Abstract

Scanning laser polarimetry (SLP), a technology for glaucoma diagnosis, uses imaging polarimetry to detect the birefringence of the retinal nerve fiber layer. A simple model of SLP suggests an algorithm for calculating birefringence that, unlike previous methods, uses all of the data available in the images to achieve better signal-to-noise ratio and lower sensitivity to depolarization. The uncertainty of the calculated retardance is estimated and an appropriate averaging strategy to reduce uncertainty is demonstrated. Averaging over a large area of the macula of the eye is used in a new method for determining anterior segment birefringence.

© 2002 Optical Society of America

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References

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  1. A. W. Dreher and K. Reiter, "Scanning laser polarimetry of the retinal nerve fiber layer," Proc. of SPIE 1746, 34-41 (1992).
    [CrossRef]
  2. A. W. Dreher and K. Reiter, "Retinal laser ellipsometry - a new method for measuring the retinal nervefiber layer thickness distribution," Clin. Vision Sci. 7, 481-488 (1992).
  3. D. S. Greenfield, R. W. Knighton and 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]
  4. R. W. Knighton, X. R. Huang and D. S. Greenfield, "Analytical model of scanning laser polarimetry for retinal nerve fiber layer assessment," Invest. Ophthalmol. Visual Sci. 43, 383-392 (2002).
  5. Q. Zhou and R. N. Weinreb, "Individualized compensation of anterior segment birefringence during scanning laser polarimetry," Invest. Ophthalmol. Visual Sci. 43, 2221-2228 (2002).
  6. A. W. Dreher and K. Reiter, inventors, Laser Diagnostic Technologies, Inc., assignee. "Retinal eye disease diagnostic system," United States Patent No. 5,303,709, April 19, 1994.
  7. K. Reiter and A. W. Dreher, inventors, Laser Diagnostic Technologies, Inc., assignee. "Eye examination apparatus employing polarized light probe," United States Patent No. 5,787,890, August 4, 1998.
  8. S.-Y. Lu and R. A. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996).
    [CrossRef]
  9. R. A. Bone, "The role of macular pigment in the detection of polarized light," Vision Res. 20, 213-220 (1980).
    [CrossRef] [PubMed]
  10. A. W. Dreher, K. Reiter and R. N. Weinreb, "Spatially resolved birefringence of the retinal nerve-fiber layer assessed with a retinal laser ellipsometer," Appl. Opt. 31, 3730-3735 (1992).
    [CrossRef] [PubMed]
  11. R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw and K. Reiter, "Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness," Arch. Ophthalmol. 108, 557-60 (1990).
    [CrossRef] [PubMed]
  12. D. S. Kliger, J. W. Lewis and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic Press, Inc., New York, 1990).
  13. Q. Zhou, inventor, Laser Diagnostic Technologies, Inc., assignee. "System and method for determining birefringence of anterior segment of a patient's eye," United States Patent No. 6,356,036, March 12, 2002.
  14. S. L. Polyak, The Retina (The University of Chicago Press, Chicago, 1941).
  15. S. C. Pollock and N. R. Miller, "The retinal nerve fiber layer," Int. Ophthalmol. Clin. 26, 201-221 (1986).
    [CrossRef] [PubMed]
  16. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (WCB/McGraw-Hill, Boston, 1992).
  17. P. S. Hauge, "Mueller matrix ellipsometry with imperfect compensators," J. Opt. Soc. Am. 68, 1519-1528 (1978).
    [CrossRef]
  18. R. M. A. Azzam, inventor, The Board of Regents of the University of Nebraska, assignee. "Polarimeter," United States Patent No. 4,306,809, Dec. 22, 1981.
  19. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannerly, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992).
  20. R. W. Knighton and X. R. Huang, "Linear birefringence of the central human cornea," Invest. Ophthalmol. Visual Sci. 43, 82-86 (2002).

Am. J. Ophthalmol. (1)

D. S. Greenfield, R. W. Knighton and 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. (1)

Arch. Ophthalmol. (1)

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw and K. Reiter, "Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness," Arch. Ophthalmol. 108, 557-60 (1990).
[CrossRef] [PubMed]

Clin. Vision Sci. (1)

A. W. Dreher and K. Reiter, "Retinal laser ellipsometry - a new method for measuring the retinal nervefiber layer thickness distribution," Clin. Vision Sci. 7, 481-488 (1992).

Int. Ophthalmol. Clin. (1)

S. C. Pollock and N. R. Miller, "The retinal nerve fiber layer," Int. Ophthalmol. Clin. 26, 201-221 (1986).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (3)

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

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

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Proc. SPIE (1)

A. W. Dreher and K. Reiter, "Scanning laser polarimetry of the retinal nerve fiber layer," Proc. of SPIE 1746, 34-41 (1992).
[CrossRef]

United States Patent No. 4,306,809, (1)

R. M. A. Azzam, inventor, The Board of Regents of the University of Nebraska, assignee. "Polarimeter," United States Patent No. 4,306,809, Dec. 22, 1981.

United States Patent No. 5,303,709, (1)

A. W. Dreher and K. Reiter, inventors, Laser Diagnostic Technologies, Inc., assignee. "Retinal eye disease diagnostic system," United States Patent No. 5,303,709, April 19, 1994.

United States Patent No. 5,787,890, (1)

K. Reiter and A. W. Dreher, inventors, Laser Diagnostic Technologies, Inc., assignee. "Eye examination apparatus employing polarized light probe," United States Patent No. 5,787,890, August 4, 1998.

United States Patent No. 6,356,036, (1)

Q. Zhou, inventor, Laser Diagnostic Technologies, Inc., assignee. "System and method for determining birefringence of anterior segment of a patient's eye," United States Patent No. 6,356,036, March 12, 2002.

Vision Res. (1)

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

Other (4)

S. L. Polyak, The Retina (The University of Chicago Press, Chicago, 1941).

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (WCB/McGraw-Hill, Boston, 1992).

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannerly, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992).

D. S. Kliger, J. W. Lewis and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic Press, Inc., New York, 1990).

Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of scanning laser polarimetry (SLP).

Fig. 2.
Fig. 2.

Theoretical outputs I × and I P vary sinusoidally with θ.

Fig. 3.
Fig. 3.

(785 KB) Movie of an image series of the optic disc and surrounding RNFL from a normal right eye. The movie runs at 40% of actual speed. Small shifts were due to residual image misalignment. The bright artifacts near the center were due to internal reflections in the instrument. The contrast of the crossed channel was enhanced to better reveal the interaction of the linearly polarized incident beam with the RNFL birefringence. This interaction forms a four-armed cross that spins as the plane of polarization rotates. The dark arms of the cross correspond to the minima of I ×. The circle encloses the pixel from which the data in Fig. 4 were extracted.

Fig. 4.
Fig. 4.

Data from the single pixel at the center of the red circle in Fig. 3 (dots) and the smooth curves used to characterize them (lines). I × (upper graph) was approximated with the first and second terms of its Fourier series (mean and fundamental); I p was described by its mean (P ave). (Note: Because I ×(θ) is theoretically the same at 0° and 90°, the average of images number 1 and 20 was used for the value at 0° when calculating the Fourier series.)

Fig. 5.
Fig. 5.

Retardance image derived from the image series in Fig. 3 by applying Eq. (4). Calculated retardance (nm) is shown for five positions (crosses) around the optic disc. The crosses were aligned with the calculated axis of retardance. In a typical clinical application this quantitative image would serve as input to more extensive analyses of RNFL integrity.

Fig. 6.
Fig. 6.

Significance testing and image averaging. (A) Retardance image of Fig. 5 with the nonsignificant pixels (p > 0.01) colored red. (B) Retardance image formed by first smoothing each image in the image series of Fig. 3 with a 5×5 averaging window before applying Eq. (4).

Fig. 7.
Fig. 7.

SLP images of a normal macula (right eye) obtained without corneal compensation. The schematic diagram depicts a theoretical specimen comprising a fixed axis linear retarder representing the cornea (C) and a radial axis linear retarder representing Henle’s fiber layer (R), with reflection from a polarization preserving reflector (PPR) at the back of the eye. The arrows show the slow axis of R. The scanning beam is shown as a single dotted line but is understood to produce an image of R+PPR. In the retardance image, a bow tie pattern centered at the fovea arises from the interaction of the corneal and macular birefringence.

Fig. 8.
Fig. 8.

SLP images of a diseased macula (right eye) obtained without corneal compensation. The diagram postulates the absence of the radial retarder, causing PPR to function as a screen onto which the corneal properties were projected. The crosses in the retardance image show the calculated retardance and axis at six locations on the fundus.

Fig. 9.
Fig. 9.

Averaging over a large area (43,847 pixels; shaded gray) of the macula in Fig. 8 produced a single value for the projected birefringence. A mask excluded from the average the central area of instrumental artifact and also pixels in the parallel channel that were saturated. The cross, placed arbitrarily, applies to the entire shaded area. The graphs, in the same format as Fig. 4, show the very smooth averaged outputs of the crossed and parallel channels.

Equations (5)

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I × = d + F 1 [ 1 cos 4 ( θ R θ ) ]
I P = d + K F 1 [ 1 cos 4 ( θ R θ ) ]
F 1 = K 4 ( 1 cos δ ) .
δ = cos 1 ( 1 4 F 1 P ave + 2 F 1 F 0 )
F 2 , n 3 = r 2 / 2 ( 1 r 2 ) / ( n 3 ) ,

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