Abstract

Mie theory can be used to provide full-color simulations of atmospheric glories. Comparison of such simulations with images of real glories suggests that most glories are caused by spherical water droplets with radii between 4 and 25 μm. This paper also examines the appearance of glories taking into account the size of the droplets and the width of the droplet size distributions. Simulations of glories viewed through a linear polarizer compare well with the few available pictures, but they show some features that need corroboration by more observations.

© 2005 Optical Society of America

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References

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  1. G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. Leipzig 25, 377–445 (1908).
    [CrossRef]
  2. S. D. Gedzelman, “Simulating glories and cloudbows in color,” Appl. Opt. 42, 429–435 (2003).
    [CrossRef] [PubMed]
  3. P. Laven, “Simulation of rainbows, coronas, and glories by use of Mie theory,” Appl. Opt. 42, 436–444 (2003).
    [CrossRef] [PubMed]
  4. R. L. Lee, “Mie theory, Airy theory, and the natural rainbow,” Appl. Opt. 37, 1506–1519 (1998).
    [CrossRef]
  5. G. P. Können, Polarized Light in Nature (Cambridge University, Cambridge, UK, 1985).
  6. C. F. Bohren, “On the gamut of colors seen through birefringent airplane windows,” Appl. Opt. 30, 3474–3478 (1991).
    [CrossRef] [PubMed]
  7. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, UK, 2001).
  8. S. D. Gedzelman, J. A. Lock, “Simulating coronas in color,” Appl. Opt. 42, 497–504 (2003).
    [CrossRef] [PubMed]
  9. J. A. Shaw, P. J. Neiman, “Coronas and iridescence in mountain wave clouds,” Appl. Opt. 42, 476–485 (2003).
    [CrossRef] [PubMed]
  10. B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
    [CrossRef]
  11. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  12. P. Laven, “How are glories formed?” Appl. Opt. 44, 5675–5683 (2005).
    [CrossRef] [PubMed]

2005 (1)

2004 (1)

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

2003 (4)

1998 (1)

1991 (1)

1908 (1)

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. Leipzig 25, 377–445 (1908).
[CrossRef]

Bohren, C. F.

Deirmendjian, D.

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

Gedzelman, S. D.

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge University, Cambridge, UK, 1985).

Laven, P.

Lee, R. L.

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, UK, 2001).

Lock, J. A.

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, UK, 2001).

Mayer, B.

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

Mie, G.

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. Leipzig 25, 377–445 (1908).
[CrossRef]

Neiman, P. J.

Preusker, R.

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

Schröder, M.

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

Schüller, L.

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

Shaw, J. A.

Ann. Phys. Leipzig (1)

G. Mie, “Beitrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. Leipzig 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (7)

Atmos. Chem. Phys. (1)

B. Mayer, M. Schröder, R. Preusker, L. Schüller, “Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study,” Atmos. Chem. Phys. 4, 1255–1263 (2004).
[CrossRef]

Other (3)

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

G. P. Können, Polarized Light in Nature (Cambridge University, Cambridge, UK, 1985).

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, UK, 2001).

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Figures (14)

Fig. 1
Fig. 1

Backscattering of monochromatic red light (λ = 650 nm) by a spherical water droplet with radius r = 10 μm as a function of scattering angle θ. Note that “perpendicular polarization” indicates light with polarization perpendicular to the scattering plane, whereas “parallel polarization” indicates polarization parallel to the scattering plane.

Fig. 2
Fig. 2

Backscattering of sunlight from a spherical droplet of water with r = 10 μm as a function of scattering angle θ. These calculations were based on a light source with an apparent angular diameter of 0.5° with the spectrum of sunlight represented by 300 discrete wavelengths between 380 nm and 700 nm. The three horizontal colored bars above the graph represent the brightness and color of the scattered light for perpendicular polarization, parallel polarization, and unpolarized light, while the color of the curves in the graph shows the saturated color of the scattered light.

Fig. 3
Fig. 3

(a) Simulation of a glory caused by scattering of sunlight from spherical water droplets with r = 10 μm (the width of the image is about ±5°). (b) As in (a) but viewed through a polarizer with its transmission axis vertical.

Fig. 4
Fig. 4

Diagram showing the appearance of a glory when viewed through a polarizer with its transmission axis vertical. Reproduced with permission of G. P. Können.

Fig. 5
Fig. 5

An unpolarized glory, shown as image (a), can be separated into two components (b) and (c), which have polarizations perpendicular and parallel to the scattering plane, respectively. When viewed through a vertical polarizer, (b) is transformed into (d), while (c) is transformed into (e). Image (d) shows that the polarizer suppresses perpendicular polarization along the vertical line through the antisolar point, but has no effect along the horizontal line. This is similar to the effect of viewing the primary rainbow through a polarizer, because the primary rainbow is dominated by perpendicular polarization. Image (e) shows that the polarizer suppresses parallel polarization along the horizontal line through the antisolar point. When (d) and (e) are combined, the resulting image (f) shows the “polarized” glory with its distinctive dark spots above and below the antisolar point. Note that the colors of the polarized glory along the horizontal line through the antisolar point correspond to perpendicular polarization, whereas those along the vertical correspond to parallel polarization. Other orientations obviously involve a mixture of the two polarizations.

Fig. 6
Fig. 6

Photographs of glories viewed through a polarizer with the transmission axis vertical. Reproduced with permission of: (a) Alistair Fraser, (b) Philip Laven, (c) Philip Laven, (d) Claudia Hinz.

Fig. 7
Fig. 7

Simulations of glories caused by water droplets with a log-normal size distribution with median value of r = 10 μm and standard deviation σ: (a) σ = 0.5 μm, (b) σ = 1 μm, (c) σ = 2 μm.

Fig. 8
Fig. 8

Scattering of sunlight by water droplets of median radius r between 5 μm and 20 μm with a log-normal size distribution and a standard deviation σ = 5% of the nominal value.

Fig. 9
Fig. 9

Scattering of sunlight by water droplets of median radius r between 1 μm and 20 μm with a log-normal size distribution and a standard deviation σ = 5% of the nominal value.

Fig. 10
Fig. 10

Simulation of the glory due to scattering by r = 30 μm droplets of water: the left side shows the glory caused by a point source of light, while the right side shows the glory caused by a light source with an apparent diameter of 0.5°.

Fig. 11
Fig. 11

(a) Glory and a Brocken specter seen in Grisedale, Cumbria, England (image reproduced with permission of Dave Newton). (b) Simulation of a glory caused by monodisperse water droplets with r = 9 μm.

Fig. 12
Fig. 12

(a) Glory and a Brocken specter seen very close to the summit (22 600 ft; 6888 m) of Mt. Aconcagua, Argentina (picture taken by Eric Wintenberger and reproduced with permission of Pedro Gonzalez). (b) Simulation of a glory caused by monodisperse water droplets with r = 11 μm.

Fig. 13
Fig. 13

(a) Glory seen from a commercial aircraft (Philip Laven). (b) Simulation of a glory caused by monodisperse water droplets with r = 4.3 μm.

Fig. 14
Fig. 14

Glory observed by the MEIDEX instrument on board the Space Shuttle Columbia (image reproduced with permission of Peter Israelevich, Tel Aviv University).

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