Abstract

Earlier results for coherent attenuation of light by pair-correlated random distributions of dielectric particles of radius a (with separation of closest centers 2<i>b</i>≥2<i>a</i> small compared to wavelength) are generalized to absorbing scatterers with higher refractivity. To facilitate applications, we reduce the total attenuation coefficient (τ) to two terms, one proportional to the absorption cross section of an isolated particle, and one to the scattering cross section times the statistical-mechanics packing correlation function <i>W</i> discussed earlier; each term is also proportional to the same simple function of the first-order coherent phase change. For lossless scatterers, the dependence of <i>W</i> on the volume fraction (W) of particles of radius <i>b</i> accounts for the transparency of correlated distributions at relatively dense packing, as well as for the opacity that arises with looser packing. For lossy scatterers, <i>W</i>(W) determines the relative influence of absorption losses and scattering losses in τ. Even if the scattering losses are the more significant for small W, the absorption losses dominate as W increases; for such cases and moderate refractivity, we show that τ(W) may have a maximum, and determine its value and the corresponding value of W in terms of the cross sections and the form of <i>W</i>.

© 1979 Optical Society of America

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  1. V. Twersky, "Transparency of pair-correlated random distributions of small scatterers with applications to the cornea," J. Opt. Soc. Am. 65, 524–530 (1975).
  2. V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978); "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).
  3. Lord Rayleigh, "On the transmission of light through the atmosphere containing small particles in suspension, and on the origin of the color of the sky," Philos. Mag. 47, 375–383 (1899).
  4. See, e.g., H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  5. R. Barer, "Refractometry and interferometry of living cells," J. Opt. Soc. Am. 47, 545–556 (1957); "Spectrophotometry of Clarified Cell Suspensions," Science 121, 709–715 (1955).
  6. V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am. 52, 145–171 (1962); "Interface effects in multiple scattering by large, low-refracting, absorbing particles," J. Opt. Soc. Am. 60, 908–914 (1970); "Absorption and multiple scattering by biological suspensions," J. Opt. Soc. Am. 60, 1084–1093 (1970).
  7. H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).
  8. V. Twersky, "Acoustic bulk parameters in distributions of paircorrelated scatterers," J. Acoust. Soc. Am. 64, 1710–1719 (1978).
  9. N. M. Anderson and P. S. Sekelj, "Light-absorbing and scattering properties of nonhaemolyzed blood," Phys. Med. Biol. 12, 173–184 (1967).
  10. F. Reiche, "Zur Theorie der Dispersion in Gasen und Dampfen," Ann. Phys. (Leipzig) 50, 1–121 (1916).
  11. L. L. Foldy, "The multiple scattering of waves," Phys. Rev. (2) 67, 107–119 (1945).
  12. M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23,287–310 (1951); "The effective field in dense systems," Phys. Rev. (2) 88, 621–629 (1952).
  13. V. Twersky, "Form and intrinsic birefringence," J. Opt. Soc. Am. 65, 239–245 (1975).
  14. D. Maurice, "The structure and transparency of the cornea," J. Physiol. (London) 136, 263–286 (1957).
  15. Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34, 481–501 (1892).
  16. O. Weiner, "Die Theorie des Mischkörpers für das Feld der stationären Strömung," Sächsische Akad. Wiss. 32, 507–604 (1912).
  17. L. G. M. Baas-Becking and E. Wayne Galliher, "Wall structure and mineralization in corraline algae," J. Phys. Chem. 35, 467–479. (1931).

1978 (1)

V. Twersky, "Acoustic bulk parameters in distributions of paircorrelated scatterers," J. Acoust. Soc. Am. 64, 1710–1719 (1978).

1977 (1)

V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978); "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

1975 (2)

1967 (1)

N. M. Anderson and P. S. Sekelj, "Light-absorbing and scattering properties of nonhaemolyzed blood," Phys. Med. Biol. 12, 173–184 (1967).

1962 (1)

1959 (1)

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).

1957 (2)

1951 (1)

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23,287–310 (1951); "The effective field in dense systems," Phys. Rev. (2) 88, 621–629 (1952).

1945 (1)

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. (2) 67, 107–119 (1945).

1931 (1)

L. G. M. Baas-Becking and E. Wayne Galliher, "Wall structure and mineralization in corraline algae," J. Phys. Chem. 35, 467–479. (1931).

1916 (1)

F. Reiche, "Zur Theorie der Dispersion in Gasen und Dampfen," Ann. Phys. (Leipzig) 50, 1–121 (1916).

1912 (1)

O. Weiner, "Die Theorie des Mischkörpers für das Feld der stationären Strömung," Sächsische Akad. Wiss. 32, 507–604 (1912).

1899 (1)

Lord Rayleigh, "On the transmission of light through the atmosphere containing small particles in suspension, and on the origin of the color of the sky," Philos. Mag. 47, 375–383 (1899).

1892 (1)

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34, 481–501 (1892).

Anderson, N. M.

N. M. Anderson and P. S. Sekelj, "Light-absorbing and scattering properties of nonhaemolyzed blood," Phys. Med. Biol. 12, 173–184 (1967).

Baas-Becking, L. G. M.

L. G. M. Baas-Becking and E. Wayne Galliher, "Wall structure and mineralization in corraline algae," J. Phys. Chem. 35, 467–479. (1931).

Barer, R.

Foldy, L. L.

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. (2) 67, 107–119 (1945).

Frisch, H. L.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).

Galliher, E. Wayne

L. G. M. Baas-Becking and E. Wayne Galliher, "Wall structure and mineralization in corraline algae," J. Phys. Chem. 35, 467–479. (1931).

Lax, M.

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23,287–310 (1951); "The effective field in dense systems," Phys. Rev. (2) 88, 621–629 (1952).

Lebowitz, J. L.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).

Maurice, D.

D. Maurice, "The structure and transparency of the cornea," J. Physiol. (London) 136, 263–286 (1957).

Rayleigh, Lord

Lord Rayleigh, "On the transmission of light through the atmosphere containing small particles in suspension, and on the origin of the color of the sky," Philos. Mag. 47, 375–383 (1899).

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34, 481–501 (1892).

Reiche, F.

F. Reiche, "Zur Theorie der Dispersion in Gasen und Dampfen," Ann. Phys. (Leipzig) 50, 1–121 (1916).

Reiss, H.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).

Sekelj, P. S.

N. M. Anderson and P. S. Sekelj, "Light-absorbing and scattering properties of nonhaemolyzed blood," Phys. Med. Biol. 12, 173–184 (1967).

Twersky, V.

V. Twersky, "Acoustic bulk parameters in distributions of paircorrelated scatterers," J. Acoust. Soc. Am. 64, 1710–1719 (1978).

V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978); "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

V. Twersky, "Transparency of pair-correlated random distributions of small scatterers with applications to the cornea," J. Opt. Soc. Am. 65, 524–530 (1975).

V. Twersky, "Form and intrinsic birefringence," J. Opt. Soc. Am. 65, 239–245 (1975).

V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am. 52, 145–171 (1962); "Interface effects in multiple scattering by large, low-refracting, absorbing particles," J. Opt. Soc. Am. 60, 908–914 (1970); "Absorption and multiple scattering by biological suspensions," J. Opt. Soc. Am. 60, 1084–1093 (1970).

van de Hulst, H. C.

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

Weiner, O.

O. Weiner, "Die Theorie des Mischkörpers für das Feld der stationären Strömung," Sächsische Akad. Wiss. 32, 507–604 (1912).

Ann. Phys. (1)

F. Reiche, "Zur Theorie der Dispersion in Gasen und Dampfen," Ann. Phys. (Leipzig) 50, 1–121 (1916).

J. Acoust. Soc. Am. (1)

V. Twersky, "Acoustic bulk parameters in distributions of paircorrelated scatterers," J. Acoust. Soc. Am. 64, 1710–1719 (1978).

J. Chem. Phys. (1)

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 379–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "Theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).

J. Math. Phys. (1)

V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978); "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

J. Opt. Soc. Am. (4)

J. Phys. Chem. (1)

L. G. M. Baas-Becking and E. Wayne Galliher, "Wall structure and mineralization in corraline algae," J. Phys. Chem. 35, 467–479. (1931).

J. Physiol. (1)

D. Maurice, "The structure and transparency of the cornea," J. Physiol. (London) 136, 263–286 (1957).

Philos. Mag. (2)

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34, 481–501 (1892).

Lord Rayleigh, "On the transmission of light through the atmosphere containing small particles in suspension, and on the origin of the color of the sky," Philos. Mag. 47, 375–383 (1899).

Phys. Med. Biol. (1)

N. M. Anderson and P. S. Sekelj, "Light-absorbing and scattering properties of nonhaemolyzed blood," Phys. Med. Biol. 12, 173–184 (1967).

Phys. Rev. 2 (1)

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. (2) 67, 107–119 (1945).

Rev. Mod. Phys. (1)

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23,287–310 (1951); "The effective field in dense systems," Phys. Rev. (2) 88, 621–629 (1952).

Sächsische Akad. Wiss. (1)

O. Weiner, "Die Theorie des Mischkörpers für das Feld der stationären Strömung," Sächsische Akad. Wiss. 32, 507–604 (1912).

Other (1)

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

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