Abstract

Simultaneous two-wavelength polarization and radiance distributions have been obtained for 22° parhelia in four Antarctic ice-crystal swarms that extended to ground level. Samples of crystals that produced these parhelia were collected and replicated. The wavelength dependence of the width of the halo polarization peak agrees with Fraunhofer diffraction theory, indicating that the broadening of the halos is caused primarily by diffraction. However, the observed broadening is much more than predicted from the size distribution of the replicated crystals. From one halo display to the other, the ratio of observed/predicted broadening is erratic, suggesting size-dependent collection efficiency in the sampling. This would imply that, for South Pole conditions, halo polarimetry (or even photometry) is a more reliable method for crystal size determination than actual sampling. It also implies that shapes of the sampled crystals need not necessarily be representative for the shapes of the halo-making crystals in the swarm. Our previous hypothesis [Appl. Opt. 33, 4569 (1994)], that a spread of interfacial angles is the dominating cause of halo broadening, has proved untenable.

© 2003 Optical Society of America

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References

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  1. G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
    [CrossRef] [PubMed]
  2. G. P. Können, J. Tinbergen, “Polarimetry of a 22° halo,” Appl. Opt. 30, 3382–3400 (1992).
    [CrossRef]
  3. W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  4. B. J. Mason, The Physics of Clouds (Clarendon, Oxford, UK, 1971), pp. 567–580.
  5. I. Langmuir, “The production of rain by a chain reaction in cumulus clouds at temperature above freezing,” J. Met. 5, 175–192 (1948).
    [CrossRef]
  6. J. Hallet, “Faceted snow crystals,” J. Opt. Soc. Am. A 4, 581–588 (1987), Plate I.
    [CrossRef]
  7. G. P. Können, J. Tinbergen, “Polarization structures in parhelic circles and in 120° parhelia,” Appl. Opt. 37, 1457–1464 (1998).
    [CrossRef]
  8. A. B. Fraser, “What size of ice crystals causes halos?” J. Opt. Soc. Am. 69, 1112–1118 (1979).
    [CrossRef]
  9. W. Tape, “Some crystals that made halos,” J. Opt. Soc. Am. 73, 1641–1645 (1983).
    [CrossRef]

1998 (1)

1994 (1)

1992 (1)

1987 (1)

1983 (1)

1979 (1)

1948 (1)

I. Langmuir, “The production of rain by a chain reaction in cumulus clouds at temperature above freezing,” J. Met. 5, 175–192 (1948).
[CrossRef]

Fraser, A. B.

Hallet, J.

Können, G. P.

Langmuir, I.

I. Langmuir, “The production of rain by a chain reaction in cumulus clouds at temperature above freezing,” J. Met. 5, 175–192 (1948).
[CrossRef]

Mason, B. J.

B. J. Mason, The Physics of Clouds (Clarendon, Oxford, UK, 1971), pp. 567–580.

Muller, S. H.

Tape, W.

W. Tape, “Some crystals that made halos,” J. Opt. Soc. Am. 73, 1641–1645 (1983).
[CrossRef]

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

Tinbergen, J.

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Figures (9)

Fig. 1
Fig. 1

Origin of the birefringence peak in parhelion polarization. Because of the polarization dependence of the refractive index of ice, the parhelion consists of two orthogonally polarized components, which are mutually shifted. For the 22° parhelion, the shift is ∼0.1° in azimuth, and the component with horizontal polarization is closest to the Sun. Its radiance is denoted by I //; that of the other component, by I . Q = I // - I is the second Stokes parameter. The solid curves give the two radiances I //, I and the Stokes parameter Q of the parhelion for the idealized situation of a point source located at infinity, perfect crystal orientation, no variability in interfacial crystal angles, and geometrical optics. The dashed curves show the broadening in a realistic situation. Among the broadening factors, only diffraction is strongly wavelength dependent.

Fig. 2
Fig. 2

Petri-dish crystal samplings, acrylic-spray crystal replicatings, polarimetric observations (pol.), and photographing sequences during the four 1997 South Pole displays. The time is South Pole local time (UT + 12 h).

Fig. 3
Fig. 3

Size distributions of the replicated crystals during the four 1997 South Pole displays. Only plate crystals were counted. The numbering of the 16 Dec displays is according to Fig. 2. The gamma distribution fit to the 1990 observation1 is included as a solid curve. All distributions are normalized according to the number density in the acrylic-spray replicas.

Fig. 4
Fig. 4

Similar to Fig. 3; logarithmic scale for number density.

Fig. 5
Fig. 5

Observed halo anomaly in the second Stokes parameter Q in the scan through the 16 Dec II parhelion. Arbitrary units. The intrinsic degrees of parhelion polarization at the maximum of the peaks are 10% and 16% for 615 and 435 nm, respectively. From the observational data the halo birefringence peak Q birefr can be calculated.1 The width of the birefringence peak relates to the size of the halo-generating crystals. Although in case of the 16 Dec II parhelion the shape of the anomaly in Q is close to that of Q birefr, an accurate determination of the width θ1/2(obs) of the birefringence peak (Table 1) should be based on Q birefr rather than straightforwardly on the shape of the halo anomaly in Q shown here.

Fig. 6
Fig. 6

Calculated half-width at half-maximum (HWHM) of the parhelion birefringence peaks θ1/2(diff), as obtained from direct integration of the Fraunhofer diffraction function with the observed slit-width distribution in the plate crystals from the replica samples (Fig. 4). Precise values of θ1/2(diff) are in Table 1.

Fig. 7
Fig. 7

Observed HWHM of the parhelion birefringence peaks θ1/2(obs). Note the difference in vertical scale with respect to Fig. 6 and the change in order of, e.g., the 16 Dec I and II displays with respect to Fig. 6. Precise values of θ1/2(obs) are in Table 1.

Fig. 8
Fig. 8

HWHM of the birefringence peaks at λ = 615 nm. θ1/2 (diff) is the value calculated from direct integration of the Fraunhofer diffraction function with the observed slit-width in the plate crystals from the replica samples; θ1/2(obs) is the observation from the birefringence peak. The 1990 observation is also included after reduction of θ1/2(obs) from λ = 590 nm to 615 nm. Precise values of θ1/2(diff) and θ1/2(obs) are in Table 1. Line A denotes the expected equality of θ1/2(diff) and θ1/2(obs). Line B is the observed relation, obtained from a least-squares fit; the correlation coefficient ρ = -0.3.

Fig. 9
Fig. 9

Modification of a size distribution by the collection efficiency of the collector, according to Eqs. (5)–(8). Assumed is an exponential size distribution with average size 45 μm in the crystal cloud (bold, dashed). The bold solid curve is the size distribution of the crystals received by the collector assuming a wind speed of 4 m/s. The thin dashed curves are the actual observed crystal size distributions in our samplings (the curves of Fig. 4).

Tables (1)

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Table 1 Half-Width at Half-Maximum Values θ1/2 of the Birefringence Peaks for the Two Wavelengths of Observationa

Equations (8)

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Qbirefr  gθ-θh,
gθ  i di4sin xi/xi2NaiΔa,x=πaθ/λ, a=0.38d,
θ1/22obs=θ1/22diff+θ1/22others.
θ1/2diff  λ/aw,
Ecol=CE,
EL=0 if K1/12,EL=1/1+0.5/K2 if K>1/12,
K=29 ρνr2/Rμ,
K=32νd2,

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