Abstract

An electro-optic device is used that permits the measurement of polarized absorption spectra (linear dichroism). The change of the polarization state of a light beam brought about by passage through the optic elements of a dichrograph are described mathematically by a transformation of the Stokes vector. The polarization or absorption properties of the optical elements are described by the Mueller matrices. The dichroic properties of sheep retina and cornea are studied in vitro.

© 2001 Optical Society of America

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References

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  1. W. K. Von Haidinger, “Über das direkte Erkennen des polarisierten Lichts und der Lage der Polarisationsebene,” Ann. Phys. Chem. 63, 29–39 (1884).
  2. M. Schliwa, The Cytoskeleton (Springer-Verlag, Vienna, 1986).
  3. O. Wiener, “Die Theorie des Mischkörpers für das Feld der Stationären Strömung,” Abh. Saechs. Ges. Akad. Wiss. Math.-Phys. Kl. 32, 507–604 (1912).
  4. A. W. Dreher, K. Reiter, R. N. Weinreb, “Spacially resolved birefringence of the retinal nerve fiber layer assessed with a retinal laser ellipsometer,” Appl. Opt. 31, 3730–3735 (1992).
    [CrossRef] [PubMed]
  5. R. P. Hemenger, “Dichroism of the macula pigment and Haidinger’s brushes,” J. Opt. Soc. Am. 72, 734–737 (1982).
    [CrossRef] [PubMed]
  6. L. Mala, “Intérêt de la polarimétrie dans les moyens d’étude objectifs de la couche de fibres optiques rétiniennes pour le diagnostic précoce de la neuropathie glaucomateuse,” Thèse de spécialité en Médecine (Université Henri Poincaré, Nancy I, Vandœuvre-lès-Nancy, France, 1997).
  7. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).
  8. H. Mueller, “The foundations of optics (abstract),” J. Opt. Soc. Am. 38, 661 (1948).
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 708.
  10. R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–219 (1980).
    [CrossRef] [PubMed]
  11. G. J. Van Blokland, 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] [PubMed]
  12. F. A. Bettelheim, “On the optical anisotropy of the lens fibers,” Exp. Eye. Res. 21, 231 (1975).
    [CrossRef] [PubMed]
  13. H. B. Klein Brink, G. J. Blokland, “Birefringence of the human foveal area assessed in vivo with Mueller-matrix ellipsometry,” J. Opt. Soc. Am. A 5, 49–57 (1987).
  14. R. A. Bone, J. T. Landrum, “Macular pigment in Henle fiber membranes: a model for Haidinger’s brushes,” Vision Res. 24, 103–108 (1984).
    [CrossRef]

1992

1987

1984

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

1982

1980

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–219 (1980).
[CrossRef] [PubMed]

1975

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

1948

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

1912

O. Wiener, “Die Theorie des Mischkörpers für das Feld der Stationären Strömung,” Abh. Saechs. Ges. Akad. Wiss. Math.-Phys. Kl. 32, 507–604 (1912).

1884

W. K. Von Haidinger, “Über das direkte Erkennen des polarisierten Lichts und der Lage der Polarisationsebene,” Ann. Phys. Chem. 63, 29–39 (1884).

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).

Bettelheim, F. A.

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

Blokland, G. J.

Bone, R. A.

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

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–219 (1980).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 708.

Dreher, A. W.

Hemenger, R. P.

Klein Brink, H. B.

Landrum, J. T.

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

Mala, L.

L. Mala, “Intérêt de la polarimétrie dans les moyens d’étude objectifs de la couche de fibres optiques rétiniennes pour le diagnostic précoce de la neuropathie glaucomateuse,” Thèse de spécialité en Médecine (Université Henri Poincaré, Nancy I, Vandœuvre-lès-Nancy, France, 1997).

Mueller, H.

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

Reiter, K.

Schliwa, M.

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

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).

Van Blokland, G. J.

Verhelst, S. C.

Von Haidinger, W. K.

W. K. Von Haidinger, “Über das direkte Erkennen des polarisierten Lichts und der Lage der Polarisationsebene,” Ann. Phys. Chem. 63, 29–39 (1884).

Weinreb, R. N.

Wiener, O.

O. Wiener, “Die Theorie des Mischkörpers für das Feld der Stationären Strömung,” Abh. Saechs. Ges. Akad. Wiss. Math.-Phys. Kl. 32, 507–604 (1912).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 708.

Abh. Saechs. Ges. Akad. Wiss. Math.-Phys. Kl.

O. Wiener, “Die Theorie des Mischkörpers für das Feld der Stationären Strömung,” Abh. Saechs. Ges. Akad. Wiss. Math.-Phys. Kl. 32, 507–604 (1912).

Ann. Phys. Chem.

W. K. Von Haidinger, “Über das direkte Erkennen des polarisierten Lichts und der Lage der Polarisationsebene,” Ann. Phys. Chem. 63, 29–39 (1884).

Appl. Opt.

Exp. Eye. Res.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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.

R. A. Bone, “The role of the macular pigment in the detection of polarized light,” Vision Res. 20, 213–219 (1980).
[CrossRef] [PubMed]

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

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 708.

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

L. Mala, “Intérêt de la polarimétrie dans les moyens d’étude objectifs de la couche de fibres optiques rétiniennes pour le diagnostic précoce de la neuropathie glaucomateuse,” Thèse de spécialité en Médecine (Université Henri Poincaré, Nancy I, Vandœuvre-lès-Nancy, France, 1997).

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Figures (3)

Fig. 1
Fig. 1

Optical setup of the dichrograph for measuring LD: S, source; M, ellipsoidal mirror; F1, F2, F3, slits; P1, P2, quartz prisms; L1, L2, L3, lenses; Cr, birefringence modulator; Cv, sample; PMT, photomultiplier.

Fig. 2
Fig. 2

Schematic diagram of the optical system and azimutal orientation of the elements: P, polarizer; Cr, modulator; Cv, studied dichroic medium; PMT, photomultiplier.

Fig. 3
Fig. 3

Spectra of the linear dichroism of a sheep eye: (a) with the retina, (b) without the retina. Experimental conditions: Number of scan, 1; cycles, 3; start, 550 nm; stop, 750 nm; integration time, 0.50 s; increment, 2.00 nm; bandpass, 2.00 nm.

Tables (1)

Tables Icon

Table 1 Dichroism of Cornea for λ = 633 nm, with R = 10.7 mm for the Major Axis and R = 9.2 mm for the Minor Axis

Equations (15)

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Ext, M=axtcosω0t-θxt, Eyt, M=aytcosω0t-θyt.
S=s0s1s2s3=ax2+ay2ax2-ay22axay cosθx-θy2axay sinθx-θy.
ñx=nx+iκx,ñy=ny+iκy,
S1=Mp×S0=1/21100110000000000s0,0000=1/2s0,0s0,000.
ST=MCv×MCr×S1, ST=s0,Ts1,Ts2,Ts3,T=12exp-2κl×cosh 2κlsinh 2κl00sinh 2κlcosh 2κl0000cos Ψ-sin Ψ00sin Ψcos Ψ×10000cos Φ0sin Φ00100-sin Φ0cos Φs0,0s0,000.
Ψ=2πλny-nxl, κ=12κy-κx, κ=12κy+κx.
ST=12s0,0 exp-2κlcosh 2κl+sinh 2κl cos Φsinh 2κl+cosh 2κl cos Φsin Ψ sin Φ-sin Ψ sin Φ=s0,Ts1,Ts2,Ts3,T.
s1,T2+s2,T2+s3,T2=s0,T2.
IT=s0,T=1/2s0,0 exp-2κlcosh 2κl+cos Φ sinh 2κl,
IT=1/2I0 exp-κy-κxl(1/2expκy-κxl+exp-κy-κxl+1/2cos Φexpκy-κxl-exp-κy-κxl}),
IT=1/2I0exp-2κylsin2Φ/2+exp-2κxlcos2Φ/2.
IT0=1/2I0 exp-2κxl, IT180=1/2I0 exp-2κyl.
LD=I-II+I=exp-2κyl-exp-2κxlexp-2κyl+exp-2κxl=expκx-κyl-exp-κx-κylexpκx-κyl+exp-κx-κyl, LD=tanhκx-κyl<0.
ΔA=A-A/A+A.
ΔA=κx-κyκx+κy<0.

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