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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 10, Iss. 3 — Mar. 1, 1971
  • pp: 459–473

Theory of Transparency of the Eye

G. B. Benedek  »View Author Affiliations


Applied Optics, Vol. 10, Issue 3, pp. 459-473 (1971)
http://dx.doi.org/10.1364/AO.10.000459


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Abstract

The present work relates the turbidity of the eye to microscopic spatial fluctuations in itsindex of refraction. Such fluctuations are indicated in electron microscope photographs. Byexamining the superposition of phases of waves scattered from each point in the medium, we provide amathematical demonstration of the Bragg reflection principle which we have recently used in theinterpretation of experimental investigations: namely, that the scattering of light is produced onlyby those fluctuations whose fourier components have a wavelength equal to or larger than one halfthe wavelength of light in the medium. This consideration is applied first to the scattering oflight from collagen fibers in the normal cornea. We demonstrate physically and quantitatively that alimited correlation in the position of near neighbor collagen fibers leads to corneal transparency.Next, the theory is extended to predict the turbidity of swollen, pathologic corneas, wherein thenormal distribution of collagen fibers is disturbed by the presence of numerouslakes—regions where collagen is absent. A quantitative expression for theturbidity of the swollen cornea is given in terms of the size and density of such lakes. Finally,the theory is applied to the case of the cataractous lens. We assume that the cataracts are producedby aggregation of the normal lens proteins into an albuminoid fraction and provide a formula for thelens turbidity in terms of the molecular weight and index of refraction of the individual albuminoidmacromolecules. We provide a crude estimate of the mean albuminoid molecular weight required forlens opacity.

© 1971 Optical Society of America

History
Original Manuscript: July 28, 1970
Published: March 1, 1971

Citation
G. B. Benedek, "Theory of Transparency of the Eye," Appl. Opt. 10, 459-473 (1971)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-10-3-459


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References

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  10. In Fig. 10 we indicate that in the region of the lakes theindex of refraction is the same as that of the ground substance. This is probably not quite correctas there is likely to be water in these lakes. This would tend to lower the index of refraction ofthe lake to a value closer to that of water. The discussion we give above can be very simplyextended to include this effect. We shall neglect this effect as it does not alter substantially theline of argument presented above.
  11. M. Abramowitz, I. Stegun, Eds. Handbook of Mathematical Functions(Dover, New York,1965), p. 364, Eq.9.2.1; p. 370, Eq. 9.4.4.
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  17. B. Phillipson, Invest. Ophthalmol. 8, 281 (1969) (especially p. 288); see also Invest. Ophthalmol. 8, 271 (1969). [PubMed]

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