Abstract

Expressions are derived from Mie theory for the cross-polarized and non-cross-polarized measurement configurations that are useful for the study of the optical glories of transparent spheres.

© 1983 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
    [Crossref]
  3. D. S. Langley and P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
    [Crossref]
  4. P. L. Marston and D. S. Langley, “Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops,” J. Opt. Soc. Am. 72, 456–459 (1982); in the final section, the equation pτ= −1 should be pτ= 1.
    [Crossref]
  5. 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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
    [Crossref]
  6. J. J. Stephens, P. S. Ray, and T. W. Kitterman, “Far-field impulse response verification of selected high-frequency optics scattering analogs,” Appl. Opt. 14, 2169–2176 (1975).
    [Crossref] [PubMed]
  7. H. M. Nussenzveig and W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 1279–1282 (1980).
    [Crossref]
  8. G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908) [English translation no. 79-21946 (National Translation Center, Chicago, Ill., 1979)].
  9. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [Crossref] [PubMed]
  10. G. Arfken, Mathematical Models for Physicists, 2nd ed. (Academic, New York, 1970), p. 84.

1982 (2)

P. L. Marston and D. S. Langley, “Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops,” J. Opt. Soc. Am. 72, 456–459 (1982); in the final section, the equation pτ= −1 should be pτ= 1.
[Crossref]

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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
[Crossref]

1981 (1)

D. S. Langley and P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[Crossref]

1980 (2)

H. M. Nussenzveig and W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 1279–1282 (1980).
[Crossref]

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

1977 (1)

V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[Crossref]

1975 (1)

1908 (1)

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908) [English translation no. 79-21946 (National Translation Center, Chicago, Ill., 1979)].

Arfken, G.

G. Arfken, Mathematical Models for Physicists, 2nd ed. (Academic, New York, 1970), p. 84.

Khare, V.

V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[Crossref]

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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
[Crossref]

Kitterman, T. W.

Langley, D. S.

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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
[Crossref]

P. L. Marston and D. S. Langley, “Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops,” J. Opt. Soc. Am. 72, 456–459 (1982); in the final section, the equation pτ= −1 should be pτ= 1.
[Crossref]

D. S. Langley and P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[Crossref]

Marston, P. 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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
[Crossref]

P. L. Marston and D. S. Langley, “Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops,” J. Opt. Soc. Am. 72, 456–459 (1982); in the final section, the equation pτ= −1 should be pτ= 1.
[Crossref]

D. S. Langley and P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[Crossref]

Mie, G.

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908) [English translation no. 79-21946 (National Translation Center, Chicago, Ill., 1979)].

Nussenzveig, H. M.

H. M. Nussenzveig and W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 1279–1282 (1980).
[Crossref]

V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[Crossref]

Ray, P. S.

Stephens, J. J.

van de Hulst, H. C.

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

Wiscombe, W. J.

H. M. Nussenzveig and W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 1279–1282 (1980).
[Crossref]

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

Ann. Phys. (Leipzig) (1)

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908) [English translation no. 79-21946 (National Translation Center, Chicago, Ill., 1979)].

Appl. Opt. (2)

Appl. Sci. Res. (1)

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, “Light scattering by bubbles in liquids: comments and application of results to circularly polarized incident light,” Appl. Sci. Res. 40, 3–5 (1983).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

H. M. Nussenzveig and W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 1279–1282 (1980).
[Crossref]

Phys. Rev. Lett. (2)

V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[Crossref]

D. S. Langley and P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[Crossref]

Other (2)

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

G. Arfken, Mathematical Models for Physicists, 2nd ed. (Academic, New York, 1970), p. 84.

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Figures (2)

Fig. 1
Fig. 1

Method for observing cross-polarized scattering and non-cross-polarized scattering similar to that used in Ref. 3 for the backward glory. The diameter of the incident beam is assumed to be much larger than the sphere’s diameter. The cameras are to be focused on infinity so that the photographs record the far-zone scattering. Other detectors may be used in place of cameras.

Fig. 2
Fig. 2

Spherical coordinates used in the description of scattering to a point Q in (a) the forward hemisphere and (b) the backward hemisphere. The sphere is centered on O. The polarizers are in planes perpendicular to the ±z axes such that they interrupt the lines OQ when r is large.

Equations (12)

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E θ = f S 2 cos φ ,             E φ = - f S 1 sin φ ,
ê 5 = h 5 ê r × ( ê x × ê r ) = h 5 [ ê x - ( ê r · ê x ) ê x ] = h 5 ( ê x - sin θ cos φ ê r ) ,
ê 6 = h 6 ê r × ( ê y × ê r ) = h 6 ( ê y - sin θ sin φ ê r ) ,
E j = f S j ,             j = 5 , 6 ,
S 5 = h 5 ( S 2 cos θ cos 2 φ + S 1 sin 2 φ ) ,
S 6 = h 6 sin φ cos φ ( S 2 cos θ - S 1 ) .
I j = I r 4 S j 2 ( k a ) - 2 .
S 5 = ½ h 5 [ S - - S + cos 2 φ + ( 1 - cos γ ) 2 S 2 cos 2 φ ] ,
S 6 = - ½ h 6 sin 2 φ [ S + - ( 1 - cos γ ) S 2 ] ,
S 5 = ½ h 5 [ S + - S - cos 2 φ - ( 1 - cos θ ) 2 S 2 cos 2 φ ] ,
S 6 = - ½ h 6 sin 2 φ [ S - + ( 1 - cos θ ) S 2 ] ,
( S 1 ) d = ( S 2 ) d = ½ ( S + ) d ( k a ) 2 α - 1 J 1 ( α ) ,