dauer des Eindruckes der Polarisationsbüschel auf die Netzhaut,” Ann. Phys. 169, 318–320 (1854).
[Crossref]

1846 (2)

W. Haidinger, “Ueber complementäre Farbeneindrücke bei Beobachtung der Lichtpolarisationsbüschel,” Ann. Phys. Berlin 143, 435–437 (1846).
[Crossref]

W. Haidinger, “Beobachtung der Licht-Polarisations-Büschel auf Flächen, welche das Licht in zwei senkrecht auf einander stehenden Richtungen polarisiren,” Ann. Phys. Berlin 144, 305–319 (1846).
[Crossref]

1844 (1)

W. Haidinger, “Ueber das directe Erkennen des polarisirten Lights und der Lage der Polarisationsebene,” Ann. Phys. Berlin 139, 29–39 (1844).
[Crossref]

Alexander, R.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

Artal, P.

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55, 849–859 (2008).
[Crossref]

Berendschot, T. T.

T. T. Berendschot and D. van Norren, “Macular pigment shows ringlike structures,” Invest. Ophthalmol. Vis. Sci. 47, 709–714 (2006).
[Crossref]

Bernstein, P. S.

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

M. Sharifzadeh, P. S. Bernstein, and W. Gellermann, “Nonmydriatic fluorescence-based quantitative imaging of human macular pigment distributions,” J. Opt. Soc. Am. A 23, 2373–2387 (2006).
[Crossref]

Bird, A. C.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Boehm, G.

G. Boehm, “Über maculare (Haidinger’sche) Polarizationsbüschel und über eine polarizationsoptischen Fehler der Auges,” Acta Ophthalmol. 18, 109–142 (1940).
[Crossref]

Bone, R. A.

R. A. Bone and J. T. Landrum, “Distribution of macular pigment components, zeaxanthin and lutein, in human retina,” Methods Enzymol. 213, 360–366 (1992).
[Crossref]

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

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–220 (1980).
[Crossref]

Bour, L. J.

L. J. Bour, “Polarized light and the eye,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, 1991), pp. 310–325.

Bowd, C.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

Brink, H. B. K.

Buck, J.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Bueno, J. M.

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55, 849–859 (2008).
[Crossref]

Cavuoto, L. A.

Charbel Issa, P.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Cheney, M. C.

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

de Vries, H.

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

Delori, F. C.

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

Dultz, W.

Elsner, A. E.

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

Fitzke, F. W.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Forster, H. W.

H. W. Forster, “The clinical use of the Haidinger’s brushes phenomenon,” Am. J. Ophthalmol. 38, 661–665 (1954).
[Crossref]

Frins, E.

Fuld, K.

B. J. Hammond and K. Fuld, “Interocular differences in macular pigment density,” Invest. Ophthalmol. Vis. Sci. 33, 350–355 (1992).

Gellermann, W.

Gliem, M.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Goldschmidt, M.

M. Goldschmidt, “A new test for function of the macula lutea,” Arch. Ophthalmol. 44, 129–135 (1950).
[Crossref]

Goldstein, D. H.

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2010).

Graham, L.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Greenfield, D. S.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

Haidinger, W.

W. Haidinger, “Dauer des Eindruckes der Polarisationsbüschel auf die Netzhaut,” Ann. Phys. 169, 318–320 (1854).
[Crossref]

W. Haidinger, “Beobachtung der Licht-Polarisations-Büschel auf Flächen, welche das Licht in zwei senkrecht auf einander stehenden Richtungen polarisiren,” Ann. Phys. Berlin 144, 305–319 (1846).
[Crossref]

W. Haidinger, “Ueber complementäre Farbeneindrücke bei Beobachtung der Lichtpolarisationsbüschel,” Ann. Phys. Berlin 143, 435–437 (1846).
[Crossref]

W. Haidinger, “Ueber das directe Erkennen des polarisirten Lights und der Lage der Polarisationsebene,” Ann. Phys. Berlin 139, 29–39 (1844).
[Crossref]

Hammond, B. J.

B. J. Hammond and K. Fuld, “Interocular differences in macular pigment density,” Invest. Ophthalmol. Vis. Sci. 33, 350–355 (1992).

Hammond, J. B. R.

Harmening, W. M.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Helmholtz, H.

H. Helmholtz, Treatise on Physiological Optics, 3rd German ed. (Optical Society of America, 1924), Vol. 2, pp. 304–308.

Hermans, P.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

Hochheimer, B. F.

B. F. Hochheimer and H. A. Kues, “Retinal polarization effects,” Appl. Opt. 21, 3811–3818 (1982).
[Crossref]

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

Holder, G. E.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Holz, F. G.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Horváth, G.

J. McGregor, S. E. Temple, and G. Horváth, “Human polarization sensitivity,” in Polarized Light and Polarization Vision in Animal Sciences, G. Horváth, ed., 2nd ed. (Springer, 2014), pp. 303–315.

Huang, X. R.

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16, 13738–13751 (2008).
[Crossref]

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

Jielof, R.

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

Knighton, R. W.

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16, 13738–13751 (2008).
[Crossref]

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

Kues, H. A.

Kupper, K.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Land, M. F.

M. F. Land and D. E. Nilsson, Animal Eyes, Oxford Animal Biology Series (Oxford University, 2002).

Landrum, J. T.

R. A. Bone and J. T. Landrum, “Distribution of macular pigment components, zeaxanthin and lutein, in human retina,” Methods Enzymol. 213, 360–366 (1992).
[Crossref]

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

Luthert, P.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

Maxwell, J. C.

J. C. Maxwell, “Manuscript on experiments on the cause of Haidinger’s brushes,” in The Scientific Letters and Papers of James Clerk Maxwell (Taylor and Francis, 1850), pp. 199–204.

McGregor, J.

J. McGregor, S. E. Temple, and G. Horváth, “Human polarization sensitivity,” in Polarized Light and Polarization Vision in Animal Sciences, G. Horváth, ed., 2nd ed. (Springer, 2014), pp. 303–315.

McGregor, J. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Miles, C.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Miller, J.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Misson, G. P.

G. P. Misson, “A Mueller matrix model of Haidinger’s brushes,” Ophthal. Physiol. Opt. 23, 441–447 (2003).
[Crossref]

G. P. Misson, “Form and behaviour of Haidinger’s brushes,” Ophthal. Physiol. Opt. 13, 392–396 (1993).
[Crossref]

Moreland, J. D.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Morrissey, T.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Muller, P. L.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Muller, S.

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

Naylor, E. J.

A. Stanworth and E. J. Naylor, “The measurement and clinical significance of the Haidinger effect,” Trans. Ophth. Soc. U.K. 75, 67–79 (1955).

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

Nilsson, D. E.

M. F. Land and D. E. Nilsson, Animal Eyes, Oxford Animal Biology Series (Oxford University, 2002).

Pauleikhoff, D.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Richer, S.

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

Roberts, N. W.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Robson, A. G.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

Rothmayer, M.

Schmitzer, H.

Scott-Samuel, N. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Sharifzadeh, M.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, 1962).

Shute, C. C.

C. C. Shute, “Haidinger’s brushes and predominant orientation of collagen in corneal stroma,” Nature 250, 163–164 (1974).
[Crossref]

Snodderly, D. M.

Spoor, A.

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

Stanworth, A.

A. Stanworth and E. J. Naylor, “The measurement and clinical significance of the Haidinger effect,” Trans. Ophth. Soc. U.K. 75, 67–79 (1955).

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

Temple, S. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

J. McGregor, S. E. Temple, and G. Horváth, “Human polarization sensitivity,” in Polarized Light and Polarization Vision in Animal Sciences, G. Horváth, ed., 2nd ed. (Springer, 2014), pp. 303–315.

Tierney, D.

Trieschmann, M.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

van Blokland, G. J.

van Kuijk, F. J. G. M.

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

van Kuijk, F. J. M.

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

van Norren, D.

T. T. Berendschot and D. van Norren, “Macular pigment shows ringlike structures,” Invest. Ophthalmol. Vis. Sci. 47, 709–714 (2006).
[Crossref]

Vannasdale, D. A.

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

Weber, A.

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

Weinreb, R. N.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

Wenzel, A. J.

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

Wooten, B. R.

Zangwill, L. M.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

Zhan, Q.

Acta Ophthalmol. (1)

G. Boehm, “Über maculare (Haidinger’sche) Polarizationsbüschel und über eine polarizationsoptischen Fehler der Auges,” Acta Ophthalmol. 18, 109–142 (1940).
[Crossref]

Am. J. Ophthalmol. (1)

H. W. Forster, “The clinical use of the Haidinger’s brushes phenomenon,” Am. J. Ophthalmol. 38, 661–665 (1954).
[Crossref]

Ann. Phys. (1)

W. Haidinger, “Dauer des Eindruckes der Polarisationsbüschel auf die Netzhaut,” Ann. Phys. 169, 318–320 (1854).
[Crossref]

Ann. Phys. Berlin (3)

W. Haidinger, “Ueber das directe Erkennen des polarisirten Lights und der Lage der Polarisationsebene,” Ann. Phys. Berlin 139, 29–39 (1844).
[Crossref]

W. Haidinger, “Ueber complementäre Farbeneindrücke bei Beobachtung der Lichtpolarisationsbüschel,” Ann. Phys. Berlin 143, 435–437 (1846).
[Crossref]

W. Haidinger, “Beobachtung der Licht-Polarisations-Büschel auf Flächen, welche das Licht in zwei senkrecht auf einander stehenden Richtungen polarisiren,” Ann. Phys. Berlin 144, 305–319 (1846).
[Crossref]

Appl. Opt. (2)

Arch. Ophthalmol. (2)

M. Goldschmidt, “A new test for function of the macula lutea,” Arch. Ophthalmol. 44, 129–135 (1950).
[Crossref]

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120, 901–906 (2002).
[Crossref]

Eye (1)

M. Trieschmann, F. J. G. M. van Kuijk, R. Alexander, P. Hermans, P. Luthert, A. C. Bird, and D. Pauleikhoff, “Macular pigment in the human retina: histological evaluation of localization and distribution,” Eye 22, 132–137 (2007).
[Crossref]

Invest. Ophthalmol. Vis. Sci. (4)

B. J. Hammond and K. Fuld, “Interocular differences in macular pigment density,” Invest. Ophthalmol. Vis. Sci. 33, 350–355 (1992).

T. T. Berendschot and D. van Norren, “Macular pigment shows ringlike structures,” Invest. Ophthalmol. Vis. Sci. 47, 709–714 (2006).
[Crossref]

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

P. L. Muller, S. Muller, M. Gliem, K. Kupper, F. G. Holz, W. M. Harmening, and P. Charbel Issa, “Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity,” Invest. Ophthalmol. Vis. Sci. 57, 1448–1456 (2016).
[Crossref]

J. Mod. Opt. (1)

J. M. Bueno and P. Artal, “Average double-pass ocular diattenuation using foveal fixation,” J. Mod. Opt. 55, 849–859 (2008).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Physiol. (1)

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

Methods Enzymol. (1)

R. A. Bone and J. T. Landrum, “Distribution of macular pigment components, zeaxanthin and lutein, in human retina,” Methods Enzymol. 213, 360–366 (1992).
[Crossref]

Nature (1)

C. C. Shute, “Haidinger’s brushes and predominant orientation of collagen in corneal stroma,” Nature 250, 163–164 (1974).
[Crossref]

Ophthal. Physiol. Opt. (2)

G. P. Misson, “Form and behaviour of Haidinger’s brushes,” Ophthal. Physiol. Opt. 13, 392–396 (1993).
[Crossref]

G. P. Misson, “A Mueller matrix model of Haidinger’s brushes,” Ophthal. Physiol. Opt. 23, 441–447 (2003).
[Crossref]

Opt. Express (1)

Physica (1)

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

Proc. R. Soc. B (1)

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. R. Soc. B 282, 20150338 (2015).
[Crossref]

Trans. Ophth. Soc. U.K. (1)

A. Stanworth and E. J. Naylor, “The measurement and clinical significance of the Haidinger effect,” Trans. Ophth. Soc. U.K. 75, 67–79 (1955).

Vis. Res. (2)

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. G. M. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vis. Res. 43, 1765–1775 (2003).
[Crossref]

P. S. Bernstein, F. C. Delori, S. Richer, F. J. M. van Kuijk, and A. J. Wenzel, “The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders,” Vis. Res. 50, 716–728 (2010).
[Crossref]

Vision Res. (4)

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–220 (1980).
[Crossref]

R. A. Bone and 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]

A. E. Elsner, A. Weber, M. C. Cheney, and D. A. Vannasdale, “Spatial distribution of macular birefringence associated with the Henle fibers,” Vision Res. 48, 2578–2585 (2008).
[Crossref]

Other (8)

J. C. Maxwell, “Manuscript on experiments on the cause of Haidinger’s brushes,” in The Scientific Letters and Papers of James Clerk Maxwell (Taylor and Francis, 1850), pp. 199–204.

H. Helmholtz, Treatise on Physiological Optics, 3rd German ed. (Optical Society of America, 1924), Vol. 2, pp. 304–308.

J. McGregor, S. E. Temple, and G. Horváth, “Human polarization sensitivity,” in Polarized Light and Polarization Vision in Animal Sciences, G. Horváth, ed., 2nd ed. (Springer, 2014), pp. 303–315.

M. F. Land and D. E. Nilsson, Animal Eyes, Oxford Animal Biology Series (Oxford University, 2002).

L. J. Bour, “Polarized light and the eye,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, 1991), pp. 310–325.

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2010).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, 1962).

Supplementary Material (5)

NameDescription
» Visualization 1       Simple HB simulation with no corneal retardation. Density function type E.
» Visualization 2       HB simulation with typical corneal retardation of 50 nm (axis horizontal). Other details as in Visualization 1.
» Visualization 3       HB simulation with high corneal retardation of 100 nm (axis horizontal). Other details as in Visualization 1.
» Visualization 4       HB simulation with high corneal retardation of 100 nm (axis at 15 degrees anticlockwise from horizontal). Other details as in Visualization 1.
» Visualization 5       HB simulation with “quarter wavelength” retardation of 115 nm at an observing wavelength of 460nm (axis horizontal). Other details as in Visualization 1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Components of the HB model for incident linear polarized light with horizontal orientation (ϵ=0). (a) Radial diattenuator (RD) simulation (k1=1, k2=0). (b) Uniform density function D(x,y)=1. Density function for macular pigment density model D1. (c) Radial diattenuator simulation (k1=1, k2=0) with density function D with superimposed 0.75 (outer), 0.50, 0.25 (inner) isotransmission contours. The outer 0.75 contour is used here to define length (L) and width (W) parameters. (d) HB simulation as in (c) but with principal transmittances k1=1, k2=0.88. Horizontal and vertical scales are degrees eccentricity from the center of RD/macula. Gray scale indicates transmission for (a), (c), and (d), and normalized density for (b).
Fig. 2.
Fig. 2. Macular pigment density (MPD function), radial diattenuator (RD), and Haidinger’s brushes (HB) simulations for MPD categories B, C, D and E. Conditions of simulations and scales as in Fig. 1. Horizontal/vertical scale (bottom left) is degrees eccentricity from center of RD/macula. Gray scale is transmission for RD and HB, and density for MPD function.
Fig. 3.
Fig. 3. HB simulations for physiological diattenuations.
Fig. 4.
Fig. 4. RD and HB simulations with retardation and rotating incident polarization. HB simulation for right eye: corneal retardation ϕ=50, 100 nm; azimuth nasally downward (α=15°), k1=1, k2=0.88. Category E MPD function for e-vector rotating between ϵ=0° and ϵ=60°. Scales as in Fig. 2.

Tables (1)

Tables Icon

Table 1. Parameters and Variables Defining MPD

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Sout[x,y,k1,k2,ϕ,α,ϵ]=MM[x,y,k1,k2]MR[ϕ,α]Sin[ϵ].
TH(x,y,k1,k2,ϕ,α,ϵ)=1D(x,y)2(x2+y2).[(2k1k2)(x2+y2)+(k1k2)[cosϕsin(2(αϵ))(sin(2α)(y2x2)2xycos(2α))+cos(2(αϵ))(cos(2α)(y2x2)+2xysin(2α))]],
MPD(x,y)=A110ρ1x2+y2+A210ρ2(x2+y2x2)2.

Metrics