Abstract

In several optical technologies for glaucoma diagnosis, polarized light is used to assess the retinal nerve fiber layer (RNFL) of the eye. For better understanding of the polarization properties of the RNFL, it was modeled as a thick birefringent slab containing parallel light-scattering cylinders, and the Mueller matrix for reflectance was derived. The model predicts that (1) the RNFL reflectance has weak intrinsic diattenuation; (2) the diattenuation spectrum depends strongly on the relative refractive indices of the cylinders; (3) both scattering and birefringence contribute to retardation; and (4) the RNFL reflectance generally preserves polarization, but depolarization may be detectable for thick RNFL at short wavelengths.

© 2003 Optical Society of America

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2003 (2)

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

X.-R. Huang, R. W. Knighton, “Diattenuation and polarization preservation of retinal nerve fiber layer,” Appl. Opt. 42, 5737–5743 (2003).
[CrossRef] [PubMed]

2002 (3)

X.-R. Huang, R. W. Knighton, “Linear birefringence of the retinal nerve fiber layer measured in vitro with a multispectral imaging micropolarimeter,” J. Biomed. Opt. 7, 199–204 (2002).
[CrossRef] [PubMed]

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, J. F. de Boer, “In vivo depth-resolved birefringence measurements of the human retinal nerve fiber layer by polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 1610–1612 (2002).
[CrossRef]

D. S. Greenfield, “Optic nerve and retinal nerve fiber layer analyzers in glaucoma,” Curr. Opin. Ophthalmol. 13, 68–76 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

R. W. Knighton, C. Qian, “An optical model of the human retinal nerve fiber layer: implications of directional reflectance for variability of clinical measurements,” J. Glaucoma 9, 56–62 (2000).
[CrossRef] [PubMed]

1999 (2)

R. W. Knighton, X.-R. Huang, “Visible and near-infrared imaging of the nerve fiber layer of the isolated rat retina,” J. Glaucoma 8, 31–37 (1999).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, “Directional and spectral reflectance of the rat retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 40, 639–647 (1999).

1998 (1)

R. W. Knighton, X.-R. Huang, Q. Zhou, “Microtubule contribution to the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 39, 189–193 (1998).

1997 (1)

1996 (3)

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

R. Varma, M. Skaf, E. Barron, “Retinal nerve fiber layer thickness in normal human eyes,” Ophthalmology 103, 2114–2119 (1996).
[PubMed]

R. O. Burk, H. E. Volcker, “Current imaging of the optic disk and retinal nerve fiber layer,” Curr. Opin. Ophthalmol. 7, 99–108 (1996).
[CrossRef] [PubMed]

1995 (2)

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

R. W. Knighton, Q. Zhou, “The relation between reflectance and thickness of the retinal nerve fiber layer,” J. Glaucoma 4, 117–123 (1995).
[CrossRef] [PubMed]

1992 (3)

R. W. Knighton, C. Baverez, A. Bhattacharya, “The directional reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Visual Sci. 33, 2603–2611 (1992).

A. W. Dreher, K. Reiter, “Retinal laser ellipsometry—a new method for measuring the retinal nerve-fiber layer thickness distribution,” Clin. Vision Sci. 7, 481–488 (1992).

A. W. Dreher, K. Reiter, 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]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990 (1)

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

1985 (1)

1984 (1)

T. E. Ogden, “Nerve fiber layer of the primate retina: morphometric analysis,” Invest. Ophthalmol. Visual Sci. 25, 19–29 (1984).

1980 (1)

D. R. Williams, “Visual consequences of the foveal pit,” Invest. Ophthalmol. Visual Sci. 19, 653–667 (1980).

1978 (1)

T. E. Ogden, “Nerve fiber layer astrocytes of the primate retina: morphology, distribution, and density,” Invest. Ophthalmol. Visual Sci. 17, 499–510 (1978).

1975 (1)

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Alvarado, J. A.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1989).

Barron, E.

R. Varma, M. Skaf, E. Barron, “Retinal nerve fiber layer thickness in normal human eyes,” Ophthalmology 103, 2114–2119 (1996).
[PubMed]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1989).

Baverez, C.

R. W. Knighton, C. Baverez, A. Bhattacharya, “The directional reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Visual Sci. 33, 2603–2611 (1992).

Benoit, A. M.

Bhattacharya, A.

R. W. Knighton, C. Baverez, A. Bhattacharya, “The directional reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Visual Sci. 33, 2603–2611 (1992).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Burk, R. O.

R. O. Burk, H. E. Volcker, “Current imaging of the optic disk and retinal nerve fiber layer,” Curr. Opin. Ophthalmol. 7, 99–108 (1996).
[CrossRef] [PubMed]

Cense, B.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, T. C.

Chipman, R. A.

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

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, E. W. van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), pp. 22.21–22.37.

Cioffi, G. A.

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

Coleman, A.

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

Collett, E.

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

Cull, G.

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

de Boer, J. F.

Dong, J.

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

Dreher, A. W.

A. W. Dreher, K. Reiter, 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]

A. W. Dreher, K. Reiter, “Retinal laser ellipsometry—a new method for measuring the retinal nerve-fiber layer thickness distribution,” Clin. Vision Sci. 7, 481–488 (1992).

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

A. W. Dreher, K. Reiter, “Scanning laser polarimetry of the retinal nerve fiber layer,” in Polarization Analysis and Measurement, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE1746, 34–41 (1992).
[CrossRef]

Ducros, M. G.

Ellis, G. W.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Farrell, R. A.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fortune, B.

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

Freund, D. E.

Fujimoto, J. G.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Greenfield, D. S.

D. S. Greenfield, “Optic nerve and retinal nerve fiber layer analyzers in glaucoma,” Curr. Opin. Ophthalmol. 13, 68–76 (2002).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hemenger, R. P.

Hertzmark, E.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

Hogan, M. J.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, X.-R.

X.-R. Huang, R. W. Knighton, “Diattenuation and polarization preservation of retinal nerve fiber layer,” Appl. Opt. 42, 5737–5743 (2003).
[CrossRef] [PubMed]

X.-R. Huang, R. W. Knighton, “Linear birefringence of the retinal nerve fiber layer measured in vitro with a multispectral imaging micropolarimeter,” J. Biomed. Opt. 7, 199–204 (2002).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, “Directional and spectral reflectance of the rat retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 40, 639–647 (1999).

R. W. Knighton, X.-R. Huang, “Visible and near-infrared imaging of the nerve fiber layer of the isolated rat retina,” J. Glaucoma 8, 31–37 (1999).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, Q. Zhou, “Microtubule contribution to the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 39, 189–193 (1998).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Inoue, S.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Izatt, J. A.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, Orlando, Fla., 1969).

Kliger, D. S.

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

Knighton, R. W.

X.-R. Huang, R. W. Knighton, “Diattenuation and polarization preservation of retinal nerve fiber layer,” Appl. Opt. 42, 5737–5743 (2003).
[CrossRef] [PubMed]

X.-R. Huang, R. W. Knighton, “Linear birefringence of the retinal nerve fiber layer measured in vitro with a multispectral imaging micropolarimeter,” J. Biomed. Opt. 7, 199–204 (2002).
[CrossRef] [PubMed]

R. W. Knighton, C. Qian, “An optical model of the human retinal nerve fiber layer: implications of directional reflectance for variability of clinical measurements,” J. Glaucoma 9, 56–62 (2000).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, “Visible and near-infrared imaging of the nerve fiber layer of the isolated rat retina,” J. Glaucoma 8, 31–37 (1999).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, “Directional and spectral reflectance of the rat retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 40, 639–647 (1999).

R. W. Knighton, X.-R. Huang, Q. Zhou, “Microtubule contribution to the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 39, 189–193 (1998).

Q. Zhou, R. W. Knighton, “Light scattering and form birefringence of parallel cylindrical arrays that represent cellular organelles of the retinal nerve fiber layer,” Appl. Opt. 36, 2273–2285 (1997).
[CrossRef] [PubMed]

R. W. Knighton, Q. Zhou, “The relation between reflectance and thickness of the retinal nerve fiber layer,” J. Glaucoma 4, 117–123 (1995).
[CrossRef] [PubMed]

R. W. Knighton, C. Baverez, A. Bhattacharya, “The directional reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Visual Sci. 33, 2603–2611 (1992).

Lewis, J. W.

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

Lin, C. P.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Louis-Dorr, V.

Lu, S.-Y.

Mala, L.

Marsack, J. D.

McCally, R. L.

Milner, T. E.

Naoun, K.

Ogden, T. E.

T. E. Ogden, “Nerve fiber layer of the primate retina: morphometric analysis,” Invest. Ophthalmol. Visual Sci. 25, 19–29 (1984).

T. E. Ogden, “Nerve fiber layer astrocytes of the primate retina: morphology, distribution, and density,” Invest. Ophthalmol. Visual Sci. 17, 499–510 (1978).

Park, B. H.

Pedut-Kloizman, T.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

Pierce, M. C.

Puliafito, C. A.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Qian, C.

R. W. Knighton, C. Qian, “An optical model of the human retinal nerve fiber layer: implications of directional reflectance for variability of clinical measurements,” J. Glaucoma 9, 56–62 (2000).
[CrossRef] [PubMed]

Quigley, H.

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

Randall, C. E.

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

Raspiller, A.

Reiter, K.

A. W. Dreher, K. Reiter, “Retinal laser ellipsometry—a new method for measuring the retinal nerve-fiber layer thickness distribution,” Clin. Vision Sci. 7, 481–488 (1992).

A. W. Dreher, K. Reiter, 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]

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

A. W. Dreher, K. Reiter, “Scanning laser polarimetry of the retinal nerve fiber layer,” in Polarization Analysis and Measurement, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE1746, 34–41 (1992).
[CrossRef]

Rylander, H. G.

Sato, H.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Schuman, J. S.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Shaw, B.

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard University, Cambridge, Mass., 1962).

Skaf, M.

R. Varma, M. Skaf, E. Barron, “Retinal nerve fiber layer thickness in normal human eyes,” Ophthalmology 103, 2114–2119 (1996).
[PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Thomsen, S. L.

van Blokland, G. J.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

Varma, R.

R. Varma, M. Skaf, E. Barron, “Retinal nerve fiber layer thickness in normal human eyes,” Ophthalmology 103, 2114–2119 (1996).
[PubMed]

Volcker, H. E.

R. O. Burk, H. E. Volcker, “Current imaging of the optic disk and retinal nerve fiber layer,” Curr. Opin. Ophthalmol. 7, 99–108 (1996).
[CrossRef] [PubMed]

Wang, L.

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

Weddell, J. E.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Weinreb, R. N.

A. W. Dreher, K. Reiter, 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]

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

Williams, D. R.

D. R. Williams, “Visual consequences of the foveal pit,” Invest. Ophthalmol. Visual Sci. 19, 653–667 (1980).

Wong, C.

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

Zhou, Q.

R. W. Knighton, X.-R. Huang, Q. Zhou, “Microtubule contribution to the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 39, 189–193 (1998).

Q. Zhou, R. W. Knighton, “Light scattering and form birefringence of parallel cylindrical arrays that represent cellular organelles of the retinal nerve fiber layer,” Appl. Opt. 36, 2273–2285 (1997).
[CrossRef] [PubMed]

R. W. Knighton, Q. Zhou, “The relation between reflectance and thickness of the retinal nerve fiber layer,” J. Glaucoma 4, 117–123 (1995).
[CrossRef] [PubMed]

Appl. Opt. (6)

Arch. Ophthalmol. (1)

R. N. Weinreb, A. W. Dreher, A. Coleman, H. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
[CrossRef] [PubMed]

Arch. Ophthalmol. (Chicago) (1)

J. S. Schuman, M. R. Hee, C. A. Puliafito, C. Wong, T. Pedut-Kloizman, C. P. Lin, E. Hertzmark, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography,” Arch. Ophthalmol. (Chicago) 113, 586–596 (1995).
[CrossRef]

Clin. Vision Sci. (1)

A. W. Dreher, K. Reiter, “Retinal laser ellipsometry—a new method for measuring the retinal nerve-fiber layer thickness distribution,” Clin. Vision Sci. 7, 481–488 (1992).

Curr. Opin. Ophthalmol. (2)

R. O. Burk, H. E. Volcker, “Current imaging of the optic disk and retinal nerve fiber layer,” Curr. Opin. Ophthalmol. 7, 99–108 (1996).
[CrossRef] [PubMed]

D. S. Greenfield, “Optic nerve and retinal nerve fiber layer analyzers in glaucoma,” Curr. Opin. Ophthalmol. 13, 68–76 (2002).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (7)

R. W. Knighton, C. Baverez, A. Bhattacharya, “The directional reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Visual Sci. 33, 2603–2611 (1992).

R. W. Knighton, X.-R. Huang, “Directional and spectral reflectance of the rat retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 40, 639–647 (1999).

R. W. Knighton, X.-R. Huang, Q. Zhou, “Microtubule contribution to the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Visual Sci. 39, 189–193 (1998).

T. E. Ogden, “Nerve fiber layer of the primate retina: morphometric analysis,” Invest. Ophthalmol. Visual Sci. 25, 19–29 (1984).

D. R. Williams, “Visual consequences of the foveal pit,” Invest. Ophthalmol. Visual Sci. 19, 653–667 (1980).

L. Wang, J. Dong, G. Cull, B. Fortune, G. A. Cioffi, “Varicosities of intraretinal ganglion cell axons in human and nonhuman primates,” Invest. Ophthalmol. Visual Sci. 44, 2–9 (2003).
[CrossRef]

T. E. Ogden, “Nerve fiber layer astrocytes of the primate retina: morphology, distribution, and density,” Invest. Ophthalmol. Visual Sci. 17, 499–510 (1978).

J. Biomed. Opt. (1)

X.-R. Huang, R. W. Knighton, “Linear birefringence of the retinal nerve fiber layer measured in vitro with a multispectral imaging micropolarimeter,” J. Biomed. Opt. 7, 199–204 (2002).
[CrossRef] [PubMed]

J. Cell Biol. (1)

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

J. Glaucoma (3)

R. W. Knighton, Q. Zhou, “The relation between reflectance and thickness of the retinal nerve fiber layer,” J. Glaucoma 4, 117–123 (1995).
[CrossRef] [PubMed]

R. W. Knighton, C. Qian, “An optical model of the human retinal nerve fiber layer: implications of directional reflectance for variability of clinical measurements,” J. Glaucoma 9, 56–62 (2000).
[CrossRef] [PubMed]

R. W. Knighton, X.-R. Huang, “Visible and near-infrared imaging of the nerve fiber layer of the isolated rat retina,” J. Glaucoma 8, 31–37 (1999).
[CrossRef] [PubMed]

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

Ophthalmology (1)

R. Varma, M. Skaf, E. Barron, “Retinal nerve fiber layer thickness in normal human eyes,” Ophthalmology 103, 2114–2119 (1996).
[PubMed]

Opt. Lett. (1)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (10)

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

A. W. Dreher, K. Reiter, “Scanning laser polarimetry of the retinal nerve fiber layer,” in Polarization Analysis and Measurement, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE1746, 34–41 (1992).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, E. W. van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), pp. 22.21–22.37.

W. A. Shurcliff, Polarized Light (Harvard University, Cambridge, Mass., 1962).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1989).

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

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

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, Orlando, Fla., 1969).

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Figures (6)

Fig. 1
Fig. 1

Geometry of light scattering by a cylinder. Incident and scattered rays are shown by the arrows. The scattered light is confined to a conical sheet coaxial with the cylinder axis. The apex angle of the cone is twice the angle between the cylinder axis and the incident ray. The incident plane is defined by the incident ray and the cylinder axis. The scattering plane for an observer at Q is defined by point Q and the cylinder axis. Cylindrical scattering is specified by two angles, incident angle ξ between the incident ray and a plane perpendicular to the cylinder and scattering angle ϕ between the incident and the scattering planes, as shown. The angle θ between the incident and scattered rays is the supplement of the scattering angle in the Rayleigh-Gans formulation. N, α1, and α2 are defined in Fig. 2.

Fig. 2
Fig. 2

RNFL reflection model, shown projected onto a plane perpendicular to the cylinders, consisted of a transparent birefringent slab of thickness T and birefringence Δn with an embedded array of parallel cylinders. An incident ray with Stokes vector S in entered the slab and traveled a distance l 1 to a layer of cylinders with thickness dt located at depth t, where it was scattered. The reflected ray then traveled a distance l 2 in the slab and exited with Stokes vector S out. The projections of the incident and reflected rays formed angles α1 and α2 with the normal (N) to the surface of the slab.

Fig. 3
Fig. 3

Relative reflectance spectra of the RNFL. The symbols are measured data of nine bundles in six retinas. The solid curve is a spectral template calculated from the weighted average of the parameters (s, w, n) fitted to each measured spectrum. The incident angles ranged from 16° to 26°, and the scattering angles ranged from 160° to 180°. Inset: Distribution of cylinder diameters in a two-mechanism light-scattering model that describes RNFL reflectance spectra. The distribution contains a population of thin fibrils with diameters that are small relative to the wavelength (arbitrarily set to 20 nm) and a population of thicker cylinders with a triangular diameter distribution that linearly declines from a maximum at diameter s to zero at diameter s + w. The number n of thin fibrils per unit area under the triangle adjusts the relative contributions of the two mechanisms.

Fig. 4
Fig. 4

Diattenuation spectra in the backscattering plane (ϕ = 180°) calculated from the RNFL reflection model for two incident angles and the parameters in Table 1. (a) ξ = 0°, m t = 1.01; (b) ξ = 0°, m t = 1.08; (c) ξ = 20°, m t = 1.01; (d) ξ = 20°, m t = 1.08. The value of m T is marked next to each curve. Also shown are the diattenuation for thin cylinders only (m T = 1.00) and the Rayleigh-Gans limit (solid curves labeled R-G). Positive diattenuation values indicate that the diattenuation axis is parallel to the backscattering plane; negative values indicate a perpendicular axis. The vertical scale factor is the same for all four graphs.

Fig. 5
Fig. 5

Retardance spectra (dashed curves) for the RNFL reflection model with m t = 1.01. (a) and (b) Δ = 0 nm; (c) and (d) Δ = 50 nm. (a) and (c) Oblique incidence and scattering; (b) and (d) direct backscattering. The solid lines show the effective retardance of the birefringent slab (Δ′) given by Eq. (6b). In (c), Δ′ = 48.64 nm. The arrows in (b) and (d) indicate that, in direct backscatter, Δs and Δ′ are additive.

Fig. 6
Fig. 6

Depolarization spectra for the RNFL reflection model in direct backscatter (m t = 1.01). Lower curves: Δ = 0 nm. The model exhibited weak depolarization that depended on m T. Upper curves: Δ = 50 nm. Depolarization was much higher; the spectra nearly superimposed and followed the curve for the depolarization power for the factor sin(Δ′)/Δ′. The short lines along the ordinate show the relation between dep and DOPmin.

Tables (1)

Tables Icon

Table 1 Diameter Distributions Used for Different Values of Relative Refractive Index for the Cylinders in the Model Array

Equations (26)

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

dS=Ml2MsMl1SindtT,
Sout=1T0TMl2MsMl1Sindt,
Sout=MSin,
M=1T0TMl2MsMl1dt,
Mlj=1000010000cosδj-sinδj00sinδjcosδj,
lj=tcosαjcosξ.
δj=2πλ ljΔn cos2ξ=2πλcosξcosαj Δnt,
δj=ΔcosξcosαjtT.
δ1=δ2=ΔtT,
Δ=Δcosξsinϕ2,
J=1000010000-100001
Ms=c=1nJMcJ,
Mc=mc11mc1200mc12mc110000mc33mc3400-mc34mc33,
mc11=12ρc12+ρc22,mc12=12ρc12-ρc22,mc33=ρc1ρc2 cosδc,mc34=ρc1ρc2 sinδc,
Ms=ms11ms1200ms12ms110000ms33-ms3400ms34ms33,
ms11=12p1+p2,ms12=12p1-p2,ms33=ρ cosΔs,ms34=ρ sinΔs,
p1=c=1nρc12,p2=c=1nρc22,ρ cosΔs=c=1nρc1ρc2 cosδc,ρ sinΔs=c=1nρc1ρc2 sinδc.
M=ms11ms1200ms12ms110000m33-m3400m34m33
m33=ρsinΔΔcosΔ+Δs,m34=ρsinΔΔsinΔ+Δs,
Mdiat=md1md200md2md10000md30000md3,Mrtd=1000010000mrt1-mrt200mrt2mrt1,Mdep=1000010000mdp0000mdp,
md1=12p1+p2, md2=12p1-p2, md3=p1p2,mrt1=cosδ0, mrt2=sinδ0, δ0=Δ+Δs,mdp=ρp1p2sinΔΔ
S=1 cos 2ω cos 2α cos 2ω sin 2α sin 2ωT,
dep=1-|trMdep-1|3,
Ms=ms11ms12-ms13ms14ms12ms22-ms23ms24ms13ms23ms33-ms34ms14ms24ms34ms44=c=1nJmc11mc12mc13mc14mc12mc22mc23mc24-mc13-mc23mc33mc34mc14mc24-mc34mc44J,
m11=ms11,m12=ms12,m13=-Ams13-Bms14,m14=-Bms13+Ams14,m21=m12,m22=ms22,m23=-Ams23-Bms24,m24=-Bms23+Ams24,m31=-m13,m32=-m23,m33=Cms33-Dms44+Ems34-ms43,m34=-Cms34-Dms43+Ems33+ms44,m41=m14,m42=m24,m43=-m34,m44=Cms44-Dms33+Ems34-ms43,
A=sin ΔΔ,B=cos Δ-1Δ,C=121+sin 2Δ2Δ,D=121-sin 2Δ2Δ,E=12cos 2Δ-12Δ,

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