Abstract

A novel effect in the scattering of white light from bubbles consists of colored bands that appear near the critical scattering angle. The bands were photographed in the far-zone scattering from a cylindrical bubble in glass. Their existence is associated with the coarse structure present in the exact scattered intensity. A digital Butterworth filter was developed to remove (from computed intensities) fine structures that are lost when the optical bandwidth is large. The colors are found to be due to the combined effects of interference and diffraction (near the critical scattering angle) and dispersion of the refractive index. Coarse structures were previously modeled in the monochromatic scattering from spherical air bubbles in water. Colors are also to be expected in the appearance of clouds of bubbles in water. Such colors were reported [C. Pulfrich, Ann. Phys. Chem. (Leipzig) 33, 209 (1888)]. Some implications for the optical measurement of bubble size and surface quality are noted.

© 1983 Optical Society of America

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  3. P. L. Marston, "Critical angle scattering by a bubble: physicaloptics approximation and observations," J. Opt. Soc. Am. 69, 1205–1211 (1979); 70, 353 (E) (1980).
  4. 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); 71, 917 (E) (1981).
  5. D. L. Kingsbury and P. L. Marston, "Mie scattering near the critical angle of bubbles in water," J. Opt. Soc. Am. 71, 358–361 (1981).
  6. D. L. Kingsbury and P. L. Marston, "Scattering by bubbles in glass: Mie theory and physical optics approximation," Appl. Opt. 20, 2348–2350 (1981).
  7. P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).
  8. D. S. Langley and P. L. Marston, "Critical-angle scattering by a bubble in water: experimental results," J. Opt. Soc. Am. 72, 1826 (1982).
  9. D. S. Langley and P. L. Marston, "Glory in optical backscattering from air bubbles," Phys. Rev. Lett. 47, 913–916 (1981); P. L. Marston, "Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light," Appl. Sci. Res. 40, 3–5 (1983).
  10. C. Pulfrich, "Ueber eine dem Regenbogen verwandte Erscheinung der Totalreflexion," Ann. Phys. Chem. (Leipzig) 33, 209–212 (1888).
  11. F. Volz, "Optik der Tropfen," in Handbuch der Geophysik, F. Linke and F. Moller, eds. (Gebruder Borntraeger, Berlin, 1961), Band 8, pp. 943–1026.
  12. P. L. Marston and D. L. Kingsbury, "Acoustic scattering from fluid spheres: diffraction and interference near the critical scattering angle," J. Acoust. Soc. Am. 70, 1488–1495 (1981).
  13. D. Ludwig, "Diffraction by a circular cavity," J. Math. Phys. 11, 1617–1630 (1970).
  14. Lord Rayleigh (J. W. Strutt), "On the Electromagnetic theory of light," Phil. Mag. 12, 81–101 (1881).
  15. W. A. Farone and M. Kerker, "Light scattering from long submicron glass cylinders at normal incidence," J. Opt. Soc. Am. 56, 481–487 (1966).
  16. P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
  17. P. Debye, "Das elektromagnetische Feld umn einen Zylinder und die Theorie des Regenbogens," Phys. Z. 9, 775–778 (1908); G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 2nd ed. (Institution of Electrical Engineers, London, 1980), Sec. 3.4.1, Eq. (138).
  18. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Sec. 5.2.1.
  19. N. J. Kreidl and J. L. Rood, "Optical materials," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 153–200.
  20. S. J. Williamson and H. Z. Cummins, Light and Color in Nature and Art (Wiley, New York, 1983), Plate 10.
  21. C. Pulfrich, "Ein experimenteller Beitrag zur Theorie des Regenbogens und der uberzahligen Bogen," Ann. Phys. Chem. (Leipzig) 33, 194–208 (1888).
  22. S. Gowing and S. C. Ling, "Measurements of microbubbles in a water tunnel," Rep. No. SPD-099201 (David W. Taylor Naval Ship R & D Center, Bethesda, Md., 1981).
  23. D. A. Glaser, "The bubble chamber," in Handbuch der Physik, (Springer-Verlag, Berlin, 1958), Band 45, pp. 314–341.
  24. P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.
  25. H. J. Orchard, "The phase and envelope delay of Butterworth and Tchebycheff filters," IRE Trans. Circuit Theory CT-7, 180–181 (1960).

1983

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

1982

P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).

D. S. Langley and P. L. Marston, "Critical-angle scattering by a bubble in water: experimental results," J. Opt. Soc. Am. 72, 1826 (1982).

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).

1981

P. L. Marston and D. L. Kingsbury, "Acoustic scattering from fluid spheres: diffraction and interference near the critical scattering angle," J. Acoust. Soc. Am. 70, 1488–1495 (1981).

S. Gowing and S. C. Ling, "Measurements of microbubbles in a water tunnel," Rep. No. SPD-099201 (David W. Taylor Naval Ship R & D Center, Bethesda, Md., 1981).

D. S. Langley and P. L. Marston, "Glory in optical backscattering from air bubbles," Phys. Rev. Lett. 47, 913–916 (1981); P. L. Marston, "Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light," Appl. Sci. Res. 40, 3–5 (1983).

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); 71, 917 (E) (1981).

D. L. Kingsbury and P. L. Marston, "Mie scattering near the critical angle of bubbles in water," J. Opt. Soc. Am. 71, 358–361 (1981).

D. L. Kingsbury and P. L. Marston, "Scattering by bubbles in glass: Mie theory and physical optics approximation," Appl. Opt. 20, 2348–2350 (1981).

1979

1970

D. Ludwig, "Diffraction by a circular cavity," J. Math. Phys. 11, 1617–1630 (1970).

1966

1965

N. J. Kreidl and J. L. Rood, "Optical materials," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 153–200.

1961

F. Volz, "Optik der Tropfen," in Handbuch der Geophysik, F. Linke and F. Moller, eds. (Gebruder Borntraeger, Berlin, 1961), Band 8, pp. 943–1026.

1960

H. J. Orchard, "The phase and envelope delay of Butterworth and Tchebycheff filters," IRE Trans. Circuit Theory CT-7, 180–181 (1960).

1958

D. A. Glaser, "The bubble chamber," in Handbuch der Physik, (Springer-Verlag, Berlin, 1958), Band 45, pp. 314–341.

1908

P. Debye, "Das elektromagnetische Feld umn einen Zylinder und die Theorie des Regenbogens," Phys. Z. 9, 775–778 (1908); G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 2nd ed. (Institution of Electrical Engineers, London, 1980), Sec. 3.4.1, Eq. (138).

1888

C. Pulfrich, "Ein experimenteller Beitrag zur Theorie des Regenbogens und der uberzahligen Bogen," Ann. Phys. Chem. (Leipzig) 33, 194–208 (1888).

C. Pulfrich, "Ueber eine dem Regenbogen verwandte Erscheinung der Totalreflexion," Ann. Phys. Chem. (Leipzig) 33, 209–212 (1888).

1881

Lord Rayleigh (J. W. Strutt), "On the Electromagnetic theory of light," Phil. Mag. 12, 81–101 (1881).

Barber, P. W.

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).

Brim, B. L.

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

Chang, R. K.

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).

Cummins, H. Z.

S. J. Williamson and H. Z. Cummins, Light and Color in Nature and Art (Wiley, New York, 1983), Plate 10.

Debye, P.

P. Debye, "Das elektromagnetische Feld umn einen Zylinder und die Theorie des Regenbogens," Phys. Z. 9, 775–778 (1908); G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 2nd ed. (Institution of Electrical Engineers, London, 1980), Sec. 3.4.1, Eq. (138).

Farone, W. A.

Glaser, D. A.

D. A. Glaser, "The bubble chamber," in Handbuch der Physik, (Springer-Verlag, Berlin, 1958), Band 45, pp. 314–341.

Gowing, S.

S. Gowing and S. C. Ling, "Measurements of microbubbles in a water tunnel," Rep. No. SPD-099201 (David W. Taylor Naval Ship R & D Center, Bethesda, Md., 1981).

Johnson, J. L.

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

Kerker, M.

W. A. Farone and M. Kerker, "Light scattering from long submicron glass cylinders at normal incidence," J. Opt. Soc. Am. 56, 481–487 (1966).

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

Kingsbury, D. L.

P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).

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); 71, 917 (E) (1981).

D. L. Kingsbury and P. L. Marston, "Mie scattering near the critical angle of bubbles in water," J. Opt. Soc. Am. 71, 358–361 (1981).

D. L. Kingsbury and P. L. Marston, "Scattering by bubbles in glass: Mie theory and physical optics approximation," Appl. Opt. 20, 2348–2350 (1981).

P. L. Marston and D. L. Kingsbury, "Acoustic scattering from fluid spheres: diffraction and interference near the critical scattering angle," J. Acoust. Soc. Am. 70, 1488–1495 (1981).

Kreidl, N. J.

N. J. Kreidl and J. L. Rood, "Optical materials," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 153–200.

Langley, D. S.

D. S. Langley and P. L. Marston, "Critical-angle scattering by a bubble in water: experimental results," J. Opt. Soc. Am. 72, 1826 (1982).

P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).

D. S. Langley and P. L. Marston, "Glory in optical backscattering from air bubbles," Phys. Rev. Lett. 47, 913–916 (1981); P. L. Marston, "Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light," Appl. Sci. Res. 40, 3–5 (1983).

Ling, S. C.

S. Gowing and S. C. Ling, "Measurements of microbubbles in a water tunnel," Rep. No. SPD-099201 (David W. Taylor Naval Ship R & D Center, Bethesda, Md., 1981).

Love, S. P.

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

Ludwig, D.

D. Ludwig, "Diffraction by a circular cavity," J. Math. Phys. 11, 1617–1630 (1970).

Marston, P. L.

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).

D. S. Langley and P. L. Marston, "Critical-angle scattering by a bubble in water: experimental results," J. Opt. Soc. Am. 72, 1826 (1982).

D. S. Langley and P. L. Marston, "Glory in optical backscattering from air bubbles," Phys. Rev. Lett. 47, 913–916 (1981); P. L. Marston, "Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light," Appl. Sci. Res. 40, 3–5 (1983).

D. L. Kingsbury and P. L. Marston, "Scattering by bubbles in glass: Mie theory and physical optics approximation," Appl. Opt. 20, 2348–2350 (1981).

D. L. Kingsbury and P. L. Marston, "Mie scattering near the critical angle of bubbles in water," J. Opt. Soc. Am. 71, 358–361 (1981).

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); 71, 917 (E) (1981).

P. L. Marston and D. L. Kingsbury, "Acoustic scattering from fluid spheres: diffraction and interference near the critical scattering angle," J. Acoust. Soc. Am. 70, 1488–1495 (1981).

P. L. Marston, "Critical angle scattering by a bubble: physicaloptics approximation and observations," J. Opt. Soc. Am. 69, 1205–1211 (1979); 70, 353 (E) (1980).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Sec. 5.2.1.

Orchard, H. J.

H. J. Orchard, "The phase and envelope delay of Butterworth and Tchebycheff filters," IRE Trans. Circuit Theory CT-7, 180–181 (1960).

Owen, J. F.

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).

Pulfrich, C.

C. Pulfrich, "Ein experimenteller Beitrag zur Theorie des Regenbogens und der uberzahligen Bogen," Ann. Phys. Chem. (Leipzig) 33, 194–208 (1888).

C. Pulfrich, "Ueber eine dem Regenbogen verwandte Erscheinung der Totalreflexion," Ann. Phys. Chem. (Leipzig) 33, 209–212 (1888).

Rayleigh, Lord

Lord Rayleigh (J. W. Strutt), "On the Electromagnetic theory of light," Phil. Mag. 12, 81–101 (1881).

Rood, J. L.

N. J. Kreidl and J. L. Rood, "Optical materials," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 153–200.

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Sec. 5.2.1.

van de Hulst, H. C.

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

Volz, F.

F. Volz, "Optik der Tropfen," in Handbuch der Geophysik, F. Linke and F. Moller, eds. (Gebruder Borntraeger, Berlin, 1961), Band 8, pp. 943–1026.

Williamson, S. J.

S. J. Williamson and H. Z. Cummins, Light and Color in Nature and Art (Wiley, New York, 1983), Plate 10.

Ann. Phys. Chem.

C. Pulfrich, "Ueber eine dem Regenbogen verwandte Erscheinung der Totalreflexion," Ann. Phys. Chem. (Leipzig) 33, 209–212 (1888).

C. Pulfrich, "Ein experimenteller Beitrag zur Theorie des Regenbogens und der uberzahligen Bogen," Ann. Phys. Chem. (Leipzig) 33, 194–208 (1888).

Appl. Opt.

Appl. Sci. Res.

P. L. Marston, D. S. Langley, and D. L. Kingsbury, "Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments," Appl. Sci. Res. 38, 373–383 (1982).

IEEE Trans. Antennas Propag.

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).

IRE Trans. Circuit Theory

H. J. Orchard, "The phase and envelope delay of Butterworth and Tchebycheff filters," IRE Trans. Circuit Theory CT-7, 180–181 (1960).

J. Acoust. Soc. Am.

P. L. Marston and D. L. Kingsbury, "Acoustic scattering from fluid spheres: diffraction and interference near the critical scattering angle," J. Acoust. Soc. Am. 70, 1488–1495 (1981).

J. Math. Phys.

D. Ludwig, "Diffraction by a circular cavity," J. Math. Phys. 11, 1617–1630 (1970).

J. Opt. Soc. Am.

Phil. Mag.

Lord Rayleigh (J. W. Strutt), "On the Electromagnetic theory of light," Phil. Mag. 12, 81–101 (1881).

Phys. Rev. Lett.

D. S. Langley and P. L. Marston, "Glory in optical backscattering from air bubbles," Phys. Rev. Lett. 47, 913–916 (1981); P. L. Marston, "Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light," Appl. Sci. Res. 40, 3–5 (1983).

Other

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

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

F. Volz, "Optik der Tropfen," in Handbuch der Geophysik, F. Linke and F. Moller, eds. (Gebruder Borntraeger, Berlin, 1961), Band 8, pp. 943–1026.

P. Debye, "Das elektromagnetische Feld umn einen Zylinder und die Theorie des Regenbogens," Phys. Z. 9, 775–778 (1908); G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 2nd ed. (Institution of Electrical Engineers, London, 1980), Sec. 3.4.1, Eq. (138).

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Sec. 5.2.1.

N. J. Kreidl and J. L. Rood, "Optical materials," in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 153–200.

S. J. Williamson and H. Z. Cummins, Light and Color in Nature and Art (Wiley, New York, 1983), Plate 10.

S. Gowing and S. C. Ling, "Measurements of microbubbles in a water tunnel," Rep. No. SPD-099201 (David W. Taylor Naval Ship R & D Center, Bethesda, Md., 1981).

D. A. Glaser, "The bubble chamber," in Handbuch der Physik, (Springer-Verlag, Berlin, 1958), Band 45, pp. 314–341.

P. L. Marston, J. L. Johnson, S. P. Love, and B. L. Brim, "Scattering of white light from a cylindrical bubble: observations of colors near the critical scattering angle," in Digest of the Topical Meeting on Meteorological Optics (Optical Society of America, Washington, D.C. 1983), pp. ThA3-1–ThA3-4.

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