Abstract

Normalized scattering phase functions and extinction efficiencies for homogeneous dielectric spheres with size parameters 200 ≤ <i>x</i> ≤ 4520 and refractive index <i>m</i> = 1.333 - Oi are calculated directly from Mie theory. The results are compared to predictions cited in the literature. Averages of the angular structure and magnitude of the glory are given as a function of the dimensionless size parameter. The periods and amplitudes of regular oscillations in the backscatter phase function are determined. Distinct backscattering oscillations with periods Δ<i>x</i> ≃ 0.41, 0.83, 1.1, and 14 are found.

© 1978 Optical Society of America

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  1. S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. H. C. Bryant and A. J. Cox, "Mie Theory and the Glory," J. Opt. Soc. Am. 56, 1529–1532 (1966).
  4. H. M. Nussenzveig, "High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory," J. Math. Phys. 10, 125–176 (1969).
  5. G. Mie, "Beitrange zur Optik Truber Medien, Speziell Kolloidaler Metallosungen," Ann. Phys. 25, 377–445 (1908).
  6. T. S. Fahlen and H. C. Bryanf, "Optical Back Scattering from Single Water Droplets," J. Opt. Soc. Am. 58, 304–310 (1968).
  7. J. V. Dave, "Scattering of Visible Light by Large Water Spheres," Appl. Opt. 8, 155–164 (1969).
  8. V. Khare and H. M. Nussenzveig, "Theory of the Glury," Phys. Rev. Lett. 38, 1279 (1977).
  9. J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Sci. Ctr. Rept. No. 320-3237, Palo Alto, (1968).
  10. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).
  11. Ref. 2, p. 263.
  12. S. T. Shipley, Ph.D. Thesis, University of Wisconsin, Madison (1978) (to be published).
  13. K. S. Shifrin and Ya. I. Rabinovich, "The Spectral Indicatrices of Large Water Drops and the Spectral Polarization of Rainbows," Bull. Acad. Sci. USSR 12, 73–89 (1957).
  14. F. Volz, "Der Regenbogen," in Handbuch der Geophysik, 8 (Borntrager, Berlin, 1961), Vol. 8.
  15. Ref. 4, Eq. 6.73, p. 162.
  16. Ref. 4, Eq. 5.27, p. 152.
  17. Ref. 2, pp. 249–258.

1977

V. Khare and H. M. Nussenzveig, "Theory of the Glury," Phys. Rev. Lett. 38, 1279 (1977).

1974

S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).

1969

H. M. Nussenzveig, "High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory," J. Math. Phys. 10, 125–176 (1969).

J. V. Dave, "Scattering of Visible Light by Large Water Spheres," Appl. Opt. 8, 155–164 (1969).

1968

1966

1957

K. S. Shifrin and Ya. I. Rabinovich, "The Spectral Indicatrices of Large Water Drops and the Spectral Polarization of Rainbows," Bull. Acad. Sci. USSR 12, 73–89 (1957).

1908

G. Mie, "Beitrange zur Optik Truber Medien, Speziell Kolloidaler Metallosungen," Ann. Phys. 25, 377–445 (1908).

Bryanf, H. C.

Bryant, H. C.

Cox, A. J.

Dave, J. V.

J. V. Dave, "Scattering of Visible Light by Large Water Spheres," Appl. Opt. 8, 155–164 (1969).

J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Sci. Ctr. Rept. No. 320-3237, Palo Alto, (1968).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

Eloranta, E. W.

S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).

Fahlen, T. S.

Khare, V.

V. Khare and H. M. Nussenzveig, "Theory of the Glury," Phys. Rev. Lett. 38, 1279 (1977).

Mie, G.

G. Mie, "Beitrange zur Optik Truber Medien, Speziell Kolloidaler Metallosungen," Ann. Phys. 25, 377–445 (1908).

Nussenzveig, H. M.

V. Khare and H. M. Nussenzveig, "Theory of the Glury," Phys. Rev. Lett. 38, 1279 (1977).

H. M. Nussenzveig, "High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory," J. Math. Phys. 10, 125–176 (1969).

Rabinovich, Ya. I.

K. S. Shifrin and Ya. I. Rabinovich, "The Spectral Indicatrices of Large Water Drops and the Spectral Polarization of Rainbows," Bull. Acad. Sci. USSR 12, 73–89 (1957).

Shifrin, K. S.

K. S. Shifrin and Ya. I. Rabinovich, "The Spectral Indicatrices of Large Water Drops and the Spectral Polarization of Rainbows," Bull. Acad. Sci. USSR 12, 73–89 (1957).

Shipley, S. T.

S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).

S. T. Shipley, Ph.D. Thesis, University of Wisconsin, Madison (1978) (to be published).

van de Hulst, H. C.

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

Volz, F.

F. Volz, "Der Regenbogen," in Handbuch der Geophysik, 8 (Borntrager, Berlin, 1961), Vol. 8.

Weinman, J. A.

S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).

Ann. Phys.

G. Mie, "Beitrange zur Optik Truber Medien, Speziell Kolloidaler Metallosungen," Ann. Phys. 25, 377–445 (1908).

Appl. Opt.

Bull. Acad. Sci. USSR

K. S. Shifrin and Ya. I. Rabinovich, "The Spectral Indicatrices of Large Water Drops and the Spectral Polarization of Rainbows," Bull. Acad. Sci. USSR 12, 73–89 (1957).

J. Appl. Meteor.

S. T. Shipley, E. W. Eloranta, and J. A. Weinman, "Measurement of Rainfall Rates by Lidar," J. Appl. Meteor. 13, 800–807 (1974).

J. Math. Phys.

H. M. Nussenzveig, "High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory," J. Math. Phys. 10, 125–176 (1969).

J. Opt. Soc. Am.

Phys. Rev. Lett.

V. Khare and H. M. Nussenzveig, "Theory of the Glury," Phys. Rev. Lett. 38, 1279 (1977).

Other

J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Sci. Ctr. Rept. No. 320-3237, Palo Alto, (1968).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

Ref. 2, p. 263.

S. T. Shipley, Ph.D. Thesis, University of Wisconsin, Madison (1978) (to be published).

F. Volz, "Der Regenbogen," in Handbuch der Geophysik, 8 (Borntrager, Berlin, 1961), Vol. 8.

Ref. 4, Eq. 6.73, p. 162.

Ref. 4, Eq. 5.27, p. 152.

Ref. 2, pp. 249–258.

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

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