Abstract

Mie-scattering algorithms were used to compute scattered intensities and phase differences for air bubbles in water. Results are plotted as a function of the scattering angle ϕ in the general range of 30–90° for size parameters ka of 25, 100, 1,000, and 10,000 (corresponding to radii a ≃ 1.3 μm to 0.8 mm). As ϕ decreases below the critical scattering angle at 82.8°, the intensity increases and undergoes broadly spaced oscillations that are described by a physical-optics approximation developed by the authors in a separate publication. Mie scattering also exhibits finely spaced oscillations.

© 1981 Optical Society of America

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References

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  1. P. L. Marston, “Critical angle scattering by a bubble: physical-optics approximation and observations,” J. Opt. Soc. Am. 69, 1205–1211 (1979); J. Opt. Soc. Am. 70, 353(E) (1980).
    [Crossref]
  2. P. L. Marston and D. L. Kingsbury, “Scattering by a bubble in water near the critical angle: interference effects,” J. Opt. Soc. Am. 71, 192–196 (1981).
    [Crossref]
  3. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
  4. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  5. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [Crossref] [PubMed]
  6. R. H. Boll, R. O. Gumprecht, and C. M. Sliepcevich, “Theoretical light scattering coefficients for relative refractive indexes less than unity and for totally reflecting spheres,” J. Opt. Soc. Am. 44, 18–21 (1954).
    [Crossref]
  7. R. H. Boll and et al., Tables of Light-Scattering Functions (U. Michigan Press, Ann Arbor, Mich., 1958).
  8. I. L. Zelmanovich and K. S. Shifrin, Tables of Light Scattering. Part III: Coefficients of Extinction, Scattering, and Light Pressure (Hydrometeorological Publishing House, Leningrad, 1968).
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  10. J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1968).
    [Crossref]
  11. W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector–Speed Computer Codes,” (National Center for Atmospheric Research, Boulder, Colo., 1979).
  12. G. E. Davis, “Scattering of light by an air bubble in water,” J. Opt. Soc. Am. 45, 572–581 (1955).
    [Crossref]
  13. B. D. Johnson and R. C. Cooke, “Bubble populations and spectra in coastal waters: a photographic approach,” J. Geophys. Res. 84, 3761–3766 (1979).
    [Crossref]
  14. A. Keller, “Ein Streulicht-Zählverfahren, angewandt zur Bestimmung des Kavitationskeimspektrums,” Optik 32, 165–176 (1970).
  15. A. Keller, “The influence of the cavitation nucleus spectrum on cavitation inception, investigated with a scattered-light counting method,” J. Basic Eng. 94, 917–925 (1972).
    [Crossref]

1981 (1)

1980 (1)

1979 (2)

B. D. Johnson and R. C. Cooke, “Bubble populations and spectra in coastal waters: a photographic approach,” J. Geophys. Res. 84, 3761–3766 (1979).
[Crossref]

P. L. Marston, “Critical angle scattering by a bubble: physical-optics approximation and observations,” J. Opt. Soc. Am. 69, 1205–1211 (1979); J. Opt. Soc. Am. 70, 353(E) (1980).
[Crossref]

1972 (1)

A. Keller, “The influence of the cavitation nucleus spectrum on cavitation inception, investigated with a scattered-light counting method,” J. Basic Eng. 94, 917–925 (1972).
[Crossref]

1970 (1)

A. Keller, “Ein Streulicht-Zählverfahren, angewandt zur Bestimmung des Kavitationskeimspektrums,” Optik 32, 165–176 (1970).

1968 (1)

1955 (1)

1954 (1)

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).

Boll, R. H.

Cooke, R. C.

B. D. Johnson and R. C. Cooke, “Bubble populations and spectra in coastal waters: a photographic approach,” J. Geophys. Res. 84, 3761–3766 (1979).
[Crossref]

Dave, J. V.

Davis, G. E.

Gumprecht, R. O.

Johnson, B. D.

B. D. Johnson and R. C. Cooke, “Bubble populations and spectra in coastal waters: a photographic approach,” J. Geophys. Res. 84, 3761–3766 (1979).
[Crossref]

Keller, A.

A. Keller, “The influence of the cavitation nucleus spectrum on cavitation inception, investigated with a scattered-light counting method,” J. Basic Eng. 94, 917–925 (1972).
[Crossref]

A. Keller, “Ein Streulicht-Zählverfahren, angewandt zur Bestimmung des Kavitationskeimspektrums,” Optik 32, 165–176 (1970).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kingsbury, D. L.

Marston, P. L.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).

Shifrin, K. S.

I. L. Zelmanovich and K. S. Shifrin, Tables of Light Scattering. Part III: Coefficients of Extinction, Scattering, and Light Pressure (Hydrometeorological Publishing House, Leningrad, 1968).

Sliepcevich, C. M.

van de Hulst, H. C.

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

Wiscombe, W. J.

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[Crossref] [PubMed]

W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector–Speed Computer Codes,” (National Center for Atmospheric Research, Boulder, Colo., 1979).

Zelmanovich, I. L.

I. L. Zelmanovich and K. S. Shifrin, Tables of Light Scattering. Part III: Coefficients of Extinction, Scattering, and Light Pressure (Hydrometeorological Publishing House, Leningrad, 1968).

Ann. Phys. (Leipzig) (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).

Appl. Opt. (2)

J. Basic Eng. (1)

A. Keller, “The influence of the cavitation nucleus spectrum on cavitation inception, investigated with a scattered-light counting method,” J. Basic Eng. 94, 917–925 (1972).
[Crossref]

J. Geophys. Res. (1)

B. D. Johnson and R. C. Cooke, “Bubble populations and spectra in coastal waters: a photographic approach,” J. Geophys. Res. 84, 3761–3766 (1979).
[Crossref]

J. Opt. Soc. Am. (4)

Optik (1)

A. Keller, “Ein Streulicht-Zählverfahren, angewandt zur Bestimmung des Kavitationskeimspektrums,” Optik 32, 165–176 (1970).

Other (5)

W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector–Speed Computer Codes,” (National Center for Atmospheric Research, Boulder, Colo., 1979).

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

R. H. Boll and et al., Tables of Light-Scattering Functions (U. Michigan Press, Ann Arbor, Mich., 1958).

I. L. Zelmanovich and K. S. Shifrin, Tables of Light Scattering. Part III: Coefficients of Extinction, Scattering, and Light Pressure (Hydrometeorological Publishing House, Leningrad, 1968).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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Figures (5)

Fig. 1
Fig. 1

Ray paths in the scattering plane with a scattering angle ϕ = 50°. The number adjacent to each ray gives the ray parameter p. The approximation given in Ref. 2 includes the interference and diffraction of waves associated with rays 0 and 1.

Fig. 2
Fig. 2

Calculated normalized scattering intensities for ka = 10,000. The electric vector is parallel to the scattering plane. The solid curve is from Mie theory. The dashed curve is the physical-optics approximation given in Ref. 2.

Fig. 3
Fig. 3

Like Fig. 2 but with (a) ka = 1000 and the electric vector perpendicular to scattering plane and (b) ka = 100 and the electric vector parallel to the scattering plane.

Fig. 4
Fig. 4

Like Fig. 2 but with ka = 25 and the electric vector (a) perpendicular and (b) parallel.

Fig. 5
Fig. 5

Phase difference for the scattering amplitudes in the two polarization states for (a) ka = 1000 and (b) ka = 100. The solid curve is from Mie theory and Eq. (1). The dashed curve is the physical-optics approximation by Eq. (28) of Ref. 2.

Equations (2)

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δ = arg ( S 2 ) - arg ( S 1 ) ,
ϕ c - ϕ 1.2 ( λ / a cos θ c ) 1 / 2 ( rad ) .