Abstract

Corneal birefringence affects polarization-sensitive optical measurements of the eye. Recent literature supports the idea that corneal birefringence is biaxial, although with some disagreement among reports and without considering corneas with very low values of central retardance. This study measured corneal retardation in eyes with a wide range of central corneal retardance by means of scanning laser polarimetry (GDx-VCC, Carl Zeiss Meditec, Inc.), which computes the retardance and slow axis of the cornea from images of the bow tie pattern formed by the radial birefringence of the macula. Measurements were obtained at many points on the cornea by translating the instrument. Data were compared to calculations of the retardation produced by a curved biaxial material between two spherical surfaces. Most corneas showed one or two small areas of zero retardance where the refracted ray within the cornea aligned with an optical axis of the material. The retardation patterns in these corneas could be mimicked, but not accurately described, by the biaxial model. Two corneas with large areas of low retardance more closely resembled a uniaxial model. We conclude that the cornea, in general, behaves as a biaxial material with its fastest axis perpendicular to its surface. Some locations in a few corneas can be uniaxial with the optical axis perpendicular to the surface. Importantly, corneal birefringence varies greatly among people and, within a single cornea, significantly with position.

© 2008 Optical Society of America

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References

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    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. R. A. Bone and G. Draper, "Optical anisotropy of the human cornea determined with a polarizing microscope," Appl. Opt. 46, 8351-8357 (2007).
    [CrossRef] [PubMed]
  6. 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).
    [PubMed]
  7. Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 43, 2221-2228 (2002).
    [PubMed]
  8. N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
    [CrossRef] [PubMed]
  9. M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
    [CrossRef] [PubMed]
  10. M. Born and E. Wolf, Principles of Optics, Seventh Edition (Cambridge University Press, 1999), Ch. XV, "Optics of crystals".
  11. M. J. Hogan, J. A. Alvarado and J. E. Weddell, Histology of the Human Eye, An Atlas and Textbook (W. B. Saunders Co., Philadelphia, 1971).
  12. R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
    [PubMed]
  13. R. W. Knighton, "Spectral dependence of corneal birefringence at visible wavelengths," Invest. Ophthalmol. Vis. Sci.  43, E-Abstract 152 (2002).
  14. C. C. Ferguson, "Intersections of ellipsoids and planes of arbitrary orientation and position," Math. Geology 11, 329-336 (1979).
    [CrossRef]
  15. G. Wyszecki and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Ed. (John Wiley & Sons, New York, 1982), Chap. 2.
  16. C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
    [CrossRef] [PubMed]
  17. G. P. Misson, "Circular polarization biomicroscope: a method for determining human corneal stromal lamellar organization in vivo," Ophthal. Physiol. Opt. 27, 256-264 (2007).
    [CrossRef]

2007

R. A. Bone and G. Draper, "Optical anisotropy of the human cornea determined with a polarizing microscope," Appl. Opt. 46, 8351-8357 (2007).
[CrossRef] [PubMed]

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

G. P. Misson, "Circular polarization biomicroscope: a method for determining human corneal stromal lamellar organization in vivo," Ophthal. Physiol. Opt. 27, 256-264 (2007).
[CrossRef]

2006

N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
[CrossRef] [PubMed]

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

2005

2004

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

2002

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

R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
[PubMed]

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).
[PubMed]

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 43, 2221-2228 (2002).
[PubMed]

1987

1979

C. C. Ferguson, "Intersections of ellipsoids and planes of arbitrary orientation and position," Math. Geology 11, 329-336 (1979).
[CrossRef]

Abahussin, M.

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

Advanced Imaging in Glaucoma Study Group, D. S.

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

Bone, R. A.

Boote, C.

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

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).
[PubMed]

Draper, G.

Farrell, R. A.

Fecher, A. F.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

Ferguson, C. C.

C. C. Ferguson, "Intersections of ellipsoids and planes of arbitrary orientation and position," Math. Geology 11, 329-336 (1979).
[CrossRef]

Götzinger, E.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

Greenfield, D. S.

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
[PubMed]

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).
[PubMed]

Hayes, S.

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

Hitzenberger, C. K.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

Huang, X.-R.

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

R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
[PubMed]

Knighton, R. W.

R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
[PubMed]

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

Lemij, H. G.

N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
[CrossRef] [PubMed]

McCally, R. L.

Meek, K. M.

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

Misson, G. P.

G. P. Misson, "Circular polarization biomicroscope: a method for determining human corneal stromal lamellar organization in vivo," Ophthal. Physiol. Opt. 27, 256-264 (2007).
[CrossRef]

Pircher, M.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

Reus, N. J.

N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
[CrossRef] [PubMed]

Rouseff, D.

Sehi, M.

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

Sticker, M.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

Ume, S.

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

van Blokland, G. J.

Verhelst, S. C.

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).
[PubMed]

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 43, 2221-2228 (2002).
[PubMed]

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).
[PubMed]

Zhou, Q.

N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
[CrossRef] [PubMed]

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 43, 2221-2228 (2002).
[PubMed]

Appl. Opt.

Arch. Ophthalmol.

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).
[PubMed]

Invest. Ophthalmol. Vis. Sci.

Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 43, 2221-2228 (2002).
[PubMed]

N. J. Reus, Q. Zhou, H. G. Lemij, "Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation," Invest. Ophthalmol. Vis. Sci. 47, 3870-3877 (2006).
[CrossRef] [PubMed]

M. Sehi, S. Ume, D. S. Greenfield, and Advanced Imaging in Glaucoma Study Group, "Scanning laser polarimetry with enhanced corneal compensation and optical coherence tomography in normal and glaucomatous eyes," Invest. Ophthalmol. Vis. Sci. 48, 2099-2104 (2007).
[CrossRef] [PubMed]

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

R. W. Knighton, X.-R. Huang, and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Vis. Sci. 43, 383-392 (2002).
[PubMed]

C. Boote, S. Hayes, M. Abahussin and K. M. Meek, "Mapping collagen organization in the human cornea: left and right eyes are structurally distinct," Invest. Ophthalmol. Vis. Sci. 47, 901-908 (2006).
[CrossRef] [PubMed]

J. Biomed. Opt.

E. Götzinger, M. Pircher, M. Sticker, A. F. Fecher and C. K. Hitzenberger, "Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography," J. Biomed. Opt. 9, 94-102 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Math. Geology

C. C. Ferguson, "Intersections of ellipsoids and planes of arbitrary orientation and position," Math. Geology 11, 329-336 (1979).
[CrossRef]

Ophthal. Physiol. Opt.

G. P. Misson, "Circular polarization biomicroscope: a method for determining human corneal stromal lamellar organization in vivo," Ophthal. Physiol. Opt. 27, 256-264 (2007).
[CrossRef]

Other

G. Wyszecki and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Ed. (John Wiley & Sons, New York, 1982), Chap. 2.

R. W. Knighton, "Spectral dependence of corneal birefringence at visible wavelengths," Invest. Ophthalmol. Vis. Sci.  43, E-Abstract 152 (2002).

M. Born and E. Wolf, Principles of Optics, Seventh Edition (Cambridge University Press, 1999), Ch. XV, "Optics of crystals".

M. J. Hogan, J. A. Alvarado and J. E. Weddell, Histology of the Human Eye, An Atlas and Textbook (W. B. Saunders Co., Philadelphia, 1971).

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Figures (12)

Fig. 1.
Fig. 1.

Curved biaxial model of corneal birefringence. (A) A small slab of cornea showing the orientation of the coordinate system along the principal axes of the refractive index. Refractive indexes nx and ny are tangential and nz is perpendicular to the corneal surface. (B) Cross section of a curved biaxial model through its apex. The section lies in the xz-plane and is illuminated by a beam of parallel rays. The red lines show the optical axes at three points. For two points on the model the refracted ray falls along an optical axis and experiences zero retardance (dashed lines). Note that the dimensions shown in this diagram do not correspond to those used to model the cornea (Sect. 3.3)

Fig. 2.
Fig. 2.

Measurement of corneal birefringence with GDx-VCC scanning laser polarimeter. (A) Macular retardance image with a bow tie pattern produced by the interaction of corneal birefringence with the radial birefringence of Henle’s fiber layer. The bow tie orientation coincides with the axes of corneal birefringence. Analysis of the retardance pattern around a circle centered on the bow tie provides the value of corneal retardance. (B) Acquisition screen with centered pupil. The yellow reticle fixed to the center of the image marks the center of the instrument scan pattern (ray O in Fig. 3) and specifies the horizontal and vertical axes in laboratory coordinates. (C) Acquisition screen with offset pupil. Data obtained in this configuration are plotted at the location of the center of the reticle relative to the pupil center (red dot).

Fig. 3.
Fig. 3.

Schematic of measurement optics. Left eye viewed from above. O: Central ray of scan pattern. F: Ray from the internal fixation target. Dashed blue lines: Translated objective lens and fixation ray.

Fig. 4.
Fig. 4.

Repeatability of corneal retardation measurements. Each short line represents one retardation measurement. The line is centered on the measured point, is oriented in the direction of the slow axis and has length proportional to retardance. Black lines are the first data set and red lines the second. Data sets were aligned at the pupil center (0,0), then the central lines were displaced slightly from each other for clarity. A 1 mm diameter dashed circle encloses the region of minimum retardance in each eye. In all figures, N denotes nasal cornea, T denotes temporal cornea, the calibration bar above the T represents 100 nm single-pass retardance and an 8 mm diameter circle centered on the pupil is provided for reference. A) Right eye, measurement interval 11 months. Central retardation — black: 38 nm, 33.5° ND; red: 35 nm, 38.1° ND. B) Right eye, measurement interval 6 days. Central retardation — black: 33 nm, 23.3° ND; red: 36 nm, 22.8° ND.

Fig. 5.
Fig. 5.

Nasally downward retardation pattern. Measurements of single-pass corneal retardation in a left eye. (A) Retardation at each point is shown as in Fig. 4. Central retardation (red line at 0,0): 49 nm, 31° ND. (B) Contour lines (10 nm interval) show the variation of retardance with position. Gray fill: Elongated zone of approximately uniform retardance. In both panels the approximate locations of zero retardance (optical axes) are marked with red asterisks and the dotted line through the center is perpendicular to the central slow axis.

Fig. 6.
Fig. 6.

Three more corneas with a nasally downward pattern, shown in the same format as Fig. 5. (A) Symmetric pattern. Left eye; data combined from three measurement sessions. Average central retardation=35 nm, 40° ND. (B) Asymmetric pattern. Right eye, same data as red lines in Fig. 4(A). Central retardation=35 nm, 35° ND. (C) Asymmetric pattern. Right eye. Central retardation=40 nm, 38° ND.

Fig. 7.
Fig. 7.

Horizontal retardation pattern. Right eye with high central retardance (62 nm) oriented nearly horizontally (5° ND).

Fig. 8.
Fig. 8.

Low retardance pattern. Right eye, central retardation: 13 nm, 21° ND. The dashed red line in B shows the 20 nm contour surrounding a large area of low retardance.

Fig. 9.
Fig. 9.

Curved biaxial model of cornea with parameters chosen to approximate the data in Fig. 5. The black dashed line connects the optical axes of the model. (A) Individual points. Red lines are the model calculated on a 0.5 mm grid, blue lines are data from Fig. 5(A). The black dotted line is the pupil bisector drawn perpendicular to the central slow axis of the data. (B) Retardance contours. Model contours (red, 20 nm intervals) superimposed on the data contours of Fig. 5(B) (blue, 10 nm intervals).

Fig. 10.
Fig. 10.

Model (red) with parameters chosen to approximate the data in Fig. 7 (blue) in the same format as Fig. 9. (A) Individual points. (B) Retardance contours.

Fig. 11.
Fig. 11.

Uniaxial model with parameters chosen to approximate the low retardance area in Fig. 8. The pupil bisector (black dotted line) emphasizes the asymmetry of this birefringence pattern. (A) Measured (blue) and calculated (red) retardance and axis. (B) Retardance contours: Model (red) superimposed on data (blue). The dashed red line shows the 20 nm contour caused by a 25% decrease in birefringence.

Fig. 12.
Fig. 12.

Schematic demonstrating in a left eye the possible consequences of a biaxial cornea for SLP. This GDx-VCC image of a patient with severe glaucoma exhibits weak RNFL birefringence. (N) Beam directed toward nasal retina. (T) Beam directed toward temporal retina. (M) Uniform macula shows good compensation of the tangential component of corneal birefringence in temporal retina. (R) Retardance signal on nasal retina due to biaxial cornea.

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