Abstract

A spectrophotometer for noninvasively measuring the intrinsic fluorescence and the reflectance of the ocular fundus is described. The instrument uses multichannel spectral analysis for recording fluorescence emission spectra (500–800 nm) with seven excitation wavelengths between 430 and 550 nm and for the determination of fundus reflectance spectra (400–800 nm). Measurements are performed from a discrete fundus area, with a spatial resolution of a 1–2° visual angle. Calibration procedures are detailed. Representative fluorescence and reflectance spectra obtained from five normal subjects indicate that the fluorescence originates from within the fundus layers. Although the absolute fundus fluorescence measurement is affected by lens absorption and ocular refraction, it is minimally influenced by the strong fluorescence of the crystalline lens.

© 1994 Optical Society of America

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  1. J. J. Vos, A. A. Munnik, J. Boogaard, “Absolute spectral reflectance of the fundus oculi,” J. Opt. Soc. Am. 55, 573–574 (1965).
    [Crossref]
  2. J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
    [Crossref] [PubMed]
  3. D. van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
    [Crossref] [PubMed]
  4. F. C. Delori, K. P. Pflibsen, “Spectral reflectance of the human ocular fundus,” Appl. Opt. 28, 1061–1077 (1989).
    [Crossref] [PubMed]
  5. D. van Norren, J. van der Kraats, “A continuously recording retinal densitometer,” Vision Res. 21, 897–905 (1981).
    [Crossref] [PubMed]
  6. A. E. Elsner, S. A. Burns, R. H. Webb, “Mapping cone photopigment optical density,” J. Opt. Soc. Am. A 10, 52–58 (1993).
    [Crossref] [PubMed]
  7. S. Trokel, “Quantitative studies of choroidal blood flow by reflective densitometry,” Invest. Ophthalmol. 4, 1129–1140 (1965).
    [PubMed]
  8. J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).
  9. F. C. Delori, “Noninvasive technique for oximetry of blood in retinal vessels,” Appl. Opt. 27, 1113–1125 (1988).
    [Crossref] [PubMed]
  10. W. Hunold, P. Malessa, “Spectrophotometric determination of melanin pigmentation of the human ocular fundus in vivo,” Ophthalmic Res. 6, 355–362 (1974).
    [Crossref]
  11. G. S. Brindley, E. N. Willmer, “The reflection of light from the macular and peripheral fundus oculi in man,” J. Physiol. 116, 350–356 (1952).
    [PubMed]
  12. J. M. Teich, “The theory and development of a noninvasive retinal fluorescence scanner with application to early diagnosis of diabetic retinopathy,” Ph.D. dissertation (Department of Electrical Engineering, MIT, Cambridge, Mass., 1985).
  13. K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
    [Crossref] [PubMed]
  14. J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
    [Crossref] [PubMed]
  15. D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
    [Crossref]
  16. J. Pokorny, V. C. Smith, M. Lutze, “Aging of the human lens,” Appl. Opt. 26, 1437–1440 (1987).
    [Crossref] [PubMed]
  17. R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
    [Crossref] [PubMed]
  18. G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
    [PubMed]
  19. L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
    [PubMed]
  20. G. E. Eldred, “Questioning the nature of the fluorophores in age pigments,” Adv. Biosci. 64, 23–36 (1987).
  21. J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
    [PubMed]
  22. H. Leibowitz et al., “The Framingham eye study monograph. An ophthalmological and epidemiological study of cataract, glaucoma, diabetic retinoopathy, macular degeneration, and visual acuity in a general population of 2631 adults, 1973–1975,” Surv. Ophthalmol. 24, 335–610 (1980).
    [PubMed]
  23. B. E. Klein, R. Klein, “Cataracts and macular degeneration in older Americans,” Arch. Ophthalmol. 100, 571–573 (1982).
    [Crossref] [PubMed]
  24. G. E. Eldred, M. L. Katz, “Fluorophores of the human retinal pigment epithelium: separation and spectral characterization,” Exp. Eye Res. 47, 71–86 (1988).
    [Crossref] [PubMed]
  25. F. C. Delori, K. A. Fitch, J. M. Gorrand, “In vivo characterization of intrinsic fundus fluorescence,” in Noninvasive Assessment of the Visual System, Vol. 3 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 72–75.
  26. F. C. Delori, “Fluorophotometer for noninvasive measurement of RPE lipofuscin,” in Noninvasive Assessment of the Visual System, Vol. 1 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 164–168.
  27. C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).
  28. The Fluorotron was designed to scan the eye from the retina to the cornea by displacing lens L1 (Fig. 1). The subject’s pupil–lens distance L0 is 2× the focal length of L0 (40 mm). The intersection of the excitation and detection beams scans the eye from the retina to the cornea; the retinal conjugate between L0 and L1 moves from being at one focal length from L0 to being at two focal lengths from L0. The image of the mask P* is at all times at one focal length of L0 (midway between the anatomical pupil and L0). This arrangement is required for vitreous fluorophotometry but is less than optimal for our purpose because the image of P* is always in front of the eye and therefore ill defined in the subject’s pupil. We therefore displaced L0 by one focal length in the direction of the subject’s eye, so that the image of P* is in the anatomical pupil. The subject’s pupil–lens distance L0 is then 1× the L0 focal length (20 mm).
  29. The f-number of the detection beam at the entrance slit of the monochromator is given by use of Eq. (1), by f-number = [(π/4)Bdet(1/4.1)2(1/Θdet)]1/2, where Bdet is the area of the detection pupil, 4.1 is the demagnification between the pupil and the slit planes, and Θdet is the optical extent of the detection system.
  30. ANSI, American National Standard for Safe Use of Lasers, in ANSI 136.1-1993 (revision of ANSI 136.1-1986) (The Laser Institute of America, Orlando, Fla., 1993).
  31. H. Davson, in “The eye,” in Visual Optics and Optical Space Science, H. Davson, ed. (Academic, New York, 1962).
  32. A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
    [Crossref]
  33. H. Littmann, “Determination of the true size of an object on the fundus of the living eye (German),” Kin. Mbl. Augenheilk. 192, 66–67(1988).
    [Crossref]
  34. A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
    [Crossref]
  35. The integrated radiance (J cm−2 sr−1) is the integral of the radiance (W cm−2 sr−1) over the exposure duration (seconds).30
  36. W. N. Charman, “Reflection of plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–39 (1980).
    [PubMed]
  37. G. J. van Blokland, “Ellipsometry of the human retina in viv: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
    [Crossref] [PubMed]
  38. R. W. Knighton, S. O. Jacobson, M. I. Roman, “Specular reflection from the surface of the retina,” in Laser Surgery: Advanced Characterization, Therapeutics, and Systems, K. Atsumi, N. R. Goldblatt, S. N. Joffe, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1066, 10–17 (1989).
  39. D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
    [PubMed]
  40. F. C. Delori, “Macular pigment density measured by reflectometry and fluorophotometry,” in Ophthalmic and Visual Optics and Noninvasive Assessment of the Visual System, Vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 240–243.
  41. F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

1993 (1)

1992 (1)

A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
[Crossref]

1989 (2)

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

K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
[Crossref] [PubMed]

1988 (3)

G. E. Eldred, M. L. Katz, “Fluorophores of the human retinal pigment epithelium: separation and spectral characterization,” Exp. Eye Res. 47, 71–86 (1988).
[Crossref] [PubMed]

F. C. Delori, “Noninvasive technique for oximetry of blood in retinal vessels,” Appl. Opt. 27, 1113–1125 (1988).
[Crossref] [PubMed]

H. Littmann, “Determination of the true size of an object on the fundus of the living eye (German),” Kin. Mbl. Augenheilk. 192, 66–67(1988).
[Crossref]

1987 (3)

J. Pokorny, V. C. Smith, M. Lutze, “Aging of the human lens,” Appl. Opt. 26, 1437–1440 (1987).
[Crossref] [PubMed]

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

G. E. Eldred, “Questioning the nature of the fluorophores in age pigments,” Adv. Biosci. 64, 23–36 (1987).

1986 (2)

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

D. van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[Crossref] [PubMed]

1985 (2)

C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).

G. J. van Blokland, “Ellipsometry of the human retina in viv: preservation of polarization,” J. Opt. Soc. Am. A 2, 72–75 (1985).
[Crossref] [PubMed]

1984 (2)

D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
[PubMed]

J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
[Crossref] [PubMed]

1982 (1)

B. E. Klein, R. Klein, “Cataracts and macular degeneration in older Americans,” Arch. Ophthalmol. 100, 571–573 (1982).
[Crossref] [PubMed]

1981 (1)

D. van Norren, J. van der Kraats, “A continuously recording retinal densitometer,” Vision Res. 21, 897–905 (1981).
[Crossref] [PubMed]

1980 (3)

H. Leibowitz et al., “The Framingham eye study monograph. An ophthalmological and epidemiological study of cataract, glaucoma, diabetic retinoopathy, macular degeneration, and visual acuity in a general population of 2631 adults, 1973–1975,” Surv. Ophthalmol. 24, 335–610 (1980).
[PubMed]

L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
[PubMed]

W. N. Charman, “Reflection of plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–39 (1980).
[PubMed]

1975 (1)

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

1974 (2)

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[Crossref]

W. Hunold, P. Malessa, “Spectrophotometric determination of melanin pigmentation of the human ocular fundus in vivo,” Ophthalmic Res. 6, 355–362 (1974).
[Crossref]

1973 (1)

R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
[Crossref] [PubMed]

1965 (2)

S. Trokel, “Quantitative studies of choroidal blood flow by reflective densitometry,” Invest. Ophthalmol. 4, 1129–1140 (1965).
[PubMed]

J. J. Vos, A. A. Munnik, J. Boogaard, “Absolute spectral reflectance of the fundus oculi,” J. Opt. Soc. Am. 55, 573–574 (1965).
[Crossref]

1962 (1)

A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
[Crossref]

1959 (1)

J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).

1952 (1)

G. S. Brindley, E. N. Willmer, “The reflection of light from the macular and peripheral fundus oculi in man,” J. Physiol. 116, 350–356 (1952).
[PubMed]

Alfieri, R.

J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
[Crossref] [PubMed]

Arend, O.

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

Auran, J. D.

D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
[PubMed]

Bennett, A.

A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
[Crossref]

Berman, E. R.

L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
[PubMed]

Bessems, G. H.

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

Boire, J.-Y.

J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
[Crossref] [PubMed]

Boogaard, J.

Brindley, G. S.

G. S. Brindley, E. N. Willmer, “The reflection of light from the macular and peripheral fundus oculi in man,” J. Physiol. 116, 350–356 (1952).
[PubMed]

Burns, S. A.

Campos, A. J.

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

Charman, W. N.

W. N. Charman, “Reflection of plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–39 (1980).
[PubMed]

Cunha-Vaz, J.

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

Davson, H.

H. Davson, in “The eye,” in Visual Optics and Optical Space Science, H. Davson, ed. (Academic, New York, 1962).

Delori, F. C.

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

F. C. Delori, “Noninvasive technique for oximetry of blood in retinal vessels,” Appl. Opt. 27, 1113–1125 (1988).
[Crossref] [PubMed]

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
[PubMed]

F. C. Delori, “Macular pigment density measured by reflectometry and fluorophotometry,” in Ophthalmic and Visual Optics and Noninvasive Assessment of the Visual System, Vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 240–243.

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

F. C. Delori, K. A. Fitch, J. M. Gorrand, “In vivo characterization of intrinsic fundus fluorescence,” in Noninvasive Assessment of the Visual System, Vol. 3 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 72–75.

F. C. Delori, “Fluorophotometer for noninvasive measurement of RPE lipofuscin,” in Noninvasive Assessment of the Visual System, Vol. 1 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 164–168.

Edgar, D. F.

A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
[Crossref]

Eldred, G. E.

G. E. Eldred, M. L. Katz, “Fluorophores of the human retinal pigment epithelium: separation and spectral characterization,” Exp. Eye Res. 47, 71–86 (1988).
[Crossref] [PubMed]

G. E. Eldred, “Questioning the nature of the fluorophores in age pigments,” Adv. Biosci. 64, 23–36 (1987).

Elsner, A. E.

Faria DeAbreau, J. R.

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

Feeney-Burns, L.

L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
[PubMed]

Figo, G. M.

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

Fitch, K. A.

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

F. C. Delori, K. A. Fitch, J. M. Gorrand, “In vivo characterization of intrinsic fundus fluorescence,” in Noninvasive Assessment of the Visual System, Vol. 3 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 72–75.

Frayser, R.

J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).

Goger, D. G.

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

Gorrand, J. M.

F. C. Delori, K. A. Fitch, J. M. Gorrand, “In vivo characterization of intrinsic fundus fluorescence,” in Noninvasive Assessment of the Visual System, Vol. 3 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 72–75.

Gorrand, J.-M.

J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
[Crossref] [PubMed]

Gray, J. R.

C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).

Hennings, D. R.

C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).

Hickam, J. B.

J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).

Hoenders, H. J.

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

Hunold, W.

W. Hunold, P. Malessa, “Spectrophotometric determination of melanin pigmentation of the human ocular fundus in vivo,” Ophthalmic Res. 6, 355–362 (1974).
[Crossref]

Jacobson, S. O.

R. W. Knighton, S. O. Jacobson, M. I. Roman, “Specular reflection from the surface of the retina,” in Laser Surgery: Advanced Characterization, Therapeutics, and Systems, K. Atsumi, N. R. Goldblatt, S. N. Joffe, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1066, 10–17 (1989).

Katz, M. L.

G. E. Eldred, M. L. Katz, “Fluorophores of the human retinal pigment epithelium: separation and spectral characterization,” Exp. Eye Res. 47, 71–86 (1988).
[Crossref] [PubMed]

Keizer, E.

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

Kitagawa, K.

K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
[Crossref] [PubMed]

Klein, B. E.

B. E. Klein, R. Klein, “Cataracts and macular degeneration in older Americans,” Arch. Ophthalmol. 100, 571–573 (1982).
[Crossref] [PubMed]

Klein, R.

B. E. Klein, R. Klein, “Cataracts and macular degeneration in older Americans,” Arch. Ophthalmol. 100, 571–573 (1982).
[Crossref] [PubMed]

Knighton, R. W.

R. W. Knighton, S. O. Jacobson, M. I. Roman, “Specular reflection from the surface of the retina,” in Laser Surgery: Advanced Characterization, Therapeutics, and Systems, K. Atsumi, N. R. Goldblatt, S. N. Joffe, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1066, 10–17 (1989).

Kurzel, R. B.

R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
[Crossref] [PubMed]

Leary, G. A.

A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
[Crossref]

Leibowitz, H.

H. Leibowitz et al., “The Framingham eye study monograph. An ophthalmological and epidemiological study of cataract, glaucoma, diabetic retinoopathy, macular degeneration, and visual acuity in a general population of 2631 adults, 1973–1975,” Surv. Ophthalmol. 24, 335–610 (1980).
[PubMed]

Littmann, H.

H. Littmann, “Determination of the true size of an object on the fundus of the living eye (German),” Kin. Mbl. Augenheilk. 192, 66–67(1988).
[Crossref]

Lutze, M.

Malessa, P.

W. Hunold, P. Malessa, “Spectrophotometric determination of melanin pigmentation of the human ocular fundus in vivo,” Ophthalmic Res. 6, 355–362 (1974).
[Crossref]

Munnerlyn, C. R.

C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).

Munnik, A. A.

Nishida, S.

K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
[Crossref] [PubMed]

Ogura, Y.

K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
[Crossref] [PubMed]

Pflibsen, K. P.

Pokorny, J.

Richards, M. J.

A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
[Crossref]

Roman, M. I.

R. W. Knighton, S. O. Jacobson, M. I. Roman, “Specular reflection from the surface of the retina,” in Laser Surgery: Advanced Characterization, Therapeutics, and Systems, K. Atsumi, N. R. Goldblatt, S. N. Joffe, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1066, 10–17 (1989).

Rothman, H.

L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
[PubMed]

Rudnicka, A. R.

A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
[Crossref]

Sieker, H. O.

J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).

Smith, V. C.

Snodderly, D. M.

D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
[PubMed]

Sorsby, A.

A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
[Crossref]

Staurenghi, G.

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

Teich, J. M.

J. M. Teich, “The theory and development of a noninvasive retinal fluorescence scanner with application to early diagnosis of diabetic retinopathy,” Ph.D. dissertation (Department of Electrical Engineering, MIT, Cambridge, Mass., 1985).

Tiemeijer, L. F.

D. van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[Crossref] [PubMed]

Trokel, S.

S. Trokel, “Quantitative studies of choroidal blood flow by reflective densitometry,” Invest. Ophthalmol. 4, 1129–1140 (1965).
[PubMed]

van Blokland, G. J.

van der Kraats, J.

D. van Norren, J. van der Kraats, “A continuously recording retinal densitometer,” Vision Res. 21, 897–905 (1981).
[Crossref] [PubMed]

van Norren, D.

D. van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[Crossref] [PubMed]

D. van Norren, J. van der Kraats, “A continuously recording retinal densitometer,” Vision Res. 21, 897–905 (1981).
[Crossref] [PubMed]

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[Crossref]

Vos, J. J.

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[Crossref]

J. J. Vos, A. A. Munnik, J. Boogaard, “Absolute spectral reflectance of the fundus oculi,” J. Opt. Soc. Am. 55, 573–574 (1965).
[Crossref]

Webb, R. H.

Weiter, J. J.

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

Willmer, E. N.

G. S. Brindley, E. N. Willmer, “The reflection of light from the macular and peripheral fundus oculi in man,” J. Physiol. 116, 350–356 (1952).
[PubMed]

Wing, G.

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

Wolbarsht, M. L.

R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
[Crossref] [PubMed]

Wollensak, J.

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

Yamanashi, B. S.

R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
[Crossref] [PubMed]

Adv. Biosci. (1)

G. E. Eldred, “Questioning the nature of the fluorophores in age pigments,” Adv. Biosci. 64, 23–36 (1987).

Am. J. Ophthalmol. (1)

L. Feeney-Burns, E. R. Berman, H. Rothman, “Lipofuscin of human retinal pigment epithelium,” Am. J. Ophthalmol. 90, 783–791 (1980).
[PubMed]

Appl. Opt. (3)

Arch. Ophthalmol. (1)

B. E. Klein, R. Klein, “Cataracts and macular degeneration in older Americans,” Arch. Ophthalmol. 100, 571–573 (1982).
[Crossref] [PubMed]

Br. J. Ophthalmol. (1)

J. Cunha-Vaz, J. R. Faria DeAbreau, A. J. Campos, G. M. Figo, “Early breakdown of the blood-retinal barrier in diabetes,” Br. J. Ophthalmol. 59, 649–656 (1975).
[Crossref] [PubMed]

Br. J. Physiol. Opt. (1)

W. N. Charman, “Reflection of plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–39 (1980).
[PubMed]

Exp. Eye Res. (2)

G. E. Eldred, M. L. Katz, “Fluorophores of the human retinal pigment epithelium: separation and spectral characterization,” Exp. Eye Res. 47, 71–86 (1988).
[Crossref] [PubMed]

R. B. Kurzel, M. L. Wolbarsht, B. S. Yamanashi, “Spectral studies on normal and cataractous intact human lenses,” Exp. Eye Res. 17, 65–71 (1973).
[Crossref] [PubMed]

Graefe’s Arch. Clin. Exp. Ophthalmol. (1)

C. R. Munnerlyn, J. R. Gray, D. R. Hennings, “Design considerations for a fluorophotometer for ocular research,” Graefe’s Arch. Clin. Exp. Ophthalmol. 222, 209–211 (1985).

Invest. Ophthalmol. (1)

S. Trokel, “Quantitative studies of choroidal blood flow by reflective densitometry,” Invest. Ophthalmol. 4, 1129–1140 (1965).
[PubMed]

Invest. Ophthalmol. Vis. Sci. (3)

G. H. Bessems, E. Keizer, J. Wollensak, H. J. Hoenders, “Nontryptophan fluorescence of crystallins from normal and cataractous human lenses,” Invest. Ophthalmol. Vis. Sci. 28, 1157–1163 (1987).
[PubMed]

J. J. Weiter, F. C. Delori, G. Wing, K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27, 145–152 (1986).
[PubMed]

D. M. Snodderly, J. D. Auran, F. C. Delori, “The macular pigment. II. Spatial distribution in primate retinas,” Invest. Ophthalmol. Vis. Sci. 25, 674–684 (1984).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Physiol. (1)

G. S. Brindley, E. N. Willmer, “The reflection of light from the macular and peripheral fundus oculi in man,” J. Physiol. 116, 350–356 (1952).
[PubMed]

Kin. Mbl. Augenheilk. (1)

H. Littmann, “Determination of the true size of an object on the fundus of the living eye (German),” Kin. Mbl. Augenheilk. 192, 66–67(1988).
[Crossref]

Ophthalmic Res. (1)

W. Hunold, P. Malessa, “Spectrophotometric determination of melanin pigmentation of the human ocular fundus in vivo,” Ophthalmic Res. 6, 355–362 (1974).
[Crossref]

Ophthalmol. Physiol. Opt. (1)

A. R. Rudnicka, D. F. Edgar, A. Bennett, “Construction of a model eye and its application,” Ophthalmol. Physiol. Opt. 12, 485–490 (1992).
[Crossref]

Ophthalmologica (1)

K. Kitagawa, S. Nishida, Y. Ogura, “In vivo quantification of autofluorescence in human retinal pigment epithelium,” Ophthalmologica 199, 116–121 (1989).
[Crossref] [PubMed]

Surv. Ophthalmol. (1)

H. Leibowitz et al., “The Framingham eye study monograph. An ophthalmological and epidemiological study of cataract, glaucoma, diabetic retinoopathy, macular degeneration, and visual acuity in a general population of 2631 adults, 1973–1975,” Surv. Ophthalmol. 24, 335–610 (1980).
[PubMed]

Trans. Am. Clin. Climatol. Assoc. (1)

J. B. Hickam, H. O. Sieker, R. Frayser, “Studies of retinal circulation and A-V oxygen difference in man,” Trans. Am. Clin. Climatol. Assoc. 71, 34–44 (1959).

Vision Res. (5)

J.-M. Gorrand, R. Alfieri, J.-Y. Boire, “Diffusion of the retinal layers of the living human eye,” Vision Res. 24, 1097–1106 (1984).
[Crossref] [PubMed]

D. van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[Crossref] [PubMed]

D. van Norren, J. van der Kraats, “A continuously recording retinal densitometer,” Vision Res. 21, 897–905 (1981).
[Crossref] [PubMed]

D. van Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[Crossref]

A. Sorsby, G. A. Leary, M. J. Richards, “Correlation ametropia and component ametropia,” Vision Res. 2, 309–313 (1962).
[Crossref]

Other (11)

The integrated radiance (J cm−2 sr−1) is the integral of the radiance (W cm−2 sr−1) over the exposure duration (seconds).30

R. W. Knighton, S. O. Jacobson, M. I. Roman, “Specular reflection from the surface of the retina,” in Laser Surgery: Advanced Characterization, Therapeutics, and Systems, K. Atsumi, N. R. Goldblatt, S. N. Joffe, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1066, 10–17 (1989).

The Fluorotron was designed to scan the eye from the retina to the cornea by displacing lens L1 (Fig. 1). The subject’s pupil–lens distance L0 is 2× the focal length of L0 (40 mm). The intersection of the excitation and detection beams scans the eye from the retina to the cornea; the retinal conjugate between L0 and L1 moves from being at one focal length from L0 to being at two focal lengths from L0. The image of the mask P* is at all times at one focal length of L0 (midway between the anatomical pupil and L0). This arrangement is required for vitreous fluorophotometry but is less than optimal for our purpose because the image of P* is always in front of the eye and therefore ill defined in the subject’s pupil. We therefore displaced L0 by one focal length in the direction of the subject’s eye, so that the image of P* is in the anatomical pupil. The subject’s pupil–lens distance L0 is then 1× the L0 focal length (20 mm).

The f-number of the detection beam at the entrance slit of the monochromator is given by use of Eq. (1), by f-number = [(π/4)Bdet(1/4.1)2(1/Θdet)]1/2, where Bdet is the area of the detection pupil, 4.1 is the demagnification between the pupil and the slit planes, and Θdet is the optical extent of the detection system.

ANSI, American National Standard for Safe Use of Lasers, in ANSI 136.1-1993 (revision of ANSI 136.1-1986) (The Laser Institute of America, Orlando, Fla., 1993).

H. Davson, in “The eye,” in Visual Optics and Optical Space Science, H. Davson, ed. (Academic, New York, 1962).

F. C. Delori, K. A. Fitch, J. M. Gorrand, “In vivo characterization of intrinsic fundus fluorescence,” in Noninvasive Assessment of the Visual System, Vol. 3 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 72–75.

F. C. Delori, “Fluorophotometer for noninvasive measurement of RPE lipofuscin,” in Noninvasive Assessment of the Visual System, Vol. 1 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 164–168.

J. M. Teich, “The theory and development of a noninvasive retinal fluorescence scanner with application to early diagnosis of diabetic retinopathy,” Ph.D. dissertation (Department of Electrical Engineering, MIT, Cambridge, Mass., 1985).

F. C. Delori, “Macular pigment density measured by reflectometry and fluorophotometry,” in Ophthalmic and Visual Optics and Noninvasive Assessment of the Visual System, Vol. 3 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 240–243.

F. C. Delori, G. Staurenghi, O. Arend, D. G. Goger, J. J. Weiter, “Estimates of ocular media absorption from fundus reflectometry,” in Vision Science and Its Applications, Vol. 2 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 220–223.

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Figures (10)

Fig. 1
Fig. 1

Optics of the fundus spectrophotometer. R and P, planes conjugate to the subject’s retina and pupil, respectively. Components to the immediate right of lens L2 are represented in three dimensions in Fig. 2A. The calibration monitor (upper left) is used for routine calibration of the system (see Subsection 3.C.4). S1, S2, beam splitters.

Fig. 2
Fig. 2

A, Three-dimensional representation of the beam optics in the proximity of mask P*. B, Configuration of the excitation, detection, illumination, and observation pupils in the plane of the subject’s anatomical pupil. The dashed–dotted line represents the effective entrance pupil used for spectral analysis of the fluorescence.

Fig. 3
Fig. 3

A, Fluorescence measurement. Excitation and detection beams are focused on the retina in concentric excitation and sampling areas centered on the area of interest. B, Baseline measurement. The excitation beam is pivoted in the pupil plane, causing the excitation spot at the retina to be displaced. The detected light then consists of contributions of lens fluorescence reflected at the site of interest (the sampling area is unchanged) and of scattered fluorescence in the lens.

Fig. 4
Fig. 4

Block diagram of the electronics and microcomputers. The SE microcomputer drives the entire system. The SI microcomputer, slaved to the SE, is responsible for spectra acquisition in conjunction with the OMA detector system. IO, input/output; CTL, control.

Fig. 5
Fig. 5

Fluorescence and reflectance spectra for subject M40. A, Excitation spectrum (triangles, measured at 620 nm) and emission spectra (excitation, all wavelengths) from an area at 7° temporal to the fovea. One derives the excitation spectrum from the emission spectra by plotting, as a function of excitation wavelength, the fluorescence at a specific emission wavelength; the dashed lines illustrate this for Φ(450, 620). B, Equivalent reflectance spectra for the same site. The arrows indicate a relatively lower reflectance that corresponds to the absorption bands of choroidal blood (540 and 575 nm).

Fig. 6
Fig. 6

Fluorescence and reflectance spectra for subject M52. The measurement sites are as follows: T 7° temporal of the fovea; F, the fovea; D, the temporal side of the optic disk. A, Excitation (measured at 620 nm) and emission spectra (excitation, 470 nm) for the three sites. The emission spectra from the retina (T, F) are smooth curves, whereas the disk spectrum (D) reveals blood-absorption characteristics because the fluorescence originates from within the disk tissue. B, Equivalent reflectance spectra. C, Curve E, log of the ratio of excitation spectra at 7° temporal and the fovea, i.e., E = log[Φ(Λ, 620)7 T /Φ(Λ, 620) F ]; curve R, log of the ratio of the reflectance spectra at 7° temporal and the fovea, i.e., R = log[ρ(λ)7 T /ρ(λ) F ]. These ratio spectra reveal the absorption spectrum of the macular pigment.

Fig. 7
Fig. 7

Fluorescence and reflectance spectra measured 7° temporal to the fovea in subjects F24, M52, M71, and in the pseudophakic subject M73. A, Excitation spectra (measured at 620 nm) and emission spectra (excitation, 510 nm). B Equivalent reflectance spectra. C, Ratios that characterize the short-wavelength slope of the excitation and reflectance spectra. The fluorescence ratio E = Φ(470, 620)/Φ(510, 620) and the reflectance ratio R = ρ(470)/ρ(5 10) are plotted against the age of the five study subjects. (The data for the phakic subjects are connected by lines.) The oldest subject, M73, is pseudophakic, and his R and E ratios are equivalent to that of the youngest subject.

Fig. 8
Fig. 8

Fluorescence spectra of the crystalline lens of subject M52. Excitation spectra measured at 520 (squares) and at 620 (circles) nm. Emission spectra are for all excitation wavelengths except 430 nm.

Fig. 9
Fig. 9

Bar graph (logarithmic scale) illustrating the relative contribution of the baseline to the total fluorescence signal for all subjects in this study. Two extreme situations, Φ(430, 520) and Φ(510, 620), are given (A and B, respectively) for 7° temporal to the fovea and for the fovea. The height of each bar is the measured total fluorescence intensity; the black area represents the baseline. The lightly shaded area is the baseline corrected signal.

Fig. 10
Fig. 10

Uncorrected fluorescence spectra (filled symbols, thick curves) and corresponding baseline spectra (open symbols, thin curves) for subject M52 measured at 7° temporal. F, B, Excitation spectra (measured at 620 nm) and emission (excitation, 510 nm) of the uncorrected fluorescence (F) and its baseline (B). F, b, Excitation spectrum (measured at 520 nm) and emission (excitation, 430 nm) of the uncorrected fluorescence (f) and its baseline (b). The wavelength axis was split and spaced between excitation and emission wavelengths to avoid spectral overlap.

Tables (3)

Tables Icon

Table 1 Retinal Exposure Characteristics and Safety Considerations

Tables Icon

Table 2 Spurious Signal Induced by Reflected Excitation Light

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Table 3 Coefficient of Variation (%) for Two Measurements of Φ(510, 620) and ρ(540)

Equations (13)

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Θ det = A Ω = n 2 A det Ω det ,
A inc = ( π / 4 ) α inc 2 f e 2 ( 1 + f e q K p ) 2 .
L λ = Φ ( Λ , λ ) Q ex , Λ T om , Λ A inc ,
F λ = L λ T om , λ A det Ω det = L λ T om , λ Θ det n - 2 ,
OMA λ = F λ T b , λ G S λ Δ λ ,
Φ ( Λ , λ ) = OMA λ ( π / 4 ) α inc 2 n 2 f e 2 T om , Λ T om , λ Θ det G Δ λ Q ex , Λ T b , λ S λ ( 1 + f e q K p ) 2 .
L λ = ρ ( λ ) ( 1 / π ) Q re , λ T om , λ ( π / 4 ) α inc 2 f e 2 ,
ρ ( λ ) = OMA λ ( π / 4 ) α inc 2 n 2 f e 2 ( 1 / π ) T om , λ 2 Θ det G Δ λ Q re , λ S λ ( 1 + f e q K p ) 2 .
Q ex , Λ = E m , Λ ( π / 4 ) α inc 2 d m 2 τ ,
L λ = 0.95 ( 1 / π ) E s l , λ ( 50 / d s l ) 2 cos ( α ) τ ,
T b , λ S λ = OMA λ ( 1 / π ) Θ det G Δ λ 0.95 s l , λ ( 50 / d s l ) 2 cos ( α ) τ .
L λ = 0.95 ( 1 / π ) Q re , λ ( π / 4 ) α inc 2 d r 2 .
Q re , λ = OMA λ ( π / 4 ) α inc 2 d r 2 Θ det G Δ λ 0.95 ( 1 / π ) S λ .

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