J. theor. Biol. (1997) 184, 291–300

0022–5193/97/030291+10 $25.00/0/jt960245 7 1997 Academic Press Limited

How Celestial Polarization Changes due to Reflection from the

Deflector Panels Used in Deflector Loft and Mirror Experiments

Studying Avian Orientation

G H I P

Biophysics Group, Department of Atomic Physics, Lorand Eotvos University,H-1088 Budapest, Puskin u. 5–7., Hungary

(Received on 9 May 1996. Accepted on 2 September 1996)

In bird experiments which investigate the role of optical orientation cues associated with sunset it isa common method to reflect the celestial sunset factors by vertical deflector panels. Similar panels arealso used in the deflector loft of homing pigeons that rotate wind and light cues in a clockwise orcounterclockwise direction. The responses of test birds in these behavioural experiments often appearto be contradictory, because the deflectors produce a polarized optical stimulus that differs bothqualitatively and quantitatively from the natural skylight polarization. This paper gives a quantitativeaccount of the change of celestial polarization in such situations. The polarization pattern of skylightreflected from different vertical deflector panels is computed as a function of the elevation of the sunfrom the horizon. It is shown that the reflection polarization of a deflector panel composed of trans-parent glass with or without white or black background cannot simulate the distribution of polarizationof light in clear sky. On the other hand, if the deflector consists of a metal plate or metal-glass mirror,it can mimic the celestial polarization pattern well, because it changes the polarization of incident lightafter reflection only slightly.

7 1997 Academic Press Limited

Introduction

The deflector loft technique utilizes a pinwheelarrangement of stationary deflector panels that rotatewind and light cues in either a clockwise orcounterclockwise direction [Fig. 1(a) and (b)]. Suchdeflector lofts are commonly used in the behaviouralexperiments studying avian navigation (Schmidt-Koenig, 1979; Helbig, 1991). Homing pigeons(Columba livia) raised in normal lofts and thenhoused in deflector lofts exhibit a deflection in releasesite orientation which corresponds to the direction ofwind and light rotation in their deflector loft. This iscalled the deflector loft effect, which is frequentlyclaimed to support the olfactory theory of pigeonnavigation (e.g. Papi, 1991). However, Phillips &Waldvogel (1988) showed that the biased orientationof short-term deflector loft birds is due to thereflection of visual cues from the glass portions of the

deflector panels, rather than being the result ofrotation of wind-borne olfactory cues.

Similar to the deflector loft method, metal ormetal-glass mirrors (so-called front surface mirrors orback surface mirrors) are used in some behaviouralexperiments investigating the role of sunset cues (viewof setting sun, sunset glow, skylight polarization) inthe migratory orientation of birds (e.g. Kramer, 1950,1951; Kramer & St. Paul, 1950; Walcott & Michener,1971; Moore, 1982, 1985; Moore & Phillips, 1988;Phillips & Waldvogel, 1988; Sandberg, 1991). In theseexperiments the shift of the direction of sunset cueswith mirrors produces a predictable shift in themigrant’s orientation. This mirror technique was firstapplied by Santschi (1911), who studied the visualorientation of desert ants. These experiments andothers (e.g. Kreithen & Keeton, 1974; Delius et al.,1976; Helbig & Wiltschko, 1989; Able, 1989, 1993;Helbig, 1990; Able & Able, 1993) demonstrated that

H1

Polar-coordinate system ofreflection-polarization patterns

0H2

θs ϕθ

Sun

Zenith

R

Zenith

RH2

θ0

ϕ

H1

θs

Sun

Observer

Horizon

SolarmeridianCelestial

hemisphere

Verticaldeflectorpanel

Ray ofskylight

90°

Deflectorloft

Deflectorpanel

Deflectorloft

Deflec

tor p

anel

Light

Wind

(b)(a)

(c)

(d)

. ´ . 292

F. 1. (a) Top view of a common deflector loft used in the experiments studying the visual and olfactory navigation of birds. Themirroring portion of each deflector panels consists of glass plate (with a brighter or darker background) or glass–metal mirror. (b) Thedeflector panel rotates both wind and light in the same direction either clockwise or counterclockwise [after Phillips & Waldvogel (1988)].(c) The geometry in the calculation of polarization patterns of skylight reflected from a vertical deflector panel, which is perpendicularto the plane of the solar meridian. (d) The polar-coordinate system used to represent the reflected celestial polarization patterns.

293

the celestial polarization pattern is one of the mostimportant visual cues in the orientation of birds,whose visual system is sensitive to polarized light.

Considering the deflector loft and mirror exper-iments on avian navigation and polarization vision, itwould be important to know how the skylightpolarization changes due to reflection from thesedeflector panels and mirrors. Until now only Phillips& Waldvogel (1988) have made an attempt tomeasure the effect that a plexiglass deflector panel hason the distribution of celestial polarization cuesvisible in a deflector loft. Since the acceptance angleof the sensor of their polarimeter was too wide (about20°), they could not determine the fine details of thereflection-polarization pattern of the deflector panel.To quantify the influence which a deflector panel hason the celestial polarization, we calculate in this workthe polarization pattern of skylight reflected fromfour different deflector panels as a function of theelevation of the sun from the horizon. On the basis ofthese computations those deflector types can beselected, which modify the celestial polarizationpattern only slightly, that is, which can be usedwithout any ‘‘reflection-polarization complication’’ infuture experiments with birds.

Methods

Figure 1(c) shows the geometry in the calculationof the polarization patterns of skylight reflected froma vertical deflector panel, which is perpendicular tothe plane of the solar meridian. The two-dimensionalreflection-polarization patterns are represented in apolar-coordinate system [Fig. 1(d)], where the viewingangles u and 8 of the observer [see Fig. 1(c)] aremeasured radially and tangentially, respectively. Theregions of the patterns with different degrees anddirections of polarization are shaded by different greytones. Since the polarization characteristics of thedeflector depend only slightly on the colour of light,all reflection-polarization patterns are computed forwavelengths in the middle of the visible range of thespectrum.

The polarization of the sky is described by thesemi-empirical Rayleigh model, which can beconsidered as a relatively good approximation(Coulson, 1988; Horvath, 1995). Using the Fresnelformulae (Azzam & Bashara, 1989), the reflection-polarization characteristics of the investigated deflec-tor panels are derived in the Appendix. Four differentdeflector panel types are considered: (i) glass on awhite substrate, (ii) glass on a black background, (iii)metal mirror, (iv) metal-glass mirror. The complexindex of refraction of the aluminium mirror studied

is Nalu =0.57− i5.19, where i0z−1 is theimaginary unit; the metal-glass mirror investigatedconsists of a plate glass with a real refractive index ofng =1.5 underlied by a thin silver layer, the complexrefractive index of which is Ns =0.1194− i3.144(Landolt & Bornstein, 1983). The repolarization ofincoherent polarized skylight reflected from asilver-glass mirror and from a glass deflector panel iscalculated in Appendices A and B. In Appendix C thedegree of polarization of incoherent unpolarizedincident light is computed after reflection from thefollowing deflector panels: glass on a black back-ground, aluminium mirror, silver-glass mirror, glasson a white background.

Results

Figures 2 and 3 show the pattern of the degree d

and direction a of polarization of skylight reflectedfrom a vertical glass deflector panel calculated forfour different elevations of the sun. Figures 4 and 5represent the corresponding differences Dd= dsky −ddeflector and Da= asky − adeflector between the degrees anddirections of polarization of skylight and reflectedskylight. The latter two figures demonstrate well thatthe glass deflector panel has a considerable influenceon the celestial polarization pattern: Dd can be asgreat as −100% [Fig. 4(a–c)] and the value of Da canapproximate −90° [Fig. 5(a–c)].

On the one hand, in the reflected polarizationpattern there are several neutral points from whichunpolarized light is reflected [Fig. 2(a–c)]. Crossingthese neutral points the alignment of the reflectedE-vector changes from parallel to perpendicularrelative to the panel [Fig. 3(a–c)]. On the other hand,the glass panel possesses a characteristic anular zone,where the reflected skylight is totally polarized (blackhalf rings in Fig. 2) and its E-vector is parallel to theglass surface (black areas in Fig. 3). Although thedirection of polarization of the glass-reflected skylightis predominantly more or less parallel to the glassplate (darker areas in Fig. 3), there are also regionswhere the reflected E-vector is perpendicular to it(brighter areas in Fig. 3). One can see that thedifference Da= asky − adeflector is always negative alongthe entire deflector panel (Fig. 5), that is, the reflectedE-vector becomes more parallel to the panel than theE-vector of incident light. On the basis of Figs 4 and5 we can establish that a simple glass plate as anoptical cue-deflecting panel cannot mimic the realcelestial polarization pattern because of its strongreflection polarization.

Though we calculated the celestial reflection-polarization patterns only for such a vertical deflector

. ´ . 294

F. 2. The pattern of the degree of polarization d of skylight reflected from a vertical glass deflector panel calculated for four differentelevations us of the sun: (a) us =60°, (b) us =40°, (c) us =20°, (d) us =0° (sun on the horizon). The mirror image of the sun is representedby a dot. The different intervals of d (measured in %) are shaded by different grey tones: the darker the tone, the greater is d.

(a)

(c)

(b)

(d)

panel, which is perpendicular to the plane of the solarmeridian, this restriction does not concern at all ourconclusions. In the bird experiments also otheralignments of the deflectors and mirrors occur, but inthese cases, at a given elevation of the sun, thereflection-polarization pattern visible in the panel canbe obtained by a corresponding rotation of thepattern computed for the panel perpendicular tothe solar meridian.

Similar to Figs. 2–5, we calculated the polarizationpattern of skylight reflected from a silver-glass mirror.Contrary to the glass deflector, we learned that sucha mirror has practically no influence on thepolarization characteristics of incident light: thedifferences between the degrees and directions ofpolarization of skylight and reflected skylight weresmaller than 2% and 2 degrees (DdQ 2%, DaQ 2°).Thus, the reflected celestial polarization pattern

F. 3. The pattern of the direction of polarization a of skylight reflected from a vertical glass deflector panel calculated for four differentelevations us of the sun: (a) us =60°, (b) us =40°, (c) us =20°, (d) us =0. The mirror image of the sun is represented by a dot. a is measuredfrom the normal of the panel and its different intervals are shaded by different grey tones: brighter shades represent regions where theE-vector is more or less perpendicular to the panel, while darker tones mean E-vectors are more or less parallel to it.

(a)

(c)

(b)

(d)

295

F. 4. The difference Dd= dsky − ddeflector between the degree of polarization dsky of skylight and ddeflector of skylight reflected from a verticalglass deflector panel calculated for four different elevations us of the sun: (a) us =60°, (b) us =40°, (c) us =20°, (d) us =0°. The mirrorimage of the sun is represented by a dot. The different intervals of Dd are shaded by different grey tones.

(a)

(c)

(b)

(d)

deflected by a common metal-glass mirror can beconsidered realistic in the deflector loft or mirrorexperiments investigating avian orientation.

The latter two conclusions are also supported byFig. 6 that shows the degree of polarization d ofunpolarized incident light after reflection fromdifferent deflector panels as a function of the incidentangle u measured from the normal of the panel.Curves (b) and (c) in Fig. 6 represent the change ofd vs u for a deflector panel composed of an aluminiumplate or a silver-glass mirror. We can see that themaximum of d reaches only a few per cent, that is, theunpolarized incident light remains almost unpolarized

after reflection from these mirrors. The light reflectedfrom the aluminium mirror is slightly more polarizedthan the light deflected by the silver-glass mirror.Contrary to this, a deflector panel made of glass ona black substrate [curve (a) in Fig. 6] or on a whitebackground [curve (d) in Fig. 6] alters significantly thepolarization of unpolarized incident light.

We can read from curve (a) in Fig. 6 that as u

increases from zero to 90° the degree of polarizationof the deflector panel consisting of glass on a blackbackground increases from zero to 100% up to theBrewster angle (uB 1 56° measured from the vertical),then d decreases to zero, but it remains always

(a)

(c)

(b)

(d)

F. 5. The difference Da= asky − adeflector between the direction of polarization asky of skylight and adeflector of skylight reflected from a verticalglass deflector panel calculated for four different elevations us of the sun: (a) us =60°, (b) us =40°, (c) us =20°, (d) us =0°. The mirrorimage of the sun is represented by a dot. The different intervals of Da are shaded by different grey tones. Since asky is always smaller thanadeflector , Da is smaller than zero in every point of the deflector.

Angle ofincidence

Deg

ree

of p

olar

izat

ion

100%

–100%

Par

alle

l E-v

ecto

rP

erpe

ndi

cula

r E

-vec

tor

Glass on a white substrate (d)

Silver-glass mirror (c)

Aluminium mirror (b)

Glass on a black substrate (a)

θ

δ

90°0°

. ´ . 296

F. 6. The degree of polarization d of unpolarized incident light after reflection from different deflector panels as a function of the incidentangle u measured from the normal of the panel composed of (a) glass on a black background, (b) aluminium plate, (c) silver-glass mirror,(d) glass on a white substrate with an albedo of A=0.8. Positive or negative d’s mean E-vectors parallel or perpendicular to the panel,respectively.

positive, that is, the reflected E-vector is alwaysparallel to the panel.

The situation is quite different in the case of adeflector made of glass on a white substrate. Here thelight component penetrating into the glass is diffuselyscattered backwards by the white background, then itis refracted at the upper glass surface. The lightemanating from the glass is always perpendicularlypolarized to the surface due to refraction at theglass–air interface (Horvath & Varju, 1995). Thisperpendicularly polarized light is superimposed withthe light component that is specularly reflected fromand parallel polarized to the upper glass surface.Apart from quite grazing angles (u1 90°) the formercomponent dominates, thus the net E-vector isperpendicular (dQ 0) to the panel. If u1 90° theparallel polarized (dq 0), specularly reflected lightcontrols the net degree of polarization, as we can seeon curve (d) in Fig. 6. Figure 7 shows the change ofd vs u as a function of the albedo A of the whitebackground. We can see that the albedo has aconsiderable influence on the reflection-polarizationcharacteristics of the panel. Increasing A, the E-vectorof reflected light becomes more and more perpendicu-lar to the panel, that is, the region of the incidentangle characterized by parallel polarized reflectedlight becomes gradually narrower. The larger the A,the weaker polarized is the reflected light withperpendicular E-vector.

Discussion and Conclusions

We have seen above that a glass deflector panelmodifies considerably the distribution of polarizationin the deflector loft or mirror experiments studyingavian orientation. In our opinion such deflectorpanels might induce a visual cue-conflict situation forthe test birds in such a way that the intensity andspectral features of the reflected skylight contradict itspolarization characteristics: a glass plate modifies thecolour and intensity of incident skylight only slightly,however, it changes significantly the celestial polariz-ation pattern after reflection. Hence, a polarization-sensitive test bird in this case is confronted with sucha deflected view of the sky, where the spatialdistribution of intensity and colour is similar to thereal one but the polarization pattern is quite differentfrom the expected pattern. Since many birds preferthe celestial polarization pattern against other opticalcues of the sky (e.g. Able, 1993), they may solve thiscue-conflict in such a way, that they begin to orientnot by means of skylight polarization, but on thebasis of other cues (for example, stars or Earthmagnetism), or they orient randomly or ambiguously.This might be one of the reasons for the frequentlyobserved ambivalent responses of test birds during thedeflector loft or mirror experiments using suchdeflector panels, that change significantly thepolarization of skylight.

Angle ofincidence

Deg

ree

of p

olar

izat

ion

100%

–100%

Par

alle

l E-v

ecto

rP

erpe

ndi

cula

r E

-vec

tor

A = 0.8

θ

δ

90°0°

A = 0.6

A = 0.4

A = 0.2

297

F. 7. The degree of polarization d of unpolarized incident light after reflection from a glass deflector panel as a function of the incidentangle u (measured from the normal of the panel) calculated for four different values of the albedo A of the underlying white substrate:A=0.2, 0.4, 0.6, 0.8.

Interestingly, the reflection-polarization character-istics of the deflector panels made of glass with orwithout a black background is qualitatively quitesimilar to those of the flat water surface. This watersurface-reflected polarization pattern plays an im-portant role in the water detection by water-seekinginsects (Schwind, 1991, 1995; Schwind & Horvath,1993; Horvath, 1995; Horvath & Zeil, 1996).

On the basis of the above we conclude the following:

(I) A deflector panel consisting of a back surface(metal-glass) mirror or front surface (pure metalplate) mirror changes the polarization of incidentlight slightly independently of the incident angle.Thus, such a deflector can mimic the celestialpolarization pattern well in the deflector loft or mirrorexperiments studying the role of skylight polarizationin the orientation of birds possessing polarizationvision.

(II) A deflector panel made of a translucent glassplate changes the polarization of incident light afterreflection considerably. Such a deflector in thedeflector loft or mirror experiments cannot simulatethe distribution of polarization in the sky at all dueto its strong reflection polarization. This might be oneof the reasons why birds frequently respondambivalently to the deflected optical cues in thesebehavioural experiments.

(III) A deflector panel made of glass on a blacksubstrate significantly alters the polarization features

of incident light due to reflection. The degree ofpolarization of reflected light is 100% at the Brewsterangle (about 56° from the normal of the panel) anddecreases farther away from this direction; thereflected E-vector is always parallel to the panel.

(IV) A deflector panel consisting of glass on awhite background considerably modifies the polariz-ation characteristics of incident light after reflection.If the incident light is unpolarized, the reflected lightpossesses an E-vector, which is perpendicular to thepanel for smaller angles of incidence. For largerincident angles the E-vector becomes parallel to thepanel. The region of perpendicular E-vector increaseswith increasing albedo of the underlying whitesubstrate. The degree of polarization of reflected lightwith perpendicular E-vector is gradually reduced asthe albedo increases.

The financial support of the National Scientific ResearchFoundation (OTKA F-014923 and OTKA T-020931) andthe Hungarian State Eotvos Stipend Fund received byG. Horvath is gratefully acknowledged. Many thanks aredue to Professors J. B. Phillips, K. Schmidt-Koenig and J.Waldvogel for reading and commenting on the manuscript.

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Appendix A

Repolarization of Incoherent Polarized Light Reflected

from a Silver-Glass Mirror

The electric field vector E0 of an incoherent,partially linearly polarized light can be composed oftwo components E>

0 and E;0 , where the former and

latter is parallel and perpendicular to the plane ofincidence. The amplitudes E>

r , E;r and the complex

conjugates E>r *, E;

r * of the electric field vectorcomponents of light reflected from a metal-glassmirror can be obtained as a sum of an infinitegeometrical series, as we can see in Fig. A1.

Er =E00ra,g + sa,gsg,arg,s sa

n=0

rng,a rn

g,se−ibn 1,

E*r =E00ra,g + sa,gsg,ar*g,s sa

m=0

rmg,a r*g,s

meibm1, (A.1)

where bn is the random phase of the n-th reflectedE-vector component, r and s are the amplitudereflection and transmission coefficients; subscripts a,g and s refer to air, glass and silver. In the derivationof the complex conjugate in (A.1) we took intoconsideration that in the mirror only the silver layerpossesses a complex refractive index, that is, amongthe amplitude reflection and transmission coefficientsonly rg,s is complex. For the sake of clarity, in (A.1)we omitted the superscripts > and ;, however, weshall use them later again. On the basis of the Fresnelformulae (Azzam & Bashara, 1989)

r>a,g =

n2g cos f0 −zn2

g −sin2f0

n2g cos f0 +zn2

g −sin2f0

, (A.2)

F. A1. Ray tracing of an incident ray of light reflected by aglass–metal mirror.

299

r;a,g =

cos f0 −zn2g −sin2f0

cos f0 +zn2g −sin2f0

, (A.3)

r>g,s =

N2s zn2

g −sin2f0 − n2g zN2

s −sin2f0

N2s zn2

g −sin2f0 + n2gzN2

s −sin2f0

, (A.4)

r;g,s =

zn2g −sin2f0 −zN2

s −sin2f0

zn2g −sin2f0 +zN2

s −sin2f0

, (A.5)

where ng is the real refractive index of glass, Ns is thecomplex index of refraction of silver, and f0 is the in-cident angle measured from the normal of the mirror.The intensity of light reflected from the mirror isproportional to the time average of the quantity ErE*r .We must take into consideration that the time averageof the terms is zero, which contain the quantities e−ibn

and e−i(bn − bm ) due to the randomness of phases bn .Thus, the time average is

�ErE*r �=E20 $r2

a,g + s2a,g s2

g,a rg,sr*g,s

× sa

n=0

(r2g,a rg,sr*g,s )n%. (A.6)

Since rg,a = − ra,g and sa,gsg,a =1− r2a,g , the net

amplitude reflection coefficients of the mirror forincoherent, partially linearly polarized light are

r( j)mirror 0

z�E( j)r E( j)

r *�E( j)

0=Xr( j)2

a,g + r( j)g,s r

( j)*g,s (1−2r( j)2

a,g )1− r( j)2

a,g r( j)g,s r( j)*

g,s

,

( j )= >;. (A.7)

Appendix B

Repolarization of Incoherent Polarized Light Reflected

from a Glass Deflector Panel

Using (A.2) and (A.3), the net amplitude reflectioncoefficients of a plate glass in air for incoherent,partially linearly polarized incident light is

rglass = r( j)a,gX 2

1+ r( j)2a,g

, ( j )= >,;. (B.1)

Appendix C

Degree of Polarization of Incoherent Unpolarized

Incident Light after Reflection from Different Deflector

Panels

If the deflector panel consists of a glass plateunderlined by a black substrate, then light is reflectedonly from the upper glass surface, because thepenetrating light component is totally absorbed bythe black background. Thus, the amplitude reflectioncoefficients of this black panel are

r>black =

n2g cos f0 −zn2

g −sin2f0

n2g cos f0 +zn2

g −sin2f0

,

r;black =

cos f0 −zn2g −sin2f0

cos f0 +zn2g −sin2f0

, (C.1)

and the degree of polarization of unpolarized incidentlight after reflection from this deflector is

dblack =r;2

black − r>2black

r;2black + r>2

black. (C.2)

In the case of an aluminium plate light is reflectedonly from the upper surface, because the penetratinglight is totally absorbed by the metal. If the complexrefractive index of aluminium is Nalu , then itsamplitude reflection coefficients are

r>alu =

N2alu cos f0 −zN2

alu −sin2f0

N2alu cos f0 +zN2

alu −sin2f0

,

r;alu =

cos f0 −zN2alu −sin2f0

cos f0 +zN2alu −sin2f0

, (C.3)

and the degree of polarization of unpolarized incidentlight after reflection from a deflector panel composedof pure aluminium plate is

dalu =r;

alu r;*alu − r>alu r>*alu

r;alu r;*alu + r>

alu r>*alu. (C.4)

-

A silver-glass mirror consists of a plate glassunderlined by a highly reflecting, thin silver layer.Using (A.2–A.5) and (A.7), the degree of polarizationof unpolarized incident light after reflection from adeflector panel made of silver-glass mirror is

dmirror =r;2

mirror − r>2mirror

r;2mirror + r>2

mirror. (C.5)

. ´ . 300

When the deflector panel is composed of a plateglass on a white substrate, one component of theincident light is directly reflected by the upper glasssurface, and the penetrating component is infinitetimes diffusely backscattered by the white underlyinglayer and reflected from and refracted at the glass–airinterface. If the albedo of the white substrate is A,then the net amplitude reflection coefficients are

r( j)white = r( j)

black +Az1−Rs( j)black s

a

n=0

AnzRn,

( j )= >,;, (C.6)

where

R=r>2

black + r;2black

2(C.7)

is the reflectivity of the upper glass surface forunpolarized incident light, and

s>black =

2ngzn2g −sin2f0

zn2g −sin2f0 + n2

g cos f0

,

s;black =

2zn2g −sin2f0

zn2g −sin2f0 + cos f0

(C.8)

are its amplitude transmission coefficients. From here

r( j)white = r( j)

black +As( j)

black z1−R

1−AzR, ( j )=;,>.

(C.9)

Finally, the degree of polarization of unpolarizedincident light after reflection from a plate glassunderlined by a white substrate with albedo A is

dwhite =r;2

white − r>2white

r;2white + r>2

white. (C.10)