Abstract

An imaging polariscope has been used to analyze the spatially resolved polarization properties of living human corneas. The apparatus is a modified double-pass setup, incorporating a liquid-crystal modulator in the analyzer pathway. Keeping the incident polarization state fixed (first passage), we recorded a series of three images of the pupil’s plane corresponding to independent polarization states of the analyzer unit. Azimuth and retardation at each point of the cornea were calculated from those images. Results show that the magnitude of retardation increases along the radius toward the periphery of the cornea. Left–right eye symmetry in retardation was also found. Maps of azimuth indicate that the direction of the corneal slow axis is nasally downward.

© 2002 Optical Society of America

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2001

R. W. Knighton, X.-R. Huang, D. S. Greenfield, “Linear birefringence measured in the central corneas of a normal population,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S131 (2001).

J. M. Bueno, “Depolarization effects in the human eye,” Vision Res. 41, 2687–2696 (2001).
[CrossRef] [PubMed]

J. M. Bueno, J. W. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

J. M. Bueno, M. C. W. Campbell, “Polarization properties for in vitro human lenses,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S161 (2001).

J. M. Bueno, P. Artal, “Polarization and retinal image quality estimates in the human eye,” J. Opt. Soc. Am. A 18, 489–496 (2001).
[CrossRef]

2000

D. Fonn, J. H. Wang, T. L. Simpson, “Topographical thickness of the epithelium and the total cornea in living human eyes using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 41, S675 (2000).

J. M. Bueno, “Measurement of parameters of polarization in the living human eye using imaging polarimetry,” Vision Res. 40, 3791–3799 (2000).
[CrossRef] [PubMed]

D. S. Greenfield, R. W. Knighton, X.-R. Huang, “Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
[CrossRef] [PubMed]

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000).
[CrossRef]

1999

1998

1997

1996

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

S. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

1995

1992

S. J. Haake, E. A. Patterson, “Photoelastic anaalysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

1990

1987

1986

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

1985

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]

E. Bernabeu, J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. (Paris) 16, 139–141 (1985).
[CrossRef]

1982

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

1981

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

1980

1978

1977

F. A. Bettelheim, K. Mahadeva, “An interpretation of small-angle light-scattering patterns of human cornea,” Invest. Ophthalmol. Visual Sci. 16, 233–236 (1977).

1974

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

1972

D. Kaplan, F. A. Bettelheim, “On the birefringence of bovine cornea,” Exp. Eye Res. 13, 219–226 (1972).
[CrossRef] [PubMed]

1968

G. W. Nyquist, “Stress-induced birefringence of the cornea,” Am. J. Ophthalmol. 65, 398–404 (1968).
[PubMed]

1966

D. Post, J. E. Gurland, “Birefringence of the cat cornea,” Exp. Eye Res. 5, 286–295 (1966).
[CrossRef] [PubMed]

1954

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

1953

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

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

1941

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

1940

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

1815

D. Brewster, “Experiments on the de-polarization of light as exhibited by various mineral, animal and vegetable bodies with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. London 1, 21–53 (1815).

Artal, P.

Azzam, R. M. A.

Bernabeu, E.

E. Bernabeu, J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. (Paris) 16, 139–141 (1985).
[CrossRef]

Bescós, J.

Bettelheim, F. A.

F. A. Bettelheim, K. Mahadeva, “An interpretation of small-angle light-scattering patterns of human cornea,” Invest. Ophthalmol. Visual Sci. 16, 233–236 (1977).

D. Kaplan, F. A. Bettelheim, “On the birefringence of bovine cornea,” Exp. Eye Res. 13, 219–226 (1972).
[CrossRef] [PubMed]

Bille, J. F.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Boehm, G.

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

Born, M.

M. Born, E. Wolf, “Principles of Optics (Pergamon Press, New York, 6th ed., 1980).

Bottinger, J. R.

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]

L. J. Bour, “Polarized light and the eye,” in Vision Optics and Instrumentation, W. N. Charman, ed. (CRC Press, Boston, Mass., 1991), Vol. 1, Chap. 13.

Brewster, D.

D. Brewster, “Experiments on the de-polarization of light as exhibited by various mineral, animal and vegetable bodies with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. London 1, 21–53 (1815).

Bueno, J. M.

J. M. Bueno, J. W. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

J. M. Bueno, “Depolarization effects in the human eye,” Vision Res. 41, 2687–2696 (2001).
[CrossRef] [PubMed]

J. M. Bueno, P. Artal, “Polarization and retinal image quality estimates in the human eye,” J. Opt. Soc. Am. A 18, 489–496 (2001).
[CrossRef]

J. M. Bueno, M. C. W. Campbell, “Polarization properties for in vitro human lenses,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S161 (2001).

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000).
[CrossRef]

J. M. Bueno, “Measurement of parameters of polarization in the living human eye using imaging polarimetry,” Vision Res. 40, 3791–3799 (2000).
[CrossRef] [PubMed]

J. M. Bueno, P. Artal, “Double-pass imaging polarimetry in the human eye,” Opt. Lett. 24, 64–66 (1999).
[CrossRef]

Burk, R. O. W.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Burns, S. A.

Campbell, M. C. W.

J. M. Bueno, M. C. W. Campbell, “Polarization properties for in vitro human lenses,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S161 (2001).

Chipman, R. A.

Chistens-Barry, W. A.

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

Cogan, D. G.

D. G. Cogan, “Some ocular phenomena produced with polarized light,” Arch. Ophthalmol. (Chicago) 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]

Delori, S. F. C.

Delplancke, F.

Donohue, D. J.

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

D. J. Donohue, B. J. Stoyanov, R. L. McCally, R. A. Farrell, “Numerical modeling of the cornea’s lamellar structure and birefringence properties,” J. Opt. Soc. Am. A 12, 1425–1438 (1995).
[CrossRef]

Elsner, A. E.

Farrell, R. A.

R. A. Farrell, R. L. McCally, “Corneal lamelar birefringence—effects of fibril anisotropic permittivity on retardation,” Invest. Ophthalmol. Visual Sci. (Suppl.) 38, S505 (1997).

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

D. J. Donohue, B. J. Stoyanov, R. L. McCally, R. A. Farrell, “Numerical modeling of the cornea’s lamellar structure and birefringence properties,” J. Opt. Soc. Am. A 12, 1425–1438 (1995).
[CrossRef]

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

Fendrich, T.

T. Fendrich, “Fourierellipsometrie,” Diplomarbeit (Universität Heidelberg, Heidelberg, Germany, 1991).

Fischer, J. P.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Fonn, D.

D. Fonn, J. H. Wang, T. L. Simpson, “Topographical thickness of the epithelium and the total cornea in living human eyes using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 41, S675 (2000).

Fry, E. S.

Gil, J. J.

E. Bernabeu, J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. (Paris) 16, 139–141 (1985).
[CrossRef]

Goelz, S.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Goldstein, D. H.

Green, W. J.

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

Greenfield, D. S.

R. W. Knighton, X.-R. Huang, D. S. Greenfield, “Linear birefringence measured in the central corneas of a normal population,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S131 (2001).

D. S. Greenfield, R. W. Knighton, X.-R. Huang, “Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
[CrossRef] [PubMed]

Gurland, J. E.

D. Post, J. E. Gurland, “Birefringence of the cat cornea,” Exp. Eye Res. 5, 286–295 (1966).
[CrossRef] [PubMed]

Haake, S. J.

S. J. Haake, E. A. Patterson, “Photoelastic anaalysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

Haszcz, D.

J. W. Jaronski, H. T. Kasprzak, D. Haszcz, J. Zagorski, “Investigation of the corneal structure by use of phase stepping imaging polarimetry,” in Proceedings of the European Optical Society Topical Meeting in Physiological Optics (European Optical Society, Wroclaw, Poland, 1999), pp. 21–22.

Hatada, T.

Y. Ichihashi, M. H. Khin, K. Ishikawa, T. Hatada, “Birefringence effect of the in vivo cornea,” Opt. Eng. 34, 693–699 (1995).
[CrossRef]

Huang, X.-R.

R. W. Knighton, X.-R. Huang, D. S. Greenfield, “Linear birefringence measured in the central corneas of a normal population,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S131 (2001).

D. S. Greenfield, R. W. Knighton, X.-R. Huang, “Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
[CrossRef] [PubMed]

Ichihashi, Y.

Y. Ichihashi, M. H. Khin, K. Ishikawa, T. Hatada, “Birefringence effect of the in vivo cornea,” Opt. Eng. 34, 693–699 (1995).
[CrossRef]

Ishikawa, K.

Y. Ichihashi, M. H. Khin, K. Ishikawa, T. Hatada, “Birefringence effect of the in vivo cornea,” Opt. Eng. 34, 693–699 (1995).
[CrossRef]

Jaronski, J. W.

J. M. Bueno, J. W. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

J. W. Jaronski, H. T. Kasprzak, “Generalized algorithm for photoelastic measurements based on phase-stepping imaging polarimetry,” Appl. Opt. 38, 7018–7025 (1999).
[CrossRef]

J. W. Jaronski, H. T. Kasprzak, D. Haszcz, J. Zagorski, “Investigation of the corneal structure by use of phase stepping imaging polarimetry,” in Proceedings of the European Optical Society Topical Meeting in Physiological Optics (European Optical Society, Wroclaw, Poland, 1999), pp. 21–22.

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]

Kaplan, D.

D. Kaplan, F. A. Bettelheim, “On the birefringence of bovine cornea,” Exp. Eye Res. 13, 219–226 (1972).
[CrossRef] [PubMed]

Kasprzak, H. T.

J. W. Jaronski, H. T. Kasprzak, “Generalized algorithm for photoelastic measurements based on phase-stepping imaging polarimetry,” Appl. Opt. 38, 7018–7025 (1999).
[CrossRef]

J. W. Jaronski, H. T. Kasprzak, D. Haszcz, J. Zagorski, “Investigation of the corneal structure by use of phase stepping imaging polarimetry,” in Proceedings of the European Optical Society Topical Meeting in Physiological Optics (European Optical Society, Wroclaw, Poland, 1999), pp. 21–22.

Keränen, E.

Khin, M. H.

Y. Ichihashi, M. H. Khin, K. Ishikawa, T. Hatada, “Birefringence effect of the in vivo cornea,” Opt. Eng. 34, 693–699 (1995).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, “Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Knighton, R. W.

R. W. Knighton, X.-R. Huang, D. S. Greenfield, “Linear birefringence measured in the central corneas of a normal population,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S131 (2001).

D. S. Greenfield, R. W. Knighton, X.-R. Huang, “Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
[CrossRef] [PubMed]

Krishnan, S.

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller matrix ellipsometry using the division-of-amplitude photopolarimeter,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, “Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Liu, J.

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]

Love, G. D.

Lu, S.

Mahadeva, K.

F. A. Bettelheim, K. Mahadeva, “An interpretation of small-angle light-scattering patterns of human cornea,” Invest. Ophthalmol. Visual Sci. 16, 233–236 (1977).

Maurice, D. M.

D. M. Maurice, “The cornea and sclera,” in The Eye, H. Davson, ed. (Academic, Orlando, Fla., 1984), pp. 1–158.
[CrossRef]

McCally, R. L.

R. A. Farrell, R. L. McCally, “Corneal lamelar birefringence—effects of fibril anisotropic permittivity on retardation,” Invest. Ophthalmol. Visual Sci. (Suppl.) 38, S505 (1997).

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

D. J. Donohue, B. J. Stoyanov, R. L. McCally, R. A. Farrell, “Numerical modeling of the cornea’s lamellar structure and birefringence properties,” J. Opt. Soc. Am. A 12, 1425–1438 (1995).
[CrossRef]

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

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,” Br. J. Ophthal. 34, 201–211 (1950).
[CrossRef]

Nordine, P. C.

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller matrix ellipsometry using the division-of-amplitude photopolarimeter,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

Nyquist, G. W.

G. W. Nyquist, “Stress-induced birefringence of the cornea,” Am. J. Ophthalmol. 65, 398–404 (1968).
[PubMed]

Patel, J. S.

Patterson, E. A.

S. J. Haake, E. A. Patterson, “Photoelastic anaalysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

Pelz, B.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Post, D.

D. Post, J. E. Gurland, “Birefringence of the cat cornea,” Exp. Eye Res. 5, 286–295 (1966).
[CrossRef] [PubMed]

Prieto, P.

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, “Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Santamaría, J.

Shurcliff, W. A.

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

Shute, C. C. D.

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

Simpson, T. L.

D. Fonn, J. H. Wang, T. L. Simpson, “Topographical thickness of the epithelium and the total cornea in living human eyes using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 41, S675 (2000).

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,” Br. J. Ophthal. 34, 201–211 (1950).
[CrossRef]

Stoyanov, B. J.

Suh, S.-W.

Thompson, R. C.

van Blokland, G. J.

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]

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

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).

van Norren, D.

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

Vargas-Martín, F.

F. Vargas-Martín, P. Prieto, P. Artal, “Correction of the aberrations in the human eye with a liquid-crystal spatial light modulator: limits to performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998).
[CrossRef]

F. Vargas-Martín, “Óptica adaptativa en oftalmoscopia: corrección de las aberraciones del ojo mediante un modulador espacial de cristal líquido,” Tesis Doctoral (Universidad de Murcia, Murcia, Spain, 1999).

Verhelst, S. C.

Wang, J. H.

D. Fonn, J. H. Wang, T. L. Simpson, “Topographical thickness of the epithelium and the total cornea in living human eyes using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 41, S675 (2000).

J. H. Wang, “Corneal and epithelial thickness changes associated with contact lens wear and eye closure comparing optical coherence tomography and optical pachometry,” M.S. thesis (University of Waterloo, Waterloo, Ontario, 2000).

Weschenmoser, C.

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

Wolbarsht, M. L.

Wolf, E.

M. Born, E. Wolf, “Principles of Optics (Pergamon Press, New York, 6th ed., 1980).

Wu, C.

Wu, S.

Yamanashi, B. S.

Ye, C.

C. Ye, E. Keränen, “Nonmechanical rotation of a linear polarizer preceding a photodetector,” J. Opt. Soc. Am. A 14, 682–685 (1997).
[CrossRef]

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
[CrossRef]

Zagorski, J.

J. W. Jaronski, H. T. Kasprzak, D. Haszcz, J. Zagorski, “Investigation of the corneal structure by use of phase stepping imaging polarimetry,” in Proceedings of the European Optical Society Topical Meeting in Physiological Optics (European Optical Society, Wroclaw, Poland, 1999), pp. 21–22.

Zhuang, Z.

Acta Ophthalmol.

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

Am. J. Ophthalmol.

G. W. Nyquist, “Stress-induced birefringence of the cornea,” Am. J. Ophthalmol. 65, 398–404 (1968).
[PubMed]

D. S. Greenfield, R. W. Knighton, X.-R. Huang, “Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry,” Am. J. Ophthalmol. 129, 715–722 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Arch. Ophthalmol. (Chicago)

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

Br. J. Ophthal.

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

Exp. Eye Res.

D. Kaplan, F. A. Bettelheim, “On the birefringence of bovine cornea,” Exp. Eye Res. 13, 219–226 (1972).
[CrossRef] [PubMed]

D. Post, J. E. Gurland, “Birefringence of the cat cornea,” Exp. Eye Res. 5, 286–295 (1966).
[CrossRef] [PubMed]

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

Exp. Mech.

S. J. Haake, E. A. Patterson, “Photoelastic anaalysis of frozen stressed specimens using spectral contents analysis,” Exp. Mech. 32, 266–272 (1992).
[CrossRef]

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

D. Fonn, J. H. Wang, T. L. Simpson, “Topographical thickness of the epithelium and the total cornea in living human eyes using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 41, S675 (2000).

Invest. Ophthalmol. Visual Sci.

F. A. Bettelheim, K. Mahadeva, “An interpretation of small-angle light-scattering patterns of human cornea,” Invest. Ophthalmol. Visual Sci. 16, 233–236 (1977).

Invest. Ophthalmol. Visual Sci. (Suppl.)

R. L. McCally, W. J. Green, W. A. Chistens-Barry, D. J. Donohue, R. A. Farrell, “Birefringence properties of human and rabbit cornea: polarization rotation component,” Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S1007 (1996).

R. A. Farrell, R. L. McCally, “Corneal lamelar birefringence—effects of fibril anisotropic permittivity on retardation,” Invest. Ophthalmol. Visual Sci. (Suppl.) 38, S505 (1997).

R. W. Knighton, X.-R. Huang, D. S. Greenfield, “Linear birefringence measured in the central corneas of a normal population,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S131 (2001).

J. M. Bueno, M. C. W. Campbell, “Polarization properties for in vitro human lenses,” Invest. Ophthalmol. Visual Sci. (Suppl.) 42, S161 (2001).

J. Exp. Biol.

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

J. Opt. (Paris)

E. Bernabeu, J. J. Gil, “An experimental device for the dynamic determination of Mueller matrices,” J. Opt. (Paris) 16, 139–141 (1985).
[CrossRef]

J. Opt. A

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. M. Bueno, P. Artal, “Polarization and retinal image quality estimates in the human eye,” J. Opt. Soc. Am. A 18, 489–496 (2001).
[CrossRef]

F. Vargas-Martín, P. Prieto, P. Artal, “Correction of the aberrations in the human eye with a liquid-crystal spatial light modulator: limits to performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998).
[CrossRef]

C. Ye, E. Keränen, “Nonmechanical rotation of a linear polarizer preceding a photodetector,” J. Opt. Soc. Am. A 14, 682–685 (1997).
[CrossRef]

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, 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]

D. H. Goldstein, R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693–700 (1990).
[CrossRef]

S. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

J. Santamaría, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical-digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[CrossRef] [PubMed]

D. J. Donohue, B. J. Stoyanov, R. L. McCally, R. A. Farrell, “Numerical modeling of the cornea’s lamellar structure and birefringence properties,” J. Opt. Soc. Am. A 12, 1425–1438 (1995).
[CrossRef]

S. A. Burns, S. Wu, S. F. C. Delori, A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[CrossRef]

J. Physiol.

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

Nature (London)

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

Ophthal. Physiol. Opt.

J. M. Bueno, J. W. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

Opt. Eng.

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
[CrossRef]

Y. Ichihashi, M. H. Khin, K. Ishikawa, T. Hatada, “Birefringence effect of the in vivo cornea,” Opt. Eng. 34, 693–699 (1995).
[CrossRef]

Opt. Lett.

Philos. Trans. R. Soc. London

D. Brewster, “Experiments on the de-polarization of light as exhibited by various mineral, animal and vegetable bodies with a reference of the phenomena to the general principles of polarization,” Philos. Trans. R. Soc. London 1, 21–53 (1815).

Physica

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.

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

J. M. Bueno, “Measurement of parameters of polarization in the living human eye using imaging polarimetry,” Vision Res. 40, 3791–3799 (2000).
[CrossRef] [PubMed]

J. M. Bueno, “Depolarization effects in the human eye,” Vision Res. 41, 2687–2696 (2001).
[CrossRef] [PubMed]

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

Other

S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller matrix ellipsometry using the division-of-amplitude photopolarimeter,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 152–156 (1996).
[CrossRef]

American National Standard for the Safe Use of Lasers ANSI Z136.1. (Laser Institute of America, Orlando, Fla., 1993).

T. Fendrich, “Fourierellipsometrie,” Diplomarbeit (Universität Heidelberg, Heidelberg, Germany, 1991).

D. S. Kliger, J. W. Lewis, C. E. Randall, “Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

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

F. Vargas-Martín, “Óptica adaptativa en oftalmoscopia: corrección de las aberraciones del ojo mediante un modulador espacial de cristal líquido,” Tesis Doctoral (Universidad de Murcia, Murcia, Spain, 1999).

L. J. Bour, “Polarized light and the eye,” in Vision Optics and Instrumentation, W. N. Charman, ed. (CRC Press, Boston, Mass., 1991), Vol. 1, Chap. 13.

D. M. Maurice, “The cornea and sclera,” in The Eye, H. Davson, ed. (Academic, Orlando, Fla., 1984), pp. 1–158.
[CrossRef]

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).

B. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” in Lasers in Ophthalmology IV, R. Birngruber, A. F. Fercher, P. Sourdille, eds., Proc. SPIE2930, 92–101 (1996).

J. W. Jaronski, H. T. Kasprzak, D. Haszcz, J. Zagorski, “Investigation of the corneal structure by use of phase stepping imaging polarimetry,” in Proceedings of the European Optical Society Topical Meeting in Physiological Optics (European Optical Society, Wroclaw, Poland, 1999), pp. 21–22.

M. Born, E. Wolf, “Principles of Optics (Pergamon Press, New York, 6th ed., 1980).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.

J. H. Wang, “Corneal and epithelial thickness changes associated with contact lens wear and eye closure comparing optical coherence tomography and optical pachometry,” M.S. thesis (University of Waterloo, Waterloo, Ontario, 2000).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the imaging polariscope. P45, linear polarizers; BS1 and BS2, pellicle beam splitters; SF, spatial filter; AP, aperture acting as stop for the first pass; BD, black diffuser; L1, L2, L3, and L4, achromatic lenses; OB, camera objective; RD, reference detector; PO, micrometric positioner.

Fig. 2
Fig. 2

Distribution of retardation for the test retardation plate in double pass. Image subtends 15 mm. Units are in degrees.

Fig. 3
Fig. 3

Spatially resolved azimuth (deg) for two different orientations of the fast axis of the retarder used for calibration: (a) 40 and (b) 0 deg. Averages: (a) 38.1 ± 2.0 deg (b) 2.4 ± 1.2 deg.

Fig. 4
Fig. 4

Orientation of the slow axis (in degrees) for the two eyes of subject PA: (a) right eye, (b) left eye. Zero is horizontal, and the angle increases counterclockwise when looking into the eye. Each image has a full size of 13.8 mm.

Fig. 5
Fig. 5

Values of azimuth along a horizontal meridian for two different subjects: AB, filled symbols; PA, open symbols; squares, left eye; circles, right eyes. Negative distances indicate temporal and nasal sides for right and left eyes, respectively.

Fig. 6
Fig. 6

Spatially resolved retardation for the cornea of subject PA. Units are in degrees.

Fig. 7
Fig. 7

Corneal retardation along two meridians of the image for subject PA (filled circles, vertical; open circles, horizontal) and one meridian for AB (squares, horizontal). Data correspond to right eyes. Negative distances represent temporal side.

Fig. 8
Fig. 8

Averaged radial retardation profile for subject FV. Error bars represent the standard deviation. Black curve represents the corresponding third polynomial fitting.

Fig. 9
Fig. 9

Right (OD) versus left eye (OS) retardation for subject FV. Solid line represents the linear fit to the data.

Tables (1)

Tables Icon

Table 1 Errors Introduced in the Calculation of Corneal Parameters when Depolarizing Properties of the Iris Are Not Taken into Accounta

Equations (13)

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

MΔ=10000c2+s2ksc(1-k)-sx0sc(1-k)s2+c2kcx0sx-cxk,
SOUT=S0S1S2S3=Ip1sc(1-k)s2+c2k-cx=MΔIp0Ip0.
M¯PSA=Mp45Mδ90=1210cos δ-sin δ000010cos δ-sin δ0000
SD(i)=M¯PSA(i)MΔαSIN=12S0+S2 cos δi-S3 sin δi0S0+S2 cos δi-S3 sin δi0=IF(i)S1D(i)S2D(i)S3D(i).
IF(1)IF(2)IF(3)=121cos δ1-sin δ11cos δ2-sin δ21cos δ3-sin δ3S=12 MPSAS,
S=S0S2S3=Ip1s2+c2k-cx=2MPSA-1IF(1)IF(2)IF(3).
Ā cos2Δ+B¯ cos Δ+C¯=0,
Ā=S2-1,B¯=S32,C¯=-Ā+B¯.
α=12 a cos- S3sin Δ.
SOUTg=S0gS1gS2gS3g=Ip1gsc1-kgs2+c2k-gcx=MgMΔαIp0Ip0,
Āg cos2 Δ+B¯g cos Δ+C¯g=0,
Āg=gS2-g2,B¯g=S32,C¯g=-Āg+B¯g.
α=12 α cos-S3gsin Δ.

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