How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation

doi:10.1242/JEB.204.17.2933

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Year: 2001

How the clear-sky angle of polarization pattern continues

underneath clouds: full-sky measurements and implications for

animal orientation

Pomozi, I; Horváth, G; Wehner, R

Pomozi, I; Horváth, G; Wehner, R. How the clear-sky angle of polarization pattern continues underneath clouds:

full-sky measurements and implications for animal orientation. J. Exp. Biol. 2001, 204(Pt 17):2933-42.

Postprint available at:

http://www.zora.unizh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.

http://www.zora.unizh.ch

Originally published at:

J. Exp. Biol. 2001, 204(Pt 17):2933-42

Pomozi, I; Horváth, G; Wehner, R. How the clear-sky angle of polarization pattern continues underneath clouds:

full-sky measurements and implications for animal orientation. J. Exp. Biol. 2001, 204(Pt 17):2933-42.

Postprint available at:

http://www.zora.unizh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.

http://www.zora.unizh.ch

Originally published at:

J. Exp. Biol. 2001, 204(Pt 17):2933-42

How the clear-sky angle of polarization pattern continues

underneath clouds: full-sky measurements and implications for

animal orientation

Abstract

One of the biologically most important parameters of the cloudy sky is the proportion P of the celestial

polarization pattern available for use in animal navigation. We evaluated this parameter by measuring

the polarization patterns of clear and cloudy skies using 180 degrees (full-sky) imaging polarimetry in

the red (650 nm), green (550 nm) and blue (450 nm) ranges of the spectrum under clear and partly

cloudy conditions. The resulting data were compared with the corresponding celestial polarization

patterns calculated using the single-scattering Rayleigh model. We show convincingly that the pattern of

the angle of polarization (e-vectors) in a clear sky continues underneath clouds if regions of the clouds

and parts of the airspace between the clouds and the earth surface (being shady at the position of the

observer) are directly lit by the sun. The scattering and polarization of direct sunlight on the cloud

particles and in the air columns underneath the clouds result in the same e-vector pattern as that present

in clear sky. This phenomenon can be exploited for animal navigation if the degree of polarization is

higher than the perceptual threshold of the visual system, because the angle rather than the degree of

polarization is the most important optical cue used in the polarization compass. Hence, the clouds

reduce the extent of sky polarization pattern that is useful for animal orientation much less than has

hitherto been assumed. We further demonstrate quantitatively that the shorter the wavelength, the

greater the proportion of celestial polarization that can be used by animals under cloudy-sky conditions.

As has already been suggested by others, this phenomenon may solve the ultraviolet paradox of

polarization vision in insects such as hymenopterans and dipterans. The present study extends previous

findings by using the technique of 180 degrees imaging polarimetry to measure and analyse celestial

polarization patterns.

Many animals use the sun as a compass. If the sun is not

visible (hidden by clouds or vegetation or landmarks, or

positioned below the horizon), several species are able to orient

by means of the extensive celestial polarization pattern either

in the ultraviolet or in the visible (blue or green) range of the

spectrum (Wehner, 1976; Wehner, 1991). For clear skies, this

pattern is quite regular and depends strongly on the celestial

position of the sun. If the sky is partly clouded, its polarization

pattern is rather complex because the polarization of the blue

sky is disturbed by the clouds. Existing measurements of the

polarization characteristics of partly clouded skies have not

been carried out under wide-ﬁeld conditions and, hence, are

inadequate if one wishes to deduce biologically relevant

information. Here, we use a 180° (full-sky) imaging

polarimeter to determine the pattern of polarization of cloudy

skies under clear and partly cloudy sky conditions in the visible

range of the spectrum.

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 5–10%

(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 animal’s 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),

2933

The Journal of Experimental Biology 204, 2933–2942 (2001)

Printed in Great Britain © The Company of Biologists Limited 2001

JEB3412

One of the biologically most important parameters of

the cloudy sky is the proportion P of the celestial

polarization pattern available for use in animal

navigation. We evaluated this parameter by measuring the

polarization patterns of clear and cloudy skies using 180°

(full-sky) imaging polarimetry in the red (650nm), green

(550nm) and blue (450nm) ranges of the spectrum under

clear and partly cloudy conditions. The resulting data

were compared with the corresponding celestial

polarization patterns calculated using the single-scattering

Rayleigh model. We show convincingly that the pattern of

the angle of polarization (e-vectors) in a clear sky

continues underneath clouds if regions of the clouds and

parts of the airspace between the clouds and the earth

surface (being shady at the position of the observer) are

directly lit by the sun. The scattering and polarization of

direct sunlight on the cloud particles and in the air

columns underneath the clouds result in the same e-vector

pattern as that present in clear sky. This phenomenon can

be exploited for animal navigation if the degree of

polarization is higher than the perceptual threshold of the

visual system, because the angle rather than the degree of

polarization is the most important optical cue used in the

polarization compass. Hence, the clouds reduce the extent

of sky polarization pattern that is useful for animal

orientation much less than has hitherto been assumed. We

further demonstrate quantitatively that the shorter the

wavelength, the greater the proportion of celestial

polarization that can be used by animals under cloudy-sky

conditions. As has already been suggested by others, this

phenomenon may solve the ultraviolet paradox of

polarization vision in insects such as hymenopterans and

dipterans. The present study extends previous ﬁndings

by using the technique of 180° imaging polarimetry to

measure and analyse celestial polarization patterns.

Key words: polarization vision, orientation, polarization compass,

skylight polarization, cloud, cloudy sky, full-sky imaging

polarimetry, ultraviolet vision.

Summary

Introduction

How the clear-sky angle of polarization pattern continues underneath clouds:

full-sky measurements and implications for animal orientation

István Pomozi

1

, Gábor Horváth

1,

* and Rüdiger Wehner

2

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@arago.elte.hu)

Accepted 8 June 2001

2934

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 earth’s

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 7–8min, 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 70–80min or

700–800min, 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 (330–390nm) 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.

Materials and methods

Polarimetric measurements

Our clear-sky polarimetric measurements were performed in

the Tunisian Chott el Djerid (33°52′ N, 8°22′ E), 10km from

Kriz, Tunisia, on 26 August 1999, when the sky was clear

throughout the day. At the measurement site, sunrise and

sunset was at 06:00h and 18:55h (local summer time =

UTC+1, where UTC is universal time code), respectively. We

measured the polarization pattern of the entire clear sky hourly

after sunrise.

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 θ

s

was approximately the same as those in the clear skies

I. POMOZI, G. HORVÁTH AND R. WEHNER

2935Polarization of cloudy skies and animal navigation

shown in Fig. 1A–C, Fig. 2A–C. To facilitate visual

comparison, the colour photographs and the patterns of the

degree and angle of polarization of the cloudy sky with a given

θ

s

of the sun were appropriately rotated until the solar azimuth

angle coincided with that in the corresponding clear sky.

Measurement of the celestial polarization pattern using full-

sky imaging polarimetry

The full-sky imaging polarimetric technique used here is

similar to the method of Voss and Liu (Voss and Liu, 1997).

An angle of view of 180° was ensured by using a ﬁsheye lens

(Nikon-Nikkor, F=2.8, focal length 8mm) including a built-in

rotating disc mounted with three broad-band (275–750nm)

neutral density (grey) linear polarization ﬁlters (HNP′B,

Polaroid Corporation, Polaroid Europe Ltd, London, UK) with

three different polarization axes (0°, 45° and 90° measured

from the radius of the disc). The detector was a photoemulsion

in a photographic camera (Nikon F801): Fujichrome Sensia II

100 ASA colour reversal ﬁlm; the maxima and half-bandwidths

of its spectral sensitivity curves were λ

red

=650±30nm,

λ

green

=550±30nm, λ

blue

=450±50nm. From a given sky, three

photographs were taken for the three different alignments of

the transmission axis of the polarizers on the built-in rotating

disc. The camera was set up on a tripod such that its axis

passing through the view-ﬁnder pointed northwards and the

optical axis of the ﬁsheye lens was vertical.

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 scanner’s 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 θ and the azimuth angle ϕ 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 δ is expressed in Equation 1 and

Equation 2 as:

δ=δ

max

sin

2

γ/(1+cos

2

γ), (1)

cosγ=sinθ

s

sinθcosψ+cosθ

s

cosθ, (2)

where γ is the angular distance between the observed celestial

point and the sun, θ

s

is the solar zenith angle and θ and ψ are

the angular distances of the observed point from the zenith and

the solar meridian, respectively. For a given θ

s

, δ

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 I

r

, I

g

, I

b

of

every pixel of the picture measured in the red, green and blue

spectral ranges, respectively, were compared with each other.

If the differences ∆I

b−r

=|I

b

–I

r

| and ∆I

b−g

=|I

b

–I

g

| were smaller

than ε=cI

b

(where c is a constant), it was assumed that the given

How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation

Summary (1 min read)

Introduction

2936 I. POMOZI, G. HORVÁTH AND R. WEHNER

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