Abstract

We consider transmission through pair-correlated random distributions of lossless dielectric (globular, cylindrical, or plate-like) scatterers with length parameter <i>a</i> and average spacing small compared to wavelength. Each optical particle is centered in a tough adherent transparent coating whose outer surface (sphere, cylinder, or slab) has radius <i>b</i> ≥ <i>a</i>. The corresponding attenuation coefficients β ∝ <i>W</i><sub><i>m</i></sub> involve an integral of the appropriate radial-distribution function. Using the scaled-particle equations of state and statistical-mechanics theorems, we evaluate <i>W</i><sub><i>m</i></sub> explicitly as a rational function of the volume fraction <i>w</i> of the fluid of rigid <i>b</i> particles. We obtain β<sub><i>m</i></sub> = β<sub>0</sub><i>W</i><sub><i>m</i></sub> with β<sub>0</sub> as the uncorrelated value; <i>W</i><sub>3</sub>(<i>w</i>) for spheres decreases more rapidly with increasing <i>w</i> than <i>w</i><sub>2</sub> for cylinders, and <i>W</i><sub>2</sub> decreases faster than <i>W</i><sub>1</sub>, the result for slabs. We apply the results for cylinders in terms of <i>W</i><sub>2</sub> to the problem of the transparency of the cornea (whose collagen fibers are the scatterers), as posed by Maurice. The value <i>w</i> ≈ 0.6 gives good accord with the essentials of the data for the transparency of the normal cornea, and the opacity that results from swelling is accounted for by. corresponding smaller values of <i>w</i>. Thus, the normal cornea is modeled as a very densely packed two-dimensional gas, with gas-particle (mechanical) radius about 60% greater than the fiber (optical) radius.

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  1. V. Twersky, J. Opt. Soc. Am. 60, 1084 (1970).
  2. V. Twersky, J. Opt. Soc. Am. 52, 145 (1962).
  3. 3H. S. Green, The Molecular Theory of Fluids (Interscience, New York, 1952), p. 62ff.
  4. S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP-15, 118 (1967).
  5. H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).
  6. E. Helfand, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 34, 1037 (1961).
  7. J. S. Rowlinson, Rep. Progr. Phys. 28, 169 (1965).
  8. G. D. Scott, Nature 187, 908 (1960).
  9. V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).
  10. C. I. Beard, T. H. Kays, and V. Twersky, IEEE Trans. AP- 15, 99 (1967).
  11. C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965).
  12. D. M. Maurice, J. Physiol. (Lond.) 136, 263 (1957).
  13. D. M. Maurice, in The Eye, edited by H. Davson (Academic, New York, 1968), Ch. 6.
  14. R. W. Hart and R. A. Farrell, J. Opt. Soc. Am. 59, 766 (1969).
  15. J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).
  16. T. Feuk, IEEE Trans. BME-17, 186 (1970); Scattering of Light in the Corneal Stroma, Tech. Rep. No. 7 (School of Elec. Eng., Chalmers Univ. of Technology, Gotteborg, Sweden, 1970).
  17. G. B. Benedek, Appl. Opt. 10, 459 (1971).
  18. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Beard, C. I.

C. I. Beard, T. H. Kays, and V. Twersky, IEEE Trans. AP- 15, 99 (1967).

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965).

Benedek, G. B.

G. B. Benedek, Appl. Opt. 10, 459 (1971).

Cox, J. L.

J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).

Farrell, R. A.

J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).

R. W. Hart and R. A. Farrell, J. Opt. Soc. Am. 59, 766 (1969).

Feuk, T.

T. Feuk, IEEE Trans. BME-17, 186 (1970); Scattering of Light in the Corneal Stroma, Tech. Rep. No. 7 (School of Elec. Eng., Chalmers Univ. of Technology, Gotteborg, Sweden, 1970).

Frisch, H. L.

E. Helfand, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 34, 1037 (1961).

H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).

Green, H. S.

3H. S. Green, The Molecular Theory of Fluids (Interscience, New York, 1952), p. 62ff.

Hart, R. W.

R. W. Hart and R. A. Farrell, J. Opt. Soc. Am. 59, 766 (1969).

J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).

Hawley, S. W.

S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP-15, 118 (1967).

Helfand, E.

E. Helfand, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 34, 1037 (1961).

Kays, T. H.

C. I. Beard, T. H. Kays, and V. Twersky, IEEE Trans. AP- 15, 99 (1967).

S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP-15, 118 (1967).

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965).

Langham, M. E.

J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).

Lebowitz, J. L.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).

E. Helfand, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 34, 1037 (1961).

Maurice, D. M.

D. M. Maurice, J. Physiol. (Lond.) 136, 263 (1957).

D. M. Maurice, in The Eye, edited by H. Davson (Academic, New York, 1968), Ch. 6.

Reiss, H.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).

Rowlinson, J. S.

J. S. Rowlinson, Rep. Progr. Phys. 28, 169 (1965).

Scott, G. D.

G. D. Scott, Nature 187, 908 (1960).

Twersky, V.

V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).

C. I. Beard, T. H. Kays, and V. Twersky, IEEE Trans. AP- 15, 99 (1967).

V. Twersky, J. Opt. Soc. Am. 60, 1084 (1970).

V. Twersky, J. Opt. Soc. Am. 52, 145 (1962).

S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP-15, 118 (1967).

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Other (18)

V. Twersky, J. Opt. Soc. Am. 60, 1084 (1970).

V. Twersky, J. Opt. Soc. Am. 52, 145 (1962).

3H. S. Green, The Molecular Theory of Fluids (Interscience, New York, 1952), p. 62ff.

S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP-15, 118 (1967).

H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).

E. Helfand, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 34, 1037 (1961).

J. S. Rowlinson, Rep. Progr. Phys. 28, 169 (1965).

G. D. Scott, Nature 187, 908 (1960).

V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).

C. I. Beard, T. H. Kays, and V. Twersky, IEEE Trans. AP- 15, 99 (1967).

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965).

D. M. Maurice, J. Physiol. (Lond.) 136, 263 (1957).

D. M. Maurice, in The Eye, edited by H. Davson (Academic, New York, 1968), Ch. 6.

R. W. Hart and R. A. Farrell, J. Opt. Soc. Am. 59, 766 (1969).

J. L. Cox, R. A. Farrell, R. W. Hart, and M. E. Langham, J. Physiol. 210, 601 (1970).

T. Feuk, IEEE Trans. BME-17, 186 (1970); Scattering of Light in the Corneal Stroma, Tech. Rep. No. 7 (School of Elec. Eng., Chalmers Univ. of Technology, Gotteborg, Sweden, 1970).

G. B. Benedek, Appl. Opt. 10, 459 (1971).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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