Abstract

The retinal nerve fiber layer (RNFL) comprises bundles of unmyelinated axons that run across the surface of the retina. The cylindrical organelles of the RNFL (axonal membranes, microtubules, neurofilaments, and mitochondria) as seen by electron microscopy were modeled as parallel cylindrical arrays in order to gain insight into their optical properties. Arrays of thin fibrils were used to represent organelles that are thin relative to wavelength, and the model took into account interference effects that may arise from spatial order. Angular and spectral light-scattering functions were calculated for the backscattering hemisphere. Scattering was much larger from axonal membranes than from microtubules or neurofilaments. Spectra from 400 to 700 nm show that scattering increases at shorter wavelengths for both axonal membranes and microtubules. At 560 nm, scattering from mitochondria modeled as thick cylinders was approximately the same as that from microtubules but showed little wavelength dependence. The model reveals differences in backscattered polarization ratios that may permit experimental discrimination between microtubule and membrane mechanisms for the RNFL reflectance. Calculated backscattering exceeds measured values by at least 1 order of magnitude, but calculated form birefringence for microtubule arrays is approximately the same as measured birefringence.

© 1997 Optical Society of America

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  37. R. N. Weinreb, A. W. Dreher, A. Coleman, H. A. Quigley, B. Shaw, K. Reiter, “Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve layer thickness,” Arch. Ophthalmol. 108, 557–560 (1990).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  41. R. W. Knighton, X. R. Huang, “A microtubule mechanism for the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Vis. Sci. 37, S1151 (1996).
  42. R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

1996 (2)

M. P. Rowe, J. M. Corless, N. Engheta, E. N. Pugh, “Scanning interferometry of sunfish cones I: longitudinal variation in single cone refractive index,” J. Opt. Soc. Am. A 13, 2141–2150. (1996).
[Crossref]

R. W. Knighton, X. R. Huang, “A microtubule mechanism for the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Vis. Sci. 37, S1151 (1996).

1995 (4)

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

Q. Zhou, R. W. Knighton, “Numerical approximation of light scattering from tenuous cylindrical membranes at normal incidence,” Appl. Opt. 34, 2354–2361 (1995).
[Crossref] [PubMed]

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

R. N. Weinreb, S. Shakib, L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol. 119, 627–636 (1995).
[PubMed]

1994 (1)

1993 (2)

Q. Zhou, R. W. Knighton, “Spectral reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Vis. Sci. 34, 1504 (1993).

A. Tuulonen, J. Lehtola, P. J. Airaksinen, “Nerve fiber layer defects with normal visual fields,” Ophthalmology 100, 587–598 (1993).
[Crossref]

1992 (1)

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

1991 (1)

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

1990 (2)

R. E. Kleinman, G. F. Roach, P. M. van den Berg, “Convergent Born series for large refractive indexes,” J. Opt. Soc. Am. A 7, 890–897 (1990).
[Crossref]

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

1989 (4)

F. C. Delori, K. P. Pflibsen, “Spectral reflectance of the human ocular fundus,” Appl. Opt. 28, 1061–1077 (1989).
[Crossref] [PubMed]

R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

J. Caprioli, J. M. Miller, “Measurement of relative nerve fiber layer surface height in glaucoma,” Ophthalmology 96, 633–639 (1989).
[Crossref]

R. P. Hemenger, “Birefringence of a medium of tenuous parallel cylinders,” Appl. Opt. 28, 4030–4034 (1989).
[Crossref] [PubMed]

1986 (2)

1984 (1)

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

1981 (1)

D. Bray, M. B. Bunge, “Serial analysis of microtubules in cultured rat sensory axons,” J. Neurocytol. 10, 589–605 (1981).
[Crossref] [PubMed]

1980 (1)

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

1979 (1)

S. Brimijoin, J. Olsen, R. Rosenson, “Comparison of the temperature-dependence of rapid axonal transport and microtubules in nerves of the rabbit and bullfrog,” J. Physiol. (London) 287, 303–314 (1979).

1978 (1)

D. Rome-Talbot, D. Andre, N. Chalazonitis, “Hypothermic decrease in microtubule density and birefringence in unmyelinated axons,” J. Neurobiol. 9, 247–254 (1978).
[Crossref] [PubMed]

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]

1973 (1)

W. F. Hoyt, L. Frisen, N. M. Newman, “Fundoscopy of nerve fiber layer defects,” Invest. Ophthalmol. 12, 814–829 (1973).
[PubMed]

1968 (2)

E. L. Rodriguez Echandia, R. S. Piezzi, “Microtubules in the nerve fibers of the toad Bufo arenarum Hensel. Effect of low temperature on the sciatic nerve,” J. Cell Biol. 39, 491–497 (1968).
[Crossref]

S. Ohki, “Dielectric constant and refractive index of lipid bi-layers,” J. Theor. Biol. 19, 97–115 (1968).
[Crossref]

1966 (1)

J. H. Richmond, “TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-14, 460–464 (1966).
[Crossref]

1965 (1)

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[Crossref]

1953 (1)

J. M. Mitchison, “A polarized light analysis of the human red cell ghost,” J. Exp. Biol. 30, 397–432 (1953).

Airaksinen, P. J.

A. Tuulonen, J. Lehtola, P. J. Airaksinen, “Nerve fiber layer defects with normal visual fields,” Ophthalmology 100, 587–598 (1993).
[Crossref]

Alvarado, J. A.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971), pp. 482–488.

Andre, D.

D. Rome-Talbot, D. Andre, N. Chalazonitis, “Hypothermic decrease in microtubule density and birefringence in unmyelinated axons,” J. Neurobiol. 9, 247–254 (1978).
[Crossref] [PubMed]

Baltimore, D.

J. Darnell, H. Lodish, D. Baltimore, Molecular Cell Biology (Scientific, New York, 1990), pp. 109–150, 491–499.

Baverez, C.

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

Bhattacharya, A.

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

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–213.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), pp. 705–707.

Bray, D.

D. Bray, M. B. Bunge, “Serial analysis of microtubules in cultured rat sensory axons,” J. Neurocytol. 10, 589–605 (1981).
[Crossref] [PubMed]

Brimijoin, S.

S. Brimijoin, J. Olsen, R. Rosenson, “Comparison of the temperature-dependence of rapid axonal transport and microtubules in nerves of the rabbit and bullfrog,” J. Physiol. (London) 287, 303–314 (1979).

Bunge, M. B.

D. Bray, M. B. Bunge, “Serial analysis of microtubules in cultured rat sensory axons,” J. Neurocytol. 10, 589–605 (1981).
[Crossref] [PubMed]

Caprioli, J.

J. Caprioli, J. M. Miller, “Measurement of relative nerve fiber layer surface height in glaucoma,” Ophthalmology 96, 633–639 (1989).
[Crossref]

Chalazonitis, N.

D. Rome-Talbot, D. Andre, N. Chalazonitis, “Hypothermic decrease in microtubule density and birefringence in unmyelinated axons,” J. Neurobiol. 9, 247–254 (1978).
[Crossref] [PubMed]

Coleman, A.

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

Corless, J. M.

Darnell, J.

J. Darnell, H. Lodish, D. Baltimore, Molecular Cell Biology (Scientific, New York, 1990), pp. 109–150, 491–499.

Delori, F. C.

Dreher, A. W.

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

Easter, S. S.

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]

Enghata, N.

Engheta, N.

Farrell, R. A.

D. E. Freund, R. L. McCally, R. A. Farrell, “Direct summation of fields for light scattering by fibrils with applications to normal corneas,” Appl. Opt. 25, 2739–2746 (1986).
[Crossref]

R. L. McCally, R. A. Farrell, “Light scattering from cornea and corneal transparency,” in Noninvasive Diagnostic Techniques in Ophthalmology, B. R. Masters, ed. (Springer-Verlag, New York, 1990), pp. 189–210.
[Crossref]

Freund, D. E.

Frisen, L.

W. F. Hoyt, L. Frisen, N. M. Newman, “Fundoscopy of nerve fiber layer defects,” Invest. Ophthalmol. 12, 814–829 (1973).
[PubMed]

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Hogan, M. J.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971), pp. 482–488.

Hoyt, W. F.

W. F. Hoyt, L. Frisen, N. M. Newman, “Fundoscopy of nerve fiber layer defects,” Invest. Ophthalmol. 12, 814–829 (1973).
[PubMed]

Huang, X. R.

R. W. Knighton, X. R. Huang, “A microtubule mechanism for the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Vis. Sci. 37, S1151 (1996).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–213.

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]

Iverson, G.

F. Snell, J. Wolken, G. Iverson, J. Lam, Physical Principles of Biological Membranes (Gordon & Breach, New York, 1970), pp. 191–202.

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Jacobson, S. G.

R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

Katz, J.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

Kemp, C. M.

R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, Orlando, Fla., 1969), pp. 255–269.
[Crossref]

Kleinman, R. E.

Knighton, R. W.

R. W. Knighton, X. R. Huang, “A microtubule mechanism for the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Vis. Sci. 37, S1151 (1996).

Q. Zhou, R. W. Knighton, “Numerical approximation of light scattering from tenuous cylindrical membranes at normal incidence,” Appl. Opt. 34, 2354–2361 (1995).
[Crossref] [PubMed]

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

Q. Zhou, R. W. Knighton, “Spectral reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Vis. Sci. 34, 1504 (1993).

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

R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

Q. Zhou, R. W. Knighton, “Light scattering from a tenuous cylindrical matrix and the reflectance of the retinal nerve fiber layer,” in Ophthalmic Technologies IV, J.-M. Parel, Q. Ren, eds., Proc. SPIE2126, 86–94 (1994).
[Crossref]

Lam, J.

F. Snell, J. Wolken, G. Iverson, J. Lam, Physical Principles of Biological Membranes (Gordon & Breach, New York, 1970), pp. 191–202.

Lehtola, J.

A. Tuulonen, J. Lehtola, P. J. Airaksinen, “Nerve fiber layer defects with normal visual fields,” Ophthalmology 100, 587–598 (1993).
[Crossref]

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Lodish, H.

J. Darnell, H. Lodish, D. Baltimore, Molecular Cell Biology (Scientific, New York, 1990), pp. 109–150, 491–499.

McCally, R. L.

D. E. Freund, R. L. McCally, R. A. Farrell, “Direct summation of fields for light scattering by fibrils with applications to normal corneas,” Appl. Opt. 25, 2739–2746 (1986).
[Crossref]

R. L. McCally, R. A. Farrell, “Light scattering from cornea and corneal transparency,” in Noninvasive Diagnostic Techniques in Ophthalmology, B. R. Masters, ed. (Springer-Verlag, New York, 1990), pp. 189–210.
[Crossref]

Miller, J. M.

J. Caprioli, J. M. Miller, “Measurement of relative nerve fiber layer surface height in glaucoma,” Ophthalmology 96, 633–639 (1989).
[Crossref]

Miller, N. R.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

S. C. Pollock, N. R. Miller, “The retinal nerve fiber layer,” Int. Ophthalmol. Clin. 26, 201–221 (1986).
[Crossref] [PubMed]

Mitchison, J. M.

J. M. Mitchison, “A polarized light analysis of the human red cell ghost,” J. Exp. Biol. 30, 397–432 (1953).

Newman, N. M.

W. F. Hoyt, L. Frisen, N. M. Newman, “Fundoscopy of nerve fiber layer defects,” Invest. Ophthalmol. 12, 814–829 (1973).
[PubMed]

Ogden, T. E.

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

Ohki, S.

S. Ohki, “Dielectric constant and refractive index of lipid bi-layers,” J. Theor. Biol. 19, 97–115 (1968).
[Crossref]

Olsen, J.

S. Brimijoin, J. Olsen, R. Rosenson, “Comparison of the temperature-dependence of rapid axonal transport and microtubules in nerves of the rabbit and bullfrog,” J. Physiol. (London) 287, 303–314 (1979).

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Pflibsen, K. P.

Piezzi, R. S.

E. L. Rodriguez Echandia, R. S. Piezzi, “Microtubules in the nerve fibers of the toad Bufo arenarum Hensel. Effect of low temperature on the sciatic nerve,” J. Cell Biol. 39, 491–497 (1968).
[Crossref]

Pollock, S. C.

S. C. Pollock, N. R. Miller, “The retinal nerve fiber layer,” Int. Ophthalmol. Clin. 26, 201–221 (1986).
[Crossref] [PubMed]

Pugh, E. N.

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Quigley, H. A.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

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

Reiter, K.

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

Richmond, J. H.

J. H. Richmond, “TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-14, 460–464 (1966).
[Crossref]

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[Crossref]

Richter, R. C.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

Roach, G. F.

Robin, A. L.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

Rodriguez Echandia, E. L.

E. L. Rodriguez Echandia, R. S. Piezzi, “Microtubules in the nerve fibers of the toad Bufo arenarum Hensel. Effect of low temperature on the sciatic nerve,” J. Cell Biol. 39, 491–497 (1968).
[Crossref]

Rome-Talbot, D.

D. Rome-Talbot, D. Andre, N. Chalazonitis, “Hypothermic decrease in microtubule density and birefringence in unmyelinated axons,” J. Neurobiol. 9, 247–254 (1978).
[Crossref] [PubMed]

Rosenson, R.

S. Brimijoin, J. Olsen, R. Rosenson, “Comparison of the temperature-dependence of rapid axonal transport and microtubules in nerves of the rabbit and bullfrog,” J. Physiol. (London) 287, 303–314 (1979).

Rowe, M. P.

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]

Schliwa, M.

M. Schliwa, The Cytoskeleton (Springer-Verlag, Vienna, 1986), pp. 51, 95.

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Shakib, S.

R. N. Weinreb, S. Shakib, L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol. 119, 627–636 (1995).
[PubMed]

Shaw, B.

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

Snell, F.

F. Snell, J. Wolken, G. Iverson, J. Lam, Physical Principles of Biological Membranes (Gordon & Breach, New York, 1970), pp. 191–202.

Sommer, A.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Tuulonen, A.

A. Tuulonen, J. Lehtola, P. J. Airaksinen, “Nerve fiber layer defects with normal visual fields,” Ophthalmology 100, 587–598 (1993).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 63–73.

van den Berg, P. M.

Weddell, J. E.

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971), pp. 482–488.

Weinreb, R. N.

R. N. Weinreb, S. Shakib, L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol. 119, 627–636 (1995).
[PubMed]

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

Williams, D. R.

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

Witt, K. A.

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), pp. 705–707.

Wolken, J.

F. Snell, J. Wolken, G. Iverson, J. Lam, Physical Principles of Biological Membranes (Gordon & Breach, New York, 1970), pp. 191–202.

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

Zangwill, L.

R. N. Weinreb, S. Shakib, L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol. 119, 627–636 (1995).
[PubMed]

Zhou, Q.

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

Q. Zhou, R. W. Knighton, “Numerical approximation of light scattering from tenuous cylindrical membranes at normal incidence,” Appl. Opt. 34, 2354–2361 (1995).
[Crossref] [PubMed]

Q. Zhou, R. W. Knighton, “Spectral reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Vis. Sci. 34, 1504 (1993).

Q. Zhou, R. W. Knighton, “Light scattering from a tenuous cylindrical matrix and the reflectance of the retinal nerve fiber layer,” in Ophthalmic Technologies IV, J.-M. Parel, Q. Ren, eds., Proc. SPIE2126, 86–94 (1994).
[Crossref]

Q. Zhou, “Light scattering from a tenuous cylindrical matrix and the reflectance of the retinal nerve fiber layer,” Ph.D. dissertation (University of Miami, Miami, Fla., 1994), available from University Microfilms, Ann Arbor, Mich., pp. 78–96.

Am. J. Ophthalmol. (1)

R. N. Weinreb, S. Shakib, L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol. 119, 627–636 (1995).
[PubMed]

Appl. Opt. (4)

Arch. Ophthalmol. (3)

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: a pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[Crossref] [PubMed]

A. Sommer, J. Katz, H. A. Quigley, N. R. Miller, A. L. Robin, R. C. Richter, K. A. Witt, “Clinically detectable nerve fiber atrophy precedes the onset of glaucomatous field loss,” Arch. Ophthalmol. 109, 77–83 (1991).
[Crossref] [PubMed]

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

IEEE Trans. Antennas Propag. (2)

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[Crossref]

J. H. Richmond, “TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape,” IEEE Trans. Antennas Propag. AP-14, 460–464 (1966).
[Crossref]

Int. Ophthalmol. Clin. (1)

S. C. Pollock, N. R. Miller, “The retinal nerve fiber layer,” Int. Ophthalmol. Clin. 26, 201–221 (1986).
[Crossref] [PubMed]

Invest. Ophthalmol. (1)

W. F. Hoyt, L. Frisen, N. M. Newman, “Fundoscopy of nerve fiber layer defects,” Invest. Ophthalmol. 12, 814–829 (1973).
[PubMed]

Invest. Ophthalmol. Vis. Sci. (6)

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

Q. Zhou, R. W. Knighton, “Spectral reflectance of the retinal nerve fiber layer of the toad,” Invest. Ophthalmol. Vis. Sci. 34, 1504 (1993).

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

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

R. W. Knighton, X. R. Huang, “A microtubule mechanism for the reflectance of the retinal nerve fiber layer,” Invest. Ophthalmol. Vis. Sci. 37, S1151 (1996).

R. W. Knighton, S. G. Jacobson, C. M. Kemp, “The spectral reflectance of the nerve fiber layer of the macaque retina,” Invest. Ophthalmol. Vis. Sci. 30, 2393–2401 (1989).

J. Cell Biol. (2)

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

E. L. Rodriguez Echandia, R. S. Piezzi, “Microtubules in the nerve fibers of the toad Bufo arenarum Hensel. Effect of low temperature on the sciatic nerve,” J. Cell Biol. 39, 491–497 (1968).
[Crossref]

J. Exp. Biol. (1)

J. M. Mitchison, “A polarized light analysis of the human red cell ghost,” J. Exp. Biol. 30, 397–432 (1953).

J. Glaucoma (1)

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

J. Neurobiol. (1)

D. Rome-Talbot, D. Andre, N. Chalazonitis, “Hypothermic decrease in microtubule density and birefringence in unmyelinated axons,” J. Neurobiol. 9, 247–254 (1978).
[Crossref] [PubMed]

J. Neurocytol. (1)

D. Bray, M. B. Bunge, “Serial analysis of microtubules in cultured rat sensory axons,” J. Neurocytol. 10, 589–605 (1981).
[Crossref] [PubMed]

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

J. Physiol. (London) (1)

S. Brimijoin, J. Olsen, R. Rosenson, “Comparison of the temperature-dependence of rapid axonal transport and microtubules in nerves of the rabbit and bullfrog,” J. Physiol. (London) 287, 303–314 (1979).

J. Theor. Biol. (1)

S. Ohki, “Dielectric constant and refractive index of lipid bi-layers,” J. Theor. Biol. 19, 97–115 (1968).
[Crossref]

Ophthalmology (2)

A. Tuulonen, J. Lehtola, P. J. Airaksinen, “Nerve fiber layer defects with normal visual fields,” Ophthalmology 100, 587–598 (1993).
[Crossref]

J. Caprioli, J. M. Miller, “Measurement of relative nerve fiber layer surface height in glaucoma,” Ophthalmology 96, 633–639 (1989).
[Crossref]

Other (11)

M. J. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971), pp. 482–488.

J. Darnell, H. Lodish, D. Baltimore, Molecular Cell Biology (Scientific, New York, 1990), pp. 109–150, 491–499.

R. L. McCally, R. A. Farrell, “Light scattering from cornea and corneal transparency,” in Noninvasive Diagnostic Techniques in Ophthalmology, B. R. Masters, ed. (Springer-Verlag, New York, 1990), pp. 189–210.
[Crossref]

Q. Zhou, R. W. Knighton, “Light scattering from a tenuous cylindrical matrix and the reflectance of the retinal nerve fiber layer,” in Ophthalmic Technologies IV, J.-M. Parel, Q. Ren, eds., Proc. SPIE2126, 86–94 (1994).
[Crossref]

Q. Zhou, “Light scattering from a tenuous cylindrical matrix and the reflectance of the retinal nerve fiber layer,” Ph.D. dissertation (University of Miami, Miami, Fla., 1994), available from University Microfilms, Ann Arbor, Mich., pp. 78–96.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 63–73.

F. Snell, J. Wolken, G. Iverson, J. Lam, Physical Principles of Biological Membranes (Gordon & Breach, New York, 1970), pp. 191–202.

M. Schliwa, The Cytoskeleton (Springer-Verlag, Vienna, 1986), pp. 51, 95.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, Orlando, Fla., 1969), pp. 255–269.
[Crossref]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–213.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), pp. 705–707.

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Figures (9)

Fig. 1
Fig. 1

Coordinate system and fibril arrays used in the calculations. A, One cylindrical fibril located at the origin. The fibril axis is parallel to the z axis and the incident light is parallel to the x axis. Incident wave I is divided into TE and TM polarization modes with electric vectors Ei perpendicular and parallel to the fibril axis. Observer O is located far from the fiber (ρ ≫ array dimensions) at scattering angle θ. B, Array of spatially separated parallel fibrils viewed in cross section. The z axis comes out of the page. The ith fibril in the array (filled circle) is located by its coordinates xi, yi. For perpendicular incidence, scattered wave S has the same polarization mode as the incident wave. C, Array of adjacent, parallel fibrils that represent a cylindrical membrane. The ith fibril is located by its coordinates xi, yi. The membrane orientation at the ith fibril is specified by φ i, the angle between the membrane normal and the incident beam.

Fig. 2
Fig. 2

Cross sections of the cylindrical arrays obtained from a 22-µm2 nerve fiber bundle. A, Axonal membranes. The arrow shows the direction of incident light used in all calculations. B, Microtubules. The five squares show the 1.5 µm × 1.5 µm boxes used on this bundle to sample the arrays of membranes and microtubules. C, Neurofilaments. D, Mitochondrial outlines. The smallest outlines probably result from sectioning near the ends of mitochondria.

Fig. 3
Fig. 3

Angular scattering functions for arrays representing AM’s and MT’s. Examples of σTM (solid curves) and σTE (dashed curves) calculated at 1° intervals from 53 1.5 µm × 1.5 µm sample boxes are shown for three wavelengths.

Fig. 4
Fig. 4

Smoothed angular scattering functions showing σTM at six wavelengths. In order to compare the function shapes for AM’s and MT’s, the ordinates of the two panels are logarithmic and span equal ranges of scale. The left-hand edge of the MT panel shows incoherent scatter by the same density of MT’s, for which σTM does not depend on θ.

Fig. 5
Fig. 5

Spectra calculated for AM and MT arrays in the backscattering (filled circles) and side scattering (open circles) directions. The average σTM¯ was computed for the two 60° ranges shown in the legend. The solid line superimposed on the MT spectra shows the λ-3 dependence expected from the same density of randomly distributed MT’s scattering incoherently. The larger symbols show experimental values derived from the reflectance per unit thickness of toad RNFL. Data from the same experiment have a common symbol. Data represented by the inverted triangle at 440 nm and the upright triangle at 500 nm are from Ref. 9; the other points were obtained by similar methods.

Fig. 6
Fig. 6

Angular scattering by an array of thick cylinders representing mitochondria. At four wavelengths σTM was calculated from 367 mitochondria with equivalent diameters of 0.18 ± 0.06 µm (mean ± s.d.) derived from a total bundle area of 186 µm2. The relative refractive index m = 1.03.

Fig. 7
Fig. 7

Parametric dependence at 560 nm of the relative TM mode scattering intensity averaged over the backscattering directions (180 ± 30°). Dependence on relative refractive index m is shown for all organelles, on membrane thickness t for AM’s, and on organelle density d for MT’s and mitochondria. A tick mark on the inside of each scale shows the standard value of the parameter. All intensity values are normalized to those for membranes with the standard parameters (m = 1.15, t = 8 nm).

Fig. 8
Fig. 8

Polarization ratios for light scattering from the membrane array (AM) are systematically higher than from the fiber array (MT). Each curve is the ratio of the corresponding pair of curves in Fig. 3. The MT curves are all identical and depict Eq. (19) for m = 1.08.

Fig. 9
Fig. 9

Parametric dependence of form birefringence for arrays of AM’s and MT’s presented in the same format as Fig. 7. The membrane thickness scale can be applied to either toad or macaque by the appropriate vertical translation.

Tables (2)

Tables Icon

Table 1 Base Values for the Optical Parameters of the Analyzed Structures

Tables Icon

Table 2 Calculated and Measured Form Birefringence of Various Arraysa

Equations (23)

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

Exif=0, Eyif=0, Ezif=1,
Exif=0, Eyif=2m2+1, Ezif=0
Exif=0, Eyif=0, Ezif=1,
Exif=-m2-12m2sin 2φi, Eyif=1-m2-12m21-cos 2φi, Ezif=0.
T1rθ=πka2m2-1J1kai=1Nr EzifSi,
T2rθ=πka2m2-1J1kai=1NrExif sin θ-Eyif cos θSi,
Si=exp-jkxiexpjkxi cos θ+yi sin θ,
σTMλ, θ=2πkAT1θ2,
σTEλ, θ=2πkAT2θ2.
Tpθ2=KK-11Kr=1KTprθ2-1Kr=1K Tprθ2.
εTM=ne2=DTMETM=f1n12+f2n22.
E1TE=2m2+1E2TE=2n22n12+n22E2TE,
ETE=f1E1TE+f2E2TE=f2+2n22n12+n22f1E2TE,
DTE=f1D1TE+f2D2TE=n22f2+2n12n22n12+n22f1E2TE.
εTE=no2=DTEETE=f2n24+1+f1n12n22f2n12+1+f1n22.
E1TE=1-AE2TE=n12+n222n12E2TE,
εTE=no2=DTEETE=f1n14+1+f2n12n22f1n22+1+f2n12.
ne-nom2-122m2+1f11-f1m4+2m2+54m2+1n.
ne-nom2-122m2+1f11-f1n.
ne-nom2-124m2f11-f13m4+2m2+38m2n.
ne-nom2-124m2f11-f1n.
σTM, incoherent=π4a4n3m2-12dλ3
σTEσTM=2 cos θm2+12.

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