How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation
1 Department of Biological Physics, Eötvös University, H-1117 Budapest, Pázmány sétány 1, Hungary,
2 Institut für Zoologie, Universität Zürich, CH-8057 Zürich, Winterthurerstrasse 190, Switzerland
*Author for correspondence (e-mail: gh{at}arago.elte.hu)
Accepted June 8, 2001
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Summary |
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Key words: polarization vision, orientation, polarization compass, skylight polarization, cloud, cloudy sky, full-sky imaging polarimetry, ultraviolet vision.
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Introduction |
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Many animals can infer the position of the sun from the distribution of the angle of polarization obtained from restricted regions of clear sky. Bees, for example, which often fly with most of their field of view obscured by vegetation, can orient correctly even if only spots of blue skylight are visible. Under certain conditions, skylight windows as small as 1° in diameter suffice (Edrich and von Helversen, 1976). Depending on the species, polarized light stimulating exclusively the ultraviolet, blue or green receptors located within specialized dorsal rim areas of the eye is sufficient for polarized light navigation. The required degree of polarization for successful navigation within a patch of skylight can be as low as 510% (bees, Wehner, 1991; crickets, Labhart, 1996).
One of the biologically most important parameters of a cloudy sky is the proportion P of the celestial polarization pattern that is available to the animals polarization compass. This parameter of clear or cloudy skies has largely been ignored in measurements of skylight polarization. Exceptions are the studies of Brines and Gould (Brines and Gould, 1982), who made point-source measurements, and of Labhart (Labhart, 1999), who used an opto-electronic model to draw qualitative conclusions on the important role of P in animal orientation.
It is a well-known phenomenon that distant objects near the horizon (e.g. forests or mountains) appear blueish in colour because of Rayleigh scattering of light between the observer and these distant objects (Können, 1985; Coulson, 1988). The same phenomenon occurs in the air column underneath clouds. If part of this column is lit directly by the sun, the distribution of the angle of polarization of scattered light originating from the sunlit part of the column is the same as that of the clear sky. It is less well known that the scattering of direct sunlight on the cloud particles results in the same e-vector pattern as that of the blue sky (Können, 1985). As a result of these scattering phenomena, the angle of polarization of the sky (the most important optical cue for the animal polarization compass if the sun is not visible) underneath certain clouds approximates that of the clear sky. The celestial e-vector pattern continues underneath clouds under certain atmospheric conditions, such as when the air columns beneath clouds or parts of clouds are lit by direct sunlight: (i) obliquely from above (for smaller solar zenith angles), (ii) from the side (as with white cumuli) or (iii) from below (as sometimes occurs at dawn and dusk). The implication here is that the earths surface has to be in sunlight, but not at the position of the observer. Below, we refer to these illumination conditions simply as directly lit by the sun. Apart from heavy overcast skies with multiple cloud layers, such conditions occur frequently if the sky is partly cloudy.
Because of the lack of appropriate techniques, satisfactory measurements of the e-vector pattern in cloudy skies are not yet available. Using a point-source scanning polarimeter, Brines and Gould (Brines and Gould, 1982) measured points at every 5° elevation and azimuth angles within a half-hemisphere of the sky in 78min, during which time the sun moved approximately 2° along its arc and clouds near the zenith might have been displaced considerably. Certain unavoidable errors were a consequence of their rapid measurement process, such as inaccuracies attendant upon setting the axes of the instrument. To enhance the spatial resolution of their samples by one or two orders of magnitude necessary to obtain the polarization pattern of the entire sky, their measurements would have required 7080min or 700800min, respectively, a period during which the celestial polarization pattern would change considerably as a result of the rotation of the earth (it takes 80min for the sun to move by 20°).
The method used by Brines and Gould (Brines and Gould, 1982) sequential measurements with a point-source scanning polarimeter is inappropriate if the recording period is of sufficient length for the optical characteristics of the sky to change considerably. This situation will occur if the sky is cloudy, because clouds move. The displacement of clouds during such measurements will inevitably introduce so-called motion artefacts to the measured values of the degree and angle of polarization of skylight, reducing their accuracy. It is clear that the polarization pattern of the whole sky cannot reliably be measured using such a time-consuming method. In contrast, an imaging polarimeter can measure reliably (without motion artefacts) the sky polarization pattern instantaneously for a huge number of celestial points, even in the presence of rapid temporal changes (e.g. displacements of clouds).
Here, we have designed and used a full-sky imaging polarimeter with which the polarization pattern of the entire sky could be measured instantaneously and accurately under diverse atmospheric conditions. Our goal was to measure and compare quantitatively the sky polarization patterns of cloudy and clear skies for different solar positions. These patterns were compared with the corresponding celestial polarization patterns calculated on the basis of the single-scattering Rayleigh model. We show firstly that the clear-sky angle of polarization pattern continues underneath clouds under certain atmospheric conditions. Secondly, we find that the shorter the wavelength in the visible range of the spectrum, the greater is the proportion of the celestial polarization pattern available underneath the clouds for animal navigation. Both results thus extend the work of Brines and Gould (Brines and Gould, 1982).
The ultraviolet-sensitivity (330390nm) of the polarization-sensitive area (POL area) in the dorsal eye region of hymenopterans and dipterans (Labhart and Meyer, 1999) is rather surprising because the degree of polarization of scattered skylight is generally lowest in the ultraviolet spectral region for clear skies; furthermore, the intensity of skylight is maximal in the blue range of the spectrum rather than the ultraviolet (Können, 1985; Coulson, 1988). Hence, the use of ultraviolet, the worst wavelength in this regard, is puzzling and here we term it the ultraviolet paradox of polarization vision. If, however, the wavelength-dependent effect observed by us continues into the ultraviolet range of the spectrum, this phenomenon may solve the ultraviolet paradox, as suggested by Brines and Gould (Brines and Gould, 1982), although they were not able to determine quantitatively the values of P.
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Materials and methods |
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The cloudy-sky polarimetric measurements were carried out at different places and times in Tunisia from the end of August to the beginning of September 1999. From the cloudy-sky polarization patterns measured using full-sky imaging polarimetry, patterns were selected in which the solar zenith angle s was approximately the same as those in the clear skies shown in Fig.1AC, Fig.2AC. To facilitate visual comparison, the colour photographs and the patterns of the degree and angle of polarization of the cloudy sky with a given
s of the sun were appropriately rotated until the solar azimuth angle coincided with that in the corresponding clear sky.
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Using a personal computer, after eight-bit (true colour) digitization (using a Hewlett Packard ScanJet 6100C) and evaluation of the three developed colour pictures for a given sky, the patterns of brightness, and the degree and angle of polarization of skylight, were determined and visualized as high-resolution, colour-coded, two-dimensional circular maps. Each map contains approximately 543000 pixels, i.e. represents approximately 543000 measured numerical values in a given region of the spectrum. These patterns were obtained in the red, green and blue spectral ranges, in which the three colour-sensitive layers of the photoemulsion used have maximal sensitivity. The red, green and blue spectral ranges were obtained by using the scanners digital image-processing program to separate the colour channels in the digitized images. This computerized evaluation of the three digitized photographs of a given sky is very similar to the videopolarimetry technique of Horváth and Varjú (Horváth and Varjú, 1997).
Our imaging polarimeter was calibrated as follows. The colour reversal films were all developed in the same professional photographic laboratory (in Budapest) using the same automatically controlled method. During evaluation of the recordings to obtain the brightness, degree and angle of polarization of skylight, the following characteristics of the recording and digitizing system were taken into consideration: (i) the measured Mueller matrix of the fisheye lens as a function of the angle of incidence with respect to the optical axis; (ii) the measured angular distortion of the fisheye lens versus the angle of incidence; (iii) the decrease in light intensity imaged on the photoemulsion because of the decrease in the effective aperture with increasing angle of incidence; (iv) the colour density curves of the colour reversal films (used as detectors) provided by the manufacturer; (v) the measured brightness and contrast transfer function of the scanner used for digitization of the colour slides of the sky. Characteristics (i-v) describe how the angular imaging, intensity, polarization and spectral composition of the incident light are influenced by the optics and detector (photoemulsion) of the polarimeter and by the scanner (digitization). Although the responses of both the photographic film and scanner were non-linear, this was taken into account, because the transfer function between the digital brightness values and the density values of the photoemulsion was measured, and the incident light intensity was calculated from this using the density-exposure characteristic curves of the film (provided by the manufacturer). Further details of the calibration of our polarimeter and the evaluation process have been published elsewhere (Gál et al., 2001).
Polarization calculations using the single-scattering Rayleigh model
The three-dimensional celestial hemisphere was represented in two dimensions by a polar-coordinate system, where the zenith angle and the azimuth angle
from West are measured radially and tangentially, respectively. In this two-dimensional coordinate system, the zenith is at the origin and the horizon corresponds to the outermost circle.
The theoretical patterns of the degree and angle of polarization of skylight were calculated using the single-scattering Rayleigh model (Coulson, 1988). In the single-scattering Rayleigh atmosphere, the degree of linear polarization of skylight is expressed in Equation 1 and Equation 2 as:
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where is the angular distance between the observed celestial point and the sun,
s is the solar zenith angle and
and
are the angular distances of the observed point from the zenith and the solar meridian, respectively. For a given
s,
max was determined from the patterns of the degree of polarization of skylight measured by full-sky imaging polarimetry. In the single-scattering Rayleigh atmosphere, the direction (or angle) of polarization is perpendicular to the plane of scattering determined by the observer, the celestial point observed and the sun. In the single-scattering Rayleigh model, the polarization of skylight is independent of the wavelength.
Algorithmic recognition of clouds and overexposed areas in the sky
Clouds were recognized in the digitized pictures of the sky using the following algorithm. The light intensities Ir, Ig, Ib of every pixel of the picture measured in the red, green and blue spectral ranges, respectively, were compared with each other. If the differences Ib-r=|IbIr| and
Ib-g=|IbIg| were smaller than
=cIb (where c is a constant), it was assumed that the given pixel belonged to a cloud, otherwise it was attributed to the clear blue sky. The essence of this algorithm is that clouds are generally colourless (ranging from dark grey to bright white) irrespective of their brightness and position in the sky, i.e. the pixels of clouds possess approximately the same light intensities in all three (red, green, blue) spectral ranges.
is the width of the narrow interval where the differences between Ir, Ig and Ib of a given pixel fall if the pixel is colourless enough and thus is detected as cloud.
is proportional to the brightness Ib measured in the blue range of the spectrum because of the blueness of scattered skylight. By setting an appropriate value of the constant c, we could reliably recognize clouds in the sky. Around the sun, the photoemulsion inevitably became overexposed. These colourless, white regions were recognized in the evaluation process by the same algorithm that recognized clouds.
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Results |
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Since there was no qualitative difference between the sky polarization patterns measured in the red, green and blue regions of the spectrum, we present only the celestial polarization patterns measured in the blue range of the spectrum. In general, the longer the wavelength, the higher the degree of polarization of skylight. This decrease in the degree of polarization towards shorter wavelengths is in agreement with the results of earlier point-source polarimetric measurements (Coulson, 1988) and is due mainly to the randomizing effects of multiple scattering. The degree of polarization resulting from a single scattering event is essentially independent of the wavelength. At shorter wavelengths, multiple scattering is stronger because of the stronger scattering (Rayleighs law).
Comparison of the measured (Fig.1B,C, Fig.2B,C) and theoretical (Fig.1D,E, Fig.2D,E) patterns indicates that, apart from regions near the sun and anti-sun, the simple single-scattering Rayleigh theory describes the gross characteristics of the sky polarization patterns relatively well: (i) the degree of skylight polarization first increases with increasing angular distance from the sun, reaching its maximum at approximately 90° from the sun, and then decreases towards the anti-sun, and (ii) the e-vector of skylight is approximately perpendicular to the scattering plane determined by the position of the observer, the sun and the point observed.
The most striking differences between the actual and the theoretical patterns are the consequences of the neutral (unpolarized) points. We can see that, in the maps, the long axis of the figure-of-eight-shaped blue-green region is shorter in the actual patterns than in the Rayleigh patterns. The Arago and Babinet neutral points are positioned at the tips of this region where positive polarization (direction of polarization more-or-less normal to the scattering plane, 45° <
135° with respect to the local meridian, shaded green and blue in Fig.1C,E, Fig.2C,E) switches to negative polarization (direction of polarization more-or-less parallel to the scattering plane, -45°
+45°, shaded yellow and red). In the single-scattering Rayleigh model, such neutral points do not occur, or rather coincide with the anti-sun and the sun. Because of these neutral points, the isolines belonging to given values of the degree and angle of polarization differ more or less from each other in the real and the Rayleigh sky. Note, however, that since in the vicinity of these neutral points the degrees of polarization are smaller than the perceptual threshold
min=510% observed in animals, the neutral points of skylight polarization are biologically irrelevant.
Fig.1G,H and Fig.2G,H represent the patterns of the degree and angle of polarization of cloudy skies shown in Fig.1F and Fig.2F, respectively, measured again in the blue (450nm) spectral range. To ease comparison, we have chosen approximately the same solar zenith angles s as those represented for clear skies in Fig.1AC and Fig.2AC. The most striking observation from Fig.1G and Fig.2G is that the degree of polarization is strongly reduced in those regions of the sky in which clouds appear. The clouds largely distort the normal distribution of the degree of polarization as it occurs in the clear sky. They produce discontinuities and holes of very low degrees of polarization in the
pattern of the blue sky. This observation is in accordance with previous results (Brines and Gould, 1982; Können, 1985).
However, in many cases, the patterns of the angle of polarization suffer only minor distortions when clouds are present. Compare, for example, the e-vector distributions in Fig.1C and Fig.2C with those in Fig.1H and Fig.2H. Depending on the type, thickness and height of the clouds and on the visibility of the sun (whether it is visible or hidden by clouds), the pattern of the angle of polarization that is characteristic for a clear sky largely continues underneath the clouds (e.g. Fig.1H, rows 15 and Fig.2H, rows 27). In certain cases, especially if the sun is close to the zenith or if it is occluded by clouds, the e-vector pattern in a cloudy sky is completely distorted (e.g. Fig.1H, rows 6,7 and Fig.2H, row 1).
To investigate the extent to which an insects e-vector compass could utilise the partially disturbed e-vector patterns in cloudy skies, we should ideally feed data recorded polarimetrically from cloudy skies into the algorithmic properties of the insects polarization-sensitive interneurons. However, the latter are not fully known. We do know from electrophysiological recordings from the polarization-sensitive (POL) interneurons in the crickets (Gryllus campestris) medulla that these neurons respond reliably to e-vectors if the degree of polarization is greater than 5% and that the standard deviation for the reliability of the e-vector measurements of these neurons is approximately ±6.5° for 5%
10% and ±4° for
> 10% (Labhart, 1988; Labhart, 1996).
If is lower than the threshold value
threshold=5%, crickets cannot perceive the skylight polarization. The polarization-sensitive visual system of crickets determines the direction of the sun from the distribution of the angle of polarization of the clear sky (
clear sky). If, in a cloudy region of the sky, the angle of polarization
cloud differs considerably from
clear sky, the use of the
cloud value will reduce the accuracy of the determination of the suns direction if
>
threshold. Crickets are not confronted with such a reduction in accuracy if the difference between
clear sky and
cloud is below a certain threshold
threshold, which is not smaller than the reliability (±46.5°) of the e-vector measurements of their POL neurons. To summarise: regions of the sky that provide reliable compass information are characterized in Equation 3 by:
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The parameter P gives the proportion of the skylight pattern that can be used by the insect for reliable e-vector orientation. Fig.3 presents two examples derived in the way described above from row 1 of Fig.1A and F. They demonstrate that surprisingly large parts of a cloudy sky can be used by the insect for compass orientation. Increasing the value of threshold and/or decreasing the value of
threshold will decrease P. Since for Fig.3 we used
threshold=6.5° instead of 4°, the numerical values of P will be slight overestimates, at least for the vision of the cricket.
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Discussion |
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In contrast to ice-clouds, water-clouds are strongly polarized not only at 90° but also at approximately 145° from the sun, where the degree of polarization can reach 60%, i.e. potentially higher values than in the background skylight (see pp. 4243 in Können, 1985). At 145° from the sun, water-clouds are markedly brighter than at other regions in the sky.
If the clouds are not thin and/or parts of them are not directly illuminated by the sun, their polarization characteristics differ from those discussed above. Under a heavily overcast sky, when the cloud layer is several kilometres thick, the illumination comes more or less from all directions and, hence, the degree of polarization of the clouds is strongly reduced (see pp. 4243 in Können, 1985). More light will come from the zenith, where the clouds look thinnest, than from the horizon, meaning that the cloud light will be horizontally polarized. The degree of polarization of this cloud light reaches maximal values of 1020% just above the horizon and decreases rapidly towards the zenith, where it is 0%. A similar polarization pattern occurs in fog not illuminated by direct sunlight. When the clouds are very thick and the visibility is poor (e.g. during rain), the illumination is extremely diffuse, so that the degree of skylight polarization is reduced to zero.
Our full-sky imaging polarimetric measurements show that, even though in cloudy skies the degree of polarization may differ markedly from that in a cloudless sky, the angle of polarization does not. Consider, for example, rows 27 in Fig.2H: the majority of the sky was covered by thin strato-cumulus and stratus clouds, which considerably reduced the degree of polarization, but the pattern of the angles of polarization remained identical to that in the corresponding clear skies (rows 27 in Fig.2C). In rows 15 of Fig.1H thicker and lower clouds were present, which totally distorted the degree of celestial polarization, but left the e-vector patterns underneath the clouds (Fig.1C, rows 15) unaltered because parts of the clouds were illuminated directly by sunlight. In contrast, in rows 6 and 7 of Fig.1H and row 1 of Fig.2H the patterns of both the degree and angle of polarization were quite different from those of clear skies (Fig.1C, rows 6,7 and Fig.2C, row 1), because the sun was hidden by thicker clouds and the clouds were not directly lit by the sun.
On the basis of the physiological properties of polarization-sensitive interneurons recorded by Labhart (Labhart, 1996), we can compute the proportion of the celestial e-vector pattern, that even under cloudy skies, can be exploited for navigation (if compared with the full e-vector pattern under clear-sky conditions). Under all but the most extreme cloud-cover conditions, this proportion is rather large. Hence, clouds decrease the extent of skylight polarization useful for animal orientation much less than hitherto assumed.
Ultraviolet paradox of polarization vision
More than a quarter of a century ago, it was discovered that desert ants Cataglyphis bicolor (Duelli and Wehner, 1973) and honey bees Apis mellifera (von Helversen and Edrich, 1974) use ultraviolet receptors in a specialized dorsal rim area of the eye (Wehner, 1982; Wehner and Strasser, 1985) as polarization analyzers. It was subsequently found that, in other groups of insects, blue and green rather than ultraviolet receptors are used as polarization analyzers (for a review, see Labhart and Meyer, 1999). Why is there such diversity and why should ultraviolet receptors be favoured by long-distance navigators such as bees and ants? This appears surprising because, in scattered light, the degree of polarization is lowest in the ultraviolet range of the spectrum (Coulson, 1988; Horváth and Wehner, 1999).
von Frisch (von Frisch, 1965) assumed that the pattern of polarized light is most stable in the ultraviolet region, but there is no theoretical basis for this assumption. Mazokhin-Porshnyakov (Mazokhin-Porshnyakov, 1969) suggested that, by using the ultraviolet spectral range, insects ensured that they used polarized light in the sky rather than polarized reflections from the ground, which are richer in long-wavelength radiation. As we now know, however, it is only a tiny area of the eye of the ant or bee that is sensitive to polarized light, and this area is oriented towards the sky, so that the ambiguities envisaged by Mazokhin-Porshnyakov (Mazokhin-Porshnyakov, 1969) are unlikely to arise. In a theoretical approach, Seliger et al. (Seliger et al., 1994) surmised that polarization-sensitive photopigments that are most efficient under conditions of a high degree of skylight polarization should have their maximum sensitivity max at 450nm, whereas ultraviolet photopigments (
max=350nm) would maximize the signal-to-noise ratio under low degrees of polarization. Finally, Brines and Gould (Brines and Gould, 1982) suggested that polarization vision might have evolved during geological times when the earths atmosphere absorbed less ultraviolet radiation than it does today. They further assumed that ultraviolet receptors might have some advantages over long-wavelength receptors under certain atmospheric conditions such as cloudy skies. Wehner (Wehner, 1994) has given a detailed description of why e-vector patterns under clouds should be more reliable in the ultraviolet. In our present account, we find that the extension of the e-vector pattern of the blue sky into the areas of the sky covered by clouds is more useful to an e-vector compass when the observer responds to shorter wavelengths, as suggested by Brines and Gould (Brines and Gould, 1982).
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Acknowledgments |
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References |
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