Abstract

An electro-optic device mounted on a slit lamp to assess the degree of polarization of a light beam that has double passed through the retina about the optic-nerve head in the living human eye is described. The asymmetric structure of the retinal nerve’s fiber layer possesses a linear-form dichroism and will partially polarize an unpolarized light beam that is scattered at the fundus of the eye and has double passed the ocular media (cornea, lens, retina). This partial polarization is a function of the retinal nerve’s fiber layer thickness, and its measurement may be used for exploring glaucoma and other retinal neuropathies. Experimental conditions allow us to neglect corneal dichroism. The first clinical measurements show a different degree of polarization between normal and glaucomatous eyes and a good correlation with the results obtained by optical coherence tomography.

© 2005 Optical Society of America

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2004

H. M. Kwok, V. W. Lee, F. S. Kwok, “Retinal nerve fiber loss in high- and normal-tension glaucoma by optical coherence tomography,” Optom. Vis. Sci. 81, 369–372 (2004).
[CrossRef]

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

V. Louis-Dorr, K. Naoun, P. Allé, A.-M. Benoit, A. Raspiller, “Linear dichroism of the cornea,” Appl. Opt. 43, 1515–1521 (2004).
[CrossRef] [PubMed]

2003

N. J. Reus, T. P. Colen, H. G. Lemij, “Visualization of localized retinal nerve fiber layer defects with the GDx with individualized and with fixed compensation of anterior segment birefringence,” Ophthalmology 110, 1512–1516 (2003).
[CrossRef] [PubMed]

T. J. M. Berendschot, P. J. D. Delint, D. Van Norren, “Fundus reflectance—historical and present ideas,” Prog. Retinal Eye Res. 21, 171–200 (2003).
[CrossRef]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

2001

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

A. M. Benoit, K. Naoun, V. Louis-Dorr, L. Mala, A. Raspiller, “Linear dichroism of the retinal nerve fiber layer expressed with Mueller matrices,” Appl. Opt. 40, 565–569 (2001).
[CrossRef]

1999

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

1995

M. R. Hee, J. A. Izatt, E. A. Swanson, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113, 325–332 (1995).
[CrossRef] [PubMed]

C. A. Puliafito, M. R. Hee, C. P. Lin, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography: pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[CrossRef]

1994

S. Miglior, L. Rosetti, L. Brigatti, “Reproductibility of the retinal nerve fiber layer evaluation by dynamic scanning laser ophthalmoscopy,” Am. J. Ophthalmol. 118, 16–23 (1994).
[PubMed]

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]

1988

H. B. Klein Brink, G. J. Van Blockland, “Birefringence of the human foveal area assessed in vivo with Mueller matrix ellipsometry,” J. Opt. Soc. Am. A 5, 49–57 (1988).
[CrossRef]

A. W. Dreher, K. Reiter, J. Bill, “Assessment of the nerve fiber layer thickness with the LTS laser tomographic scanner,” Invest. Ophthalmol. Visual Sci. 29, 355 (1988).

1987

1986

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

G. J. Van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef]

1984

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haindinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

1982

1975

F. A. Bettelheim, “On the optical anisotropy of the lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

R. A. Weale, “Sex, age, and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1975).
[CrossRef]

1953

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

1948

H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661(A)(1948).

1852

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Allé, P.

Amini, P.

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Arkell, S. A.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

Artal, P.

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

Bagga, H.

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

Benoit, A. M.

Benoit, A.-M.

Berendschot, T. J. M.

T. J. M. Berendschot, P. J. D. Delint, D. Van Norren, “Fundus reflectance—historical and present ideas,” Prog. Retinal Eye Res. 21, 171–200 (2003).
[CrossRef]

Berrio, E.

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

Bettelheim, F. A.

F. A. Bettelheim, “On the optical anisotropy of the lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

Bill, J.

A. W. Dreher, K. Reiter, J. Bill, “Assessment of the nerve fiber layer thickness with the LTS laser tomographic scanner,” Invest. Ophthalmol. Visual Sci. 29, 355 (1988).

Boden, C.

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Bone, R. A.

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haindinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1965).

Bour, L. J.

L. J. Bour, Polarized Light and the Eye, Vol. 1 of Visual Optics and Instrumentation (CRC, 1991).

Bowd, C.

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Brigatti, L.

S. Miglior, L. Rosetti, L. Brigatti, “Reproductibility of the retinal nerve fiber layer evaluation by dynamic scanning laser ophthalmoscopy,” Am. J. Ophthalmol. 118, 16–23 (1994).
[PubMed]

Bueno, J. M.

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

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

Chan, K.

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

Ching, F. C.

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

Chipman, R. A.

R. A. Chipman, Handbook of Optics (McGraw-Hill, 1995).

Colen, T. P.

N. J. Reus, T. P. Colen, H. G. Lemij, “Visualization of localized retinal nerve fiber layer defects with the GDx with individualized and with fixed compensation of anterior segment birefringence,” Ophthalmology 110, 1512–1516 (2003).
[CrossRef] [PubMed]

Crowston, J.

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

D’Anna, S. A.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

Delint, P. J. D.

T. J. M. Berendschot, P. J. D. Delint, D. Van Norren, “Fundus reflectance—historical and present ideas,” Prog. Retinal Eye Res. 21, 171–200 (2003).
[CrossRef]

Dreher, A. W.

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]

A. W. Dreher, K. Reiter, J. Bill, “Assessment of the nerve fiber layer thickness with the LTS laser tomographic scanner,” Invest. Ophthalmol. Visual Sci. 29, 355 (1988).

El Beltagi, T. A.

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Feuer, W.

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

Goldbaum, M. H.

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

Greenfield, D. S.

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

Hee, M. R.

M. R. Hee, J. A. Izatt, E. A. Swanson, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113, 325–332 (1995).
[CrossRef] [PubMed]

C. A. Puliafito, M. R. Hee, C. P. Lin, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography: pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[CrossRef]

Hemenger, R. P.

Hochheimer, B. F.

Izatt, J. A.

M. R. Hee, J. A. Izatt, E. A. Swanson, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113, 325–332 (1995).
[CrossRef] [PubMed]

Jaronski, J.

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

Jicuang, H.

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

Klein Brink, H. B.

Knighton, R. W.

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

Kues, H. A.

Kues, H. A. D.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

Kwok, F. S.

H. M. Kwok, V. W. Lee, F. S. Kwok, “Retinal nerve fiber loss in high- and normal-tension glaucoma by optical coherence tomography,” Optom. Vis. Sci. 81, 369–372 (2004).
[CrossRef]

Kwok, H. M.

H. M. Kwok, V. W. Lee, F. S. Kwok, “Retinal nerve fiber loss in high- and normal-tension glaucoma by optical coherence tomography,” Optom. Vis. Sci. 81, 369–372 (2004).
[CrossRef]

Landrum, J. T.

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haindinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

Lee, T. W.

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

Lee, V. W.

H. M. Kwok, V. W. Lee, F. S. Kwok, “Retinal nerve fiber loss in high- and normal-tension glaucoma by optical coherence tomography,” Optom. Vis. Sci. 81, 369–372 (2004).
[CrossRef]

Lemij, H. G.

N. J. Reus, T. P. Colen, H. G. Lemij, “Visualization of localized retinal nerve fiber layer defects with the GDx with individualized and with fixed compensation of anterior segment birefringence,” Ophthalmology 110, 1512–1516 (2003).
[CrossRef] [PubMed]

Lin, C. P.

C. A. Puliafito, M. R. Hee, C. P. Lin, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography: pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[CrossRef]

Louis-Dorr, V.

Mala, L.

Medeiros, F. A.

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

Meideros, F. A.

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

Miglior, S.

S. Miglior, L. Rosetti, L. Brigatti, “Reproductibility of the retinal nerve fiber layer evaluation by dynamic scanning laser ophthalmoscopy,” Am. J. Ophthalmol. 118, 16–23 (1994).
[PubMed]

Mohammadi, K.

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

Mueller, H.

H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661(A)(1948).

Naoun, K.

Naylor, E. J.

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

Ozolinsh, M.

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

Puliafito, C. A.

C. A. Puliafito, M. R. Hee, C. P. Lin, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography: pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[CrossRef]

Quigley, H. A.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

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]

A. W. Dreher, K. Reiter, J. Bill, “Assessment of the nerve fiber layer thickness with the LTS laser tomographic scanner,” Invest. Ophthalmol. Visual Sci. 29, 355 (1988).

Reus, N. J.

N. J. Reus, T. P. Colen, H. G. Lemij, “Visualization of localized retinal nerve fiber layer defects with the GDx with individualized and with fixed compensation of anterior segment birefringence,” Ophthalmology 110, 1512–1516 (2003).
[CrossRef] [PubMed]

Robin, S.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

Rosetti, L.

S. Miglior, L. Rosetti, L. Brigatti, “Reproductibility of the retinal nerve fiber layer evaluation by dynamic scanning laser ophthalmoscopy,” Am. J. Ophthalmol. 118, 16–23 (1994).
[PubMed]

Sample, P. A.

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Sejnowski, T. J.

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. Press, 1962).

Stanworth, A.

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

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Summer, A.

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

Swanson, E. A.

M. R. Hee, J. A. Izatt, E. A. Swanson, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113, 325–332 (1995).
[CrossRef] [PubMed]

Van Blockland, G. J.

H. B. Klein Brink, G. J. Van Blockland, “Birefringence of the human foveal area assessed in vivo with Mueller matrix ellipsometry,” J. Opt. Soc. Am. A 5, 49–57 (1988).
[CrossRef]

G. J. Van Blockland, S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4, 82–90 (1987).
[CrossRef]

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

G. J. Van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef]

Van Norren, D.

T. J. M. Berendschot, P. J. D. Delint, D. Van Norren, “Fundus reflectance—historical and present ideas,” Prog. Retinal Eye Res. 21, 171–200 (2003).
[CrossRef]

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

Verhelst, S. C.

Weale, R. A.

R. A. Weale, “Sex, age, and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1975).
[CrossRef]

Weinreb, R. N.

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

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]

Williams, J. M.

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1965).

Zangwill, L. M.

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

Am. J. Ophthalmol.

H. Bagga, D. S. Greenfield, W. Feuer, R. W. Knighton, “Scanning laser polarimetry with variable corneal compensation and optical coherence tomography in normal and glaucomatous eyes,” Am. J. Ophthalmol. 135, 521–529 (2003).
[CrossRef] [PubMed]

S. Miglior, L. Rosetti, L. Brigatti, “Reproductibility of the retinal nerve fiber layer evaluation by dynamic scanning laser ophthalmoscopy,” Am. J. Ophthalmol. 118, 16–23 (1994).
[PubMed]

K. Mohammadi, C. Bowd, R. N. Weinreb, F. A. Meideros, P. A. Sample, L. M. Zangwill, “Retinal nerve fiber layer thickness measurements with scanning laser polarimetry predict glaucomatous visual field loss,” Am. J. Ophthalmol. 138, 592–601 (2004).
[CrossRef] [PubMed]

Appl. Opt.

Arch. Ophthalmol.

F. A. Meideros, L. M. Zangwill, C. Bowd, R. N. Weinreb, “Comparison of the GDx VCC scanning laser polarimeter, HRT II confocal scanning laser ophthalmoscope, and Stratus OCT optical coherence tomograph for the detection of glaucoma,” Arch. Ophthalmol. 122, 827–837 (2004).
[CrossRef]

A. Summer, H. A. D. Kues, S. A. D’Anna, S. A. Arkell, S. Robin, H. A. Quigley, “Cross-polarization photography of the nerve fiber layer,” Arch. Ophthalmol. 102, 864–869 (1984).
[CrossRef]

M. R. Hee, J. A. Izatt, E. A. Swanson, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113, 325–332 (1995).
[CrossRef] [PubMed]

C. A. Puliafito, M. R. Hee, C. P. Lin, “Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography: pilot study,” Arch. Ophthalmol. 113, 586–596 (1995).
[CrossRef]

Clin. Vision Sci.

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).

Exp. Eye Res.

F. A. Bettelheim, “On the optical anisotropy of the lens fiber cells,” Exp. Eye Res. 21, 231–234 (1975).
[CrossRef] [PubMed]

R. A. Weale, “Sex, age, and birefringence of the human crystalline lens,” Exp. Eye Res. 29, 449–461 (1975).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

A. W. Dreher, K. Reiter, J. Bill, “Assessment of the nerve fiber layer thickness with the LTS laser tomographic scanner,” Invest. Ophthalmol. Visual Sci. 29, 355 (1988).

C. Bowd, L. M. Zangwill, F. A. Medeiros, H. Jicuang, K. Chan, T. W. Lee, T. J. Sejnowski, M. H. Goldbaum, P. A. Sample, J. Crowston, R. N. Weinreb, “Confocal scanning laser ophthalmoscopy classifiers and stereophotograph evaluation for prediction of visual field abnormalities in glaucoma-suspect eyes,” Invest. Ophthalmol. Visual Sci. 45, 2255–2262 (2004).
[CrossRef]

Invest. Ophthalmol. Visual. Sci.

L. M. Zangwill, K. Chan, C. Bowd, H. Jicuang, T. W. Lee, R. N. Weinreb, T. J. Sejnowski, M. H. Goldbaum, “Heidelberg retina tomograph measurements of the optic disc and parapapillary retina for detecting glaucoma analyzed by machine learning classifiers,” Invest. Ophthalmol. Visual. Sci. 45, 3144–3151 (2004).
[CrossRef]

J. Exp. Biol.

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

J. Opt. Soc. Am

J. M. Bueno, E. Berrio, M. Ozolinsh, P. Artal, “Degree of polarization as an objective method of estimating scattering,” J. Opt. Soc. Am 21, 1316–1327 (2004).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthal. Physiol. Opt.

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

Ophthalmology

N. J. Reus, T. P. Colen, H. G. Lemij, “Visualization of localized retinal nerve fiber layer defects with the GDx with individualized and with fixed compensation of anterior segment birefringence,” Ophthalmology 110, 1512–1516 (2003).
[CrossRef] [PubMed]

T. A. El Beltagi, C. Bowd, C. Boden, P. Amini, P. A. Sample, L. M. Zangwill, R. N. Weinreb, “Retinal nerve fiber layer thickness measured with optical coherence tomography is related to visual function in glaucomatous eyes,” Ophthalmology 110, 2185–2191 (2003).
[CrossRef] [PubMed]

Optom. Vis. Sci.

H. M. Kwok, V. W. Lee, F. S. Kwok, “Retinal nerve fiber loss in high- and normal-tension glaucoma by optical coherence tomography,” Optom. Vis. Sci. 81, 369–372 (2004).
[CrossRef]

L. M. Zangwill, F. C. Ching, J. M. Williams, R. N. Weinreb, “New technologies for diagnosing and monitoring glaucomatous optic neuropathy,” Optom. Vis. Sci. 76, 526–536 (1999).
[CrossRef] [PubMed]

Prog. Retinal Eye Res.

T. J. M. Berendschot, P. J. D. Delint, D. Van Norren, “Fundus reflectance—historical and present ideas,” Prog. Retinal Eye Res. 21, 171–200 (2003).
[CrossRef]

Trans. Cambridge Philos. Soc.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Vision Res.

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

G. J. Van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef]

R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haindinger’s brushes,” Vision Res. 24, 103–108 (1984).
[CrossRef]

Other

W. A. Shurcliff, Polarized Light (Harvard U. Press, 1962).

R. A. Chipman, Handbook of Optics (McGraw-Hill, 1995).

American National Standards Institute, Safe Use of Lasers, ANSI Standard Z136.1-2000 (American National Standards Institute, 2000).

M. Born, E. Wolf, Principles of Optics (Pergamon, 1965).

L. J. Bour, Polarized Light and the Eye, Vol. 1 of Visual Optics and Instrumentation (CRC, 1991).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the device.

Fig. 2
Fig. 2

Functional diagram of the experimental sensor for measuring degree of polarization.

Fig. 3
Fig. 3

Locations on the retina: 1, inferior location (Inf); 2, superior location (Sup); 3, nasal location (Nas); 4, temporal location (Temp).

Fig. 4
Fig. 4

Thickness of the NFLT obtained by OCT for glaucomatous eye 6 with a superior arcuate defect.

Fig. 5
Fig. 5

(a) Signals for point 1 of normal eye 1; (b) signals for point 4 of glaucomatous eye 6.

Fig. 6
Fig. 6

Graphic representation of 100 × P (measured by ADR) for different locations (points 1–4) of normal eyes 1–5 and glaucomatous eyes 6–10.

Fig. 7
Fig. 7

Graphic representation of lr (measured by OCT) for the locations (points 1–4) of normal eyes 1–5 and glaucomatous eyes 6–10.

Tables (2)

Tables Icon

Table 1 Values of 100 × P Measured by ADR, lr Measured by OCT, and Δκ = (κy − κx) = a tan(P/2lR) for the Locations (Points 1–4) of Normal Eyes 1–5a

Tables Icon

Table 2 Values of 100 × P Measured by ADR, lr Measured by OCT, and Δκ = (κy − κx) = a tan(P/2lR) for the Locations (Points 1–4) of the Glaucomatous Eyes 6–10

Equations (22)

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

P = ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 S 0 .
S T = M C , 2 × M R × M C , 1 × S 0 .
M C , 1 × S 0 = exp ( 2 κ s , C l C ) × | cosh 2 κ d , C l C sinh 2 κ d , C l C 0 0 sinh 2 κ d , C l C cosh 2 κ d , C l C 0 0 0 0 cos φ C sin φ C 0 0 sin φ C cos φ C | [ S 0 , 0 0 0 0 ] = I 0 exp ( 2 κ s , C l C ) [ cosh 2 κ d , C l C sinh 2 κ d , C l C 0 0 ] ,
M R = exp ( 4 κ s , R l R ) × | cosh 4 κ d , R l R sinh 4 κ d , R l R 0 0 sinh 4 κ d , R l R cosh 4 κ d , R l R 0 0 0 0 cos φ R sin φ R 0 0 sin φ R cos φ R | ,
S T = [ S 0 , T S 1 , T S 2 , T S 3 , T ] = I 0 exp [ 4 ( κ s , C l C + κ s , R l R ) ] × [ cosh 4 ( κ d , C l C + κ d , R l R ) sinh 4 ( κ d , C l C + κ d , R l R ) 0 0 ] .
P = ( S 1 , T 2 + S 2 , T 2 + S 3 , T 2 ) 1 / 2 S 0 , T = sinh 4 ( κ d , C l C + κ d , R l R ) cosh 4 ( κ d , C l C + κ d , R l R ) = tanh [ 4 ( κ d , C l C + κ d , R l R ) ] .
S A = M A × S T ,
S A = 1 2 I 0 [ 1 cos 2 θ sin 2 θ 0 cos 2 θ cos 2 2 θ sin 2 θ cos 2 θ 0 sin 2 θ sin 2 θ cos 2 θ sin 2 2 θ 0 0 0 0 0 ] exp [ 4 ( κ s , C l C + κ s , R l R ) ] [ cosh 4 ( κ d , C l C + κ d , R l R ) sinh 4 ( κ d , C l C + κ d , R l R ) 0 0 ] , [ S 0 , A S 1 , A S 2 , A S 3 , A ] = I 0 2 exp [ 4 ( κ s , C l C + κ s , R l R ) ] [ cosh 4 ( κ d , C l C + κ d , R l R ) + cos 2 θ sinh 4 ( κ d , C l C + κ d , R l R ) cos 2 θ cosh 4 ( κ d , C l C + κ d , R l R ) + cos 2 2 θ sinh 4 ( κ d , C l C + κ d , R l R ) sin 2 θ cosh 4 ( κ d , C l C + κ d , R l R ) + sin 2 θ cos 2 θ sinh 4 ( κ d , C l C + κ d , R l R ) 0 ] .
I A ( θ ) = S 0 , A = I 0 2 exp [ 4 ( κ s , C l C + κ s , R l R ) ] × [ cosh 4 ( κ d , C l C + κ d , R l R ) + cos 2 θ sinh 4 ( κ d , C l C + κ d , R l R ) ] ,
I A , max = I 0 2 exp [ 4 ( κ s , C l C + κ s , R l R ) ] [ cosh 4 ( κ d , C l C + κ d , R l R ) + sinh 4 ( κ d , C l C + κ d , R l R ) ] , I A , min = I 0 2 exp [ 4 ( κ s , C l C + κ s , R l R ) ] [ cosh 4 ( κ d , C l C + κ d , R l R ) sinh 4 ( κ d , C l C + κ d , R l R ) ] .
I A , max I A , min I A , max + I A , min = tanh 4 ( κ d , C l C + κ d , R l R ) .
P = tanh 4 ( κ d , C l C + κ d , R l R ) = tanh 2 [ ( κ κ ) l C + ( κ y κ x ) l R ] = I A , max I A , min I A , max + I A , min .
P = I A , max I A , min I A , max + I A , min = tanh 2 [ ( κ y κ x ) l R ] .
δ P = 2 ( κ y κ x ) δ l R cosh 2 [ 2 ( κ y κ x ) l R ] .
I A ( θ ) = I 0 2 exp [ 2 ( κ y + κ x ) l R ] [ cosh 2 ( κ y κ x ) l R + cos 2 θ sinh 2 ( κ y κ x ) l R ] = I 0 2 [ exp [ 4 ( κ x l R ) cos 2 θ + exp ( 4 κ y l R ) sin 2 θ ] .
I max = I 0 2 exp ( 4 κ x l R ) = A 2 , I min = I 0 2 exp ( 4 κ y l R ) = B 2 ;
I A ( θ ) = ( A 2 + B 2 ) / 2 + [ ( A 2 B 2 ) / 2 ] cos 2 Ω t ,
P = I A , max I A , min I A , max + I A , min = A 2 B 2 A 2 + B 2 .
U = K cc ( A 2 + B 2 ) / 2 + K ac [ ( A 2 B 2 ) / 2 ] cos 2 Ω t = U cc + u ac cos 2 Ω t .
U cc ( nTe ) = K cc ( A 2 + B 2 ) / 2 , u ac ( nTe ) = K cc [ ( A 2 B 2 ) / 2 ] cos 2 Ω nTe = u ac cos 2 Ω nTe ,
A 2 = U cc K cc + u ac K ac , B 2 = U cc K cc u ac K ac .
P = u ac / K ac U cc / K cc = K cc u ac K ac U cc .

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