Abstract

By numerical simulation of light scattering by birch and pine pollen grains, we create color plates of coronas with vertical elliptical shapes and strong brightenings, respectively. The shape of the pollen is modeled by the union of n ellipsoids. The Fraunhofer integral is solved by the use of the fast Hartley transform. The sensitivity of the patterns to pollen orientation, Sun elevation, and pollen shape and size is discussed. Good agreement is obtained with amazing photographs made by a Finnish network of amateur astonomers, in the case of strong vertical orientation of the pollen axis.

© 1994 Optical Society of America

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References

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  1. J. A. Lock, L. Yang, “Mie theory of the corona,” Appl. Opt. 30, 3408–3414 (1991).
    [CrossRef] [PubMed]
  2. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).
  3. E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  4. K. Sassen, “Corona-producing cirrus cloud properties derived from polarization lidar and photographic analyses,” Appl. Opt. 30, 3421–3428 (1991).
    [CrossRef] [PubMed]
  5. F. E. Volz, “Die Optik und Meteorolgie der atmosphärischen Trübung,” Ber. Dtsch. Wetterdienstes 2(13), 1–47 (1954).
  6. E. S. Green, A. Deepak, B. J. Lipofsky, “Interpretation of the sun's aureole based on atmospheric aerosol models,” Appl. Opt. 10, 1263–1279 (1971).
    [CrossRef] [PubMed]
  7. F. E. Volz, “Scattering functions near the Sun by large aerosols,” Appl. Opt. 32, 2773–2779 (1993).
    [CrossRef] [PubMed]
  8. P. Parviainen, C. F. Bohren, V. Mäkelä, “Vertical elliptical coronas,” Appl. Opt. 33, 4548–4551 (1994).
    [CrossRef] [PubMed]
  9. G. Erdtman, An Introduction to Pollen Analysis (Chronica Botanica, Waltham, Mass., 1943).
  10. G. Erdtman, Pollen Morphology and Plant Taxonomy. Angiosperms, Vol. I of An Introduction to Palynology (Almquist, Stockholm, 1952).
  11. G. Erdtman, Pollen Morphology and Plant Taxonomy. Gymniosperms, Pteridophytes, Bryophytes, Vol. II of An Introduction to Palynology (Almquist, Stockholm, 1957).
  12. F. A. Fischbach, S. Brooks, J. Bond, “Interpretation of small-angle light scattering maxima of single oriented microparticles” Opt. Lett. 10, 523–525 (1985).
    [CrossRef] [PubMed]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), p. 399.
  14. R. L. Edmonds, ed., Aerobiology: The Ecological System Approach (Dowden, Hutchingson & Ross, Stroudsbourg, Pa., 1979), p. 341.
  15. R. C. Smith, J. S. Marsh, “Diffraction patterns of simple apertures,” J. Opt. Soc. Am. 64, 798–803 (1974).
    [CrossRef]
  16. H. C. van de Hulst, Light Scattering from Small Particles (Wiley. New York, 1957), p. 106.
  17. J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
    [CrossRef]
  18. R. N. Bracewell, The Hartley Transform (Oxford, New York, 1986), p. 102.
  19. “Standard specification for solar constant and air mass zero solar spectral irradiance standard,” in Annual Book of ASTM Standards, Part 41, E490-73a (American Society for Testing and Materials, Philadelphia, Pa., 1974).
  20. C. F. Bohren, G. Koh, “Forward scattering corrected extinction by nonspherical particles,” Appl. Opt. 24, 1023–1029 (1985).
    [CrossRef] [PubMed]

1994 (1)

1993 (2)

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

F. E. Volz, “Scattering functions near the Sun by large aerosols,” Appl. Opt. 32, 2773–2779 (1993).
[CrossRef] [PubMed]

1991 (2)

1987 (1)

1985 (2)

1983 (1)

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

1974 (1)

1971 (1)

1954 (1)

F. E. Volz, “Die Optik und Meteorolgie der atmosphärischen Trübung,” Ber. Dtsch. Wetterdienstes 2(13), 1–47 (1954).

Asano, S.

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

Bohren, C. F.

Bond, J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), p. 399.

Bracewell, R. N.

R. N. Bracewell, The Hartley Transform (Oxford, New York, 1986), p. 102.

Brooks, S.

Deepak, A.

Erdtman, G.

G. Erdtman, An Introduction to Pollen Analysis (Chronica Botanica, Waltham, Mass., 1943).

G. Erdtman, Pollen Morphology and Plant Taxonomy. Angiosperms, Vol. I of An Introduction to Palynology (Almquist, Stockholm, 1952).

G. Erdtman, Pollen Morphology and Plant Taxonomy. Gymniosperms, Pteridophytes, Bryophytes, Vol. II of An Introduction to Palynology (Almquist, Stockholm, 1957).

Fischbach, F. A.

Green, E. S.

Greenler, R. G.

Hovenac, E. A.

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

Koh, G.

Lipofsky, B. J.

Lock, J. A.

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

J. A. Lock, L. Yang, “Mie theory of the corona,” Appl. Opt. 30, 3408–3414 (1991).
[CrossRef] [PubMed]

Mäkelä, V.

Marsh, J. S.

Parviainen, P.

Sassen, K.

Smith, R. C.

Takano, Y.

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

Tränkle, E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering from Small Particles (Wiley. New York, 1957), p. 106.

Volz, F. E.

F. E. Volz, “Scattering functions near the Sun by large aerosols,” Appl. Opt. 32, 2773–2779 (1993).
[CrossRef] [PubMed]

F. E. Volz, “Die Optik und Meteorolgie der atmosphärischen Trübung,” Ber. Dtsch. Wetterdienstes 2(13), 1–47 (1954).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), p. 399.

Yang, L.

Am. J. Phys. (1)

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

Appl. Opt. (6)

Ber. Dtsch. Wetterdienstes (1)

F. E. Volz, “Die Optik und Meteorolgie der atmosphärischen Trübung,” Ber. Dtsch. Wetterdienstes 2(13), 1–47 (1954).

J. Meteorol. Soc. Jpn. (1)

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (8)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), p. 399.

R. L. Edmonds, ed., Aerobiology: The Ecological System Approach (Dowden, Hutchingson & Ross, Stroudsbourg, Pa., 1979), p. 341.

H. C. van de Hulst, Light Scattering from Small Particles (Wiley. New York, 1957), p. 106.

R. N. Bracewell, The Hartley Transform (Oxford, New York, 1986), p. 102.

“Standard specification for solar constant and air mass zero solar spectral irradiance standard,” in Annual Book of ASTM Standards, Part 41, E490-73a (American Society for Testing and Materials, Philadelphia, Pa., 1974).

G. Erdtman, An Introduction to Pollen Analysis (Chronica Botanica, Waltham, Mass., 1943).

G. Erdtman, Pollen Morphology and Plant Taxonomy. Angiosperms, Vol. I of An Introduction to Palynology (Almquist, Stockholm, 1952).

G. Erdtman, Pollen Morphology and Plant Taxonomy. Gymniosperms, Pteridophytes, Bryophytes, Vol. II of An Introduction to Palynology (Almquist, Stockholm, 1957).

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Figures (14)

Fig. 1
Fig. 1

Sketch of pollen for a, pine; b, birch. a is the length of the largest axis of the grain (not including the two air bags and the three small lobes).

Fig. 2
Fig. 2

Flow diagram of the computation.

Fig. 3
Fig. 3

Strong vertical orientation of pine pollen (θ = 0°). Diffraction patterns of a single pollen grain for different rotation angles of a, 0°, b, 9°, c, 18°, …, k, 90°; l, corona pattern obtained by summing up the patterns.

Fig. 4
Fig. 4

Strong horizontal orientation of pine pollen (θ = 0°), the same as in Fig. 3.

Fig. 5
Fig. 5

Dependence of corona patterns on Sun elevation for a strong vertical orientation of pine pollen: a, 0°; b, 30°; c, 60°; d, 90°.

Fig. 6
Fig. 6

Radial variance of intensity of the corona patterns shown in Fig. 5.

Fig. 7
Fig. 7

Global variance of intensity versus Sun elevation for a strong vertical orientation of pine pollen.

Fig. 8
Fig. 8

Aspect ratio of the aureole center versus Sun elevation for a strong vertical orientation of pine pollen.

Fig. 9
Fig. 9

Change of corona patterns at Sun elevations of 5° and 34° by a tilt of 30° for a vertical orientation of pine pollen: a, 5°, θmax = 0°; b, 5°, θmax = 30°; c, 34°, θmax = 0°; d, 34°, θmax = 30°.

Fig. 10
Fig. 10

Global variance of the intensity versus tilting angle for a vertical orientation of pine pollen.

Fig. 11
Fig. 11

Aspect ratio of the aureole center versus tilting angle for a vertical orientation of pine pollen

Fig. 12
Fig. 12

Loss of ring separation for strong vertically oriented birch pollen by variations of pollen shape a and overall size s. The spheroid model is used. a, a = 0%, s = 0%; b, a = 20%, s = 0%; c, a = 0%, s = 10%, d, a = 20%, s = 10%.

Fig. 13
Fig. 13

Change of brightenings for strong vertically oriented pine pollen by variations of the overall size s. a, s = 0%; b, s = 5%; c, s = 10%; d, s = 20%.

Fig. 14
Fig. 14

Aspect ratio of the aureole center and the first ring versus Sun elevation for strong vertically oriented birch pollen. A four-ellipsoid model is used. Data are from Ref. 8. The aspect ratio of the pollen grain is 0.8. For comparision, the prediction of the spheroid model is included.

Tables (2)

Tables Icon

Table 1 Number of Pollen-Shape Parameters in the n-Ellipsoid Model

Tables Icon

Table 2 Sensitivity with Respect to the Variation of Nine Pollen-Shape Parameters

Equations (10)

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I ( ξ , η ) = I 0 λ 2 r 2 | S exp [ ik ( ξ x + η y ) ] d x d y | 2 ,
G ( x , y ) = { 1 for all points inside the shadow 0 for all points inside the shadow ,
I ( ξ k , η l ) = I 0 λ 2 r 2 Δ x 2 Δ y 2 | i = N / 2 N / 2 1 j = N / 2 N / 2 1 G ( x i , y j ) × exp [ 2 π i λ ( ξ k x i + η l y j ) ] | 2 ,
Δ ξ = Δ η = λ N Δ x .
I ( ξ , η ) = ψ θ φ a ( ψ , θ , φ ) I ( ξ , η , ψ , θ , φ ) sin ( θ ) d ψ d θ d φ .
I ( ξ , η ) = ϕ ( s ) I r [ ξ ϕ ( s ) ϕ ( s 0 ) , η ϕ ( s ) ϕ ( s 0 ) ] d s ,
I ( ξ , η ) = I r ( ξ τ , η δ ) S ( τ , δ ) d τ d δ ,
x i ( ξ , η ) = λ min λ max I r ( ξ λ λ 0 , η λ λ 0 ) r i ( λ ) b ( λ ) d λ , i = R , G , B ,
I = log [ 1 exp ( α I ) + β ] ,
a = a , b = [ a 2 sin 2 ( θ ) + b 2 cos 2 ( θ ) ] 1 / 2 .

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