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: http://www.adass.org/adass/proceedings/adass03/P5-6/
Дата изменения: Sat Aug 14 04:05:22 2004 Дата индексирования: Tue Oct 2 04:34:04 2012 Кодировка: Поисковые слова: comet tail |
Shadow bands are natural phenomena that appear just before and just after totality during solar eclipses. They arise from the superposition of atmospheric speckle patterns from elements of an incoherent, extended line source (the remaining visible crescent of the Sun). They are linear patterns moving across the ground with typical speeds of a few m/s in the direction perpendicular to their elongation. They align parallel to the tangent to the centre of the solar crescent (Marschall et al., 1984). It has been observed that shadow band spacing decreases and their contrast increases as totality approaches (Codona, 1986; Jones, 1996, 1999).
Shadow bands were recorded during total eclipse of 4 December 2002 in Botswana. The imaging system consisted of a white, diffusely - reflective screen (surface was perpendicular to the line of sight to the eclipsed Sun) and a digital video recorder on a tripod in front of it. For the purpose of observation the aperture was locked fully open, exposure time was 1 ms (so that the phenomenon was "frozen"). The recorder was capturing 25 non-interlaced frames per second.
The bands were also observed visually. They were weak and disorganized and resembled the surface of boiling water rather than linear patterns.
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where x, y are the coordinates of a point in the object plane, and u, v are the
coordinates of the same point in the image plane. The inverse transformation,
(u, v) (x, y), was applied to every image using the reciprocal
formulae. The eight parameters
were found using known positions of the four corners of
the screen before and after the transformation. This meant solving a system of
eight linear equations with eight unknowns. Bi-cubic interpolation was used for
image scaling.
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Two batches of 1480 images (59.2 s) before and after totality were used for further analysis. Operations that could be used to detect shadow bands are:
Cross-correlation for different pairs of raw (without contrast enhancement) images revealed nothing but a peak at (0, 0) coordinates. This means that structure of the screen (hardly visible with an un-aided eye) is more pronounced than the shadow bands (meaning zero-shift between the images). Besides that, 25 fps means 40 ms between frames while coherence time (t0) for the atmosphere is usually not more than 10 ms (Monnier, 2003). Shadow bands change their shape too much from one image to another for the cross-correlation to detect them; the temporal-spatial approach was not useful in practice. The theory describing shadow bands is mostly based in the spatial domain, so the use of spatial approach in the analysis is more relevant.
Power spectral density functions were more likely to reveal shadow bands as they are calculated in the spatial domain so that low fps limit of the digital video recorder played no role here. We recorded ambient noise at a low light level with the recorder (same settings as on the observation day), and calculated averaged and normalized psds for the resulting ensemble of images. The psd of an image is a two-dimensional function but for the purpose of this study a one-dimensional psd was calculated in order to make comparisons with Codona's plots. Power spectra for the pixel vectors at a right angle to the tangent to the crescent were calculated separately, added and averaged to produce a psd(k) plot. The psd of the noise was then subtracted from each psd of shadow bands. 60 such functions were computed before and after totality, setting the interval between measurements to 1 s. Smoothing with a rectangular window, 4 pixels wide, was used. The cut-off frequency was imposed by the Nyquist theorem. In some cases noise cancelled the signal in the very low frequency range, but that part of the plots was not significant for further analysis.
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The qualitative resemblance between our power spectral density functions and the plot resulting from theoretical assumptions in Codona's paper is striking. According to Codona, shadow bands' psds display three characteristic scales. First characteristic scale is controlled by the geometry of the crescent and corresponds to the low-frequency peak in the spectrum. The next scale relates to the first minimum in the plots and is due to the first null of the source's spectrum. Third scale corresponds to the fast oscillating term in the analytic expression, called the "Fresnel filter" (starting at the second minimum in the plots). Which of them will be the dominant shadow band scale visible to the human eye depends on the distance of the atmospheric scattering layer from the observer and the time to totality. Codona derived formulae relating the height of the scattering layer, z, to the dominant spatial frequency of a psd plot. The derivation of the values of z is the goal of the next stage of the shadow bands' data analysis.
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Lindler, D., Bohlin, R., Hartig, G., Keyes, C., 1993. FOS Instrument Science Report CAL/FOS-088
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Monnier, J. D., 2003. Reports on Progress in Physics, 66, 789