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S. Sabbah and N. Shashar Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. A 2049

Light polarization under water near sunrise

Shai Sabbah1 and Nadav Shashar2,*1Green Vision Systems, Ltd., 27 Habarzel Street, Tel-Aviv, 69710, Israel

2Department of Life Sciences, Eilat Campus, Ben Gurion University, P.O. Box 469, Eilat, 88103, Israel*Corresponding author: nadavs@huji.ac.il

Received December 5, 2006; accepted February 9, 2007;posted March 7, 2007 (Doc. ID 77715); published June 13, 2007

Dramatic and rapid changes in the intensity and spectrum of light under water at dusk and dawn are wellknown, but reports regarding the light’s polarization at these periods are sparse. Using a rapid spectropola-rimeter, we examined the spatial and spectral characteristics of the underwater polarization patterns fromsunrise to midday and compared them with a Rayleigh-based model for e-vector orientation and percent po-larization. With the Sun near the horizon, the underwater polarization patterns were distinctive. Unlike thepolarization at small solar zenith angles, the underwater polarization at large solar zenith angles cannot bepredicted by simple Rayleigh scattering, most likely because of the relatively high contribution of skylight. Atsunrise, the underwater polarization pattern outside of Snell’s window differed from that found during the dayin percent polarization, spatial distribution, and wavelength dependence. These unique polarization charac-teristics may provide a polarization-sensitive animal with a distinct cue for mediating dial vertical migrationperformed by plankton or with another timing signal. © 2007 Optical Society of America

OCIS codes: 260.5430, 120.5410, 170.1420.

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. INTRODUCTIONusk and dawn are the periods during the day in whichramatic and rapid changes in the intensity and spec-rum of light occur. During twilight, light intensity canary by 5 to 6 orders of magnitude, with intensity chang-ng at rates of approximately 50% per min [1,2]. Duringhese periods, a reduction in the green and orange–redavelengths of light also occurs [2–4]. The polarization of

ight is expected to change during twilight as well. Yet toate, reports concerning this attribute are sparse [4,5].Light whose electric field preferentially oscillates on a

pecific plane is said to be partially linearly polarized. Al-hough the Sun radiates unpolarized light, due to scatter-ng and differential refraction events the Sun’s light mayecome partially polarized when it enters and passeshrough the atmosphere and hydrosphere [6]. Under wa-er, except for elliptical polarization next to Snell’s win-ow (the circular region on the water surface above an un-erwater observer with an aperture angle ofpproximately 97.5°, into which the entire celestial hemi-phere above the water is compressed due to refraction) athallow waters [7], light is predominantly partially lin-arly polarized [3]. For this reason and since sensitivity tolliptical polarization has not yet been found in the ani-al kingdom [3,8], this manuscript focuses solely on lin-

ar polarization and all references to polarized light refero linearly polarized light.

A linearly polarized light beam can be described byhree wavelength-dependent parameters: the e-vectorrientation—the light’s electric field orientation, the per-ent polarization—the relative intensity of the polarizedomponent out of the total light intensity (also known asegree of polarization or partial polarization), and theverall light intensity.

Throughout the photic zone, during the day, sunlight

1084-7529/07/072049-8/$15.00 © 2

nd skylight are the main sources of light under water.hen the Sun is visible, its position is the foremost factor

ffecting the underwater polarization patterns. Thus, theistributions of the e-vector orientation and percent polar-zation are subjected to spatial and temporal variationsorresponding to the variations in the Sun’s position. Theefinitions used hereafter to describe the geometrical dis-ribution of underwater polarization are presented inig. 1.The distribution of polarization under water during the

ay was described elsewhere [4,5,9–15]. In short and asn approximation, within Snell’s window, shallow-waterolarization is mostly affected by the sky polarization andy the refraction of light at the water surface. Outside ofnell’s window, and in clear calm waters, the e-vector ori-ntation is strongly correlated to the solar zenith angle asalculated by the angle of refraction, reaching a maxi-um tilt of 48.6° away from the zenith (see Fig. 2 for an

llustration for typical polarization in clear shallow wa-ers). During daytime, the maximal percent polarizationeasured in the field was approximately 50% [4,11,16].lthough a wealth of reports regarding the underwaterolarization patterns is available, most do not include theharacteristics of these patterns at large solar zenithngles, including dusk and dawn. However, at crepuscu-ar periods, Waterman and Westell [5] found the percentolarization to be very low at zenith and azimuthal view-ng angles of 90°, reaching only 10%. Novales Flamariquend Hawryshyn [4], on the other hand, measured 67% po-arization in water at sunset when facing the zenith.

Outside of Snell’s window the polarization pattern isavelength dependent, and the minimum percent polar-

zation occurs at the water’s most penetrable wavelength,hich is the color of the water mass �450–500 nm�

11,12]. At crepuscular periods, although the proportion of

007 Optical Society of America

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2050 J. Opt. Soc. Am. A/Vol. 24, No. 7 /July 2007 S. Sabbah and N. Shashar

he short wavelengths’ intensity to that of the total spec-rum within Snell’s window increases [3,4], reports con-erning the relationship between the percent polarizationnd the wavelength are not yet available.Apart from polarization measurements, throughout the

ears, considerable theoretical work has also been per-ormed. In contrast to the empirical-type model of Water-an and Westell [5], Ivanoff and Waterman [7],imofeyeva [9], and Waterman [3] further described inection 2, using the Monte Carlo technique, Kattawar etl. [17] and Adams and Kattawar [18] were able to de-cribe multiple scattering, Mie scattering, reflection andefraction from sea surface, and absorption processes. Ac-ording to their simulations, near the ocean surface, theattern of the percent polarization as a function of scat-ering angle resembles that of Rayleigh single scattering,n which the percent polarization reaches a maximum at0° from the direction of incidence.Polarization sensitivity has been demonstrated in nu-erous marine animals including crustaceans, cephalo-

ods, and vertebrates (reviewed by Waterman [3], Wehner19], Horváth and Varjú [8], and Sabbah et al. [20]). Usinghe underwater polarization patterns, polarization-ensitive animals orient themselves [21–26], escape offhore [27–29], break the countershading of light-eflecting silvery fish [30,31], and detect transparent prey

ig. 1. Definitions of light directionality. Solar zenith angle�s�—the vertical angle between the zenith and the Sun asiewed from outside the water, ranging from 0° when the Sun ist the zenith, through 90° when the Sun is at the horizon, tongles greater than 90° when the Sun is below the horizon. Theertical angle between the refracted light beam and the zenith�r� ranges from 0° when the Sun is at the zenith to 48.6° whenhe Sun is at the horizon, to larger angles when the Sun is belowhe horizon. The detector zenith angle (�p; also referred to as theiewing zenith angle) is the vertical angle between the zenithnd the detector and ranges from 0° when the detector is facinghe zenith, to 90° when the detector is facing horizontally, to 180°hen the detector is pointing toward the nadir. The solar and de-

ector azimuthal angles ��s� and ��p� are the horizontal anglesetween the north direction and the Sun or the detector, respec-ively (the azimuthal angles are measured clockwise from theorth when looking downward). The viewing azimuthal angle ���

s the horizontal angle between the two vertical planes contain-ng the Sun and the detector.

32,33]. Polarization-sensitive marine animals were alsoostulated, though not tested, to utilize the special polar-zation patterns that occur when the Sun is near the ho-izon (large solar zenith angles) to mediate their dial ver-ical migration [34] and as a timing signal [1].

In this study we (i) describe the polarization patternst sunrise and at large solar zenith angles, (ii) comparehe e-vector orientation and percent polarization as pre-icted by Rayleigh scattering theory with the values mea-ured at large solar zenith angles, and (iii) discuss theossible implications of the polarization patterns formednderwater when the Sun is near the horizon forolarization-sensitive marine animals.

. MATERIALS AND METHODS. Underwater Polarization Measurementsxamination of the spatial and spectral characteristics of

he underwater polarization patterns at sunrise and largeolar zenith angles was conducted over a coral reef inront of the H. Steinitz Marine Biology Laboratory, Eilat,ed Sea �29°30 020 N,34°55 010 E�.

ig. 2. Qualitative illustration of the e-vector orientation andercent polarization at (a) sunrise and (b) midday. Data areased on measurements and calculations corresponding to thereen spectral region ��500 nm�. The polarization state is pre-ented for five viewing azimuthal angles (0°, 45°, 90°, 135°, and80°) and four viewing zenith angles (0°, 30°, 70°, and 90°). Thehaded circle represents the theoretical location of Snell’s win-ow. The e-vector orientation is indicated by the tilt of the arrowelative to a tangent to the circle passing through that point, andhe percent polarization is indicated by the thickness of the ar-ows. Consistent with the nomenclature previously used, the fig-re was reconstructed after Waterman [10], Horváth and Varjú14], and Cronin and Shashar [11].

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S. Sabbah and N. Shashar Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. A 2051

Recordings were performed using a custom-built rapid-ampling polarimeter, described in detail by Shashar etl. [35]. The polarimeter is based on a three-channel spec-rophotometer (Ocean Optics ADC-1000-USB). Eachhannel is equipped with a fiber optic (Ocean Optics UV/IS 600 �m) with a 5° acceptance angle restrictor; aolarization-neutral, spectra-flattening, colored filterRosco Supergel #02—Bastard Amber); and a linear polar-zer (Polaroid H’NPB UV/VIS). The transmission axes ofhe polarizers were set to 0°, 45°, and 90° off the horizon.he heads and filters of each of the three fibers were in-erted into a submersible housing that was fixed on a ro-ating apparatus, attached to a vertical pole at a depth ofm. Integration times ranged between 1 and 5000 ms tollow for sufficient intensity within the 350–700 nm spec-ral range. To avoid wave-induced fluctuations in theeadings, automatic averaging of several integrated re-ordings was applied to provide a total recording durationf no less than 5 s/measurement, which was higher thanhe waves’ period at the time (typically 0.89–1.67 s) [36].

Measurements were completed during 16 days underully clear blue sky conditions. The detector was alignedt viewing zenith angles of 0°, 30°, 70°, and 90°, and eachorning the detector was adjusted to face one of five

iewing azimuthal angles, 0°, 45°, 90°, 135°, and 180°,nd remained fixed throughout the day. The Sun’s posi-ion at sunrise was obtained from the U.S. Navy Web sitettp://aa.usno.navy.mil/data/docs/AltAz.html. A day ofeasurements commenced at a solar zenith angle of 95°

nd continued until midday, when the Sun reached itsighest altitude (smallest solar zenith angle). Eilat, at theip of the Gulf of Aqaba, is surrounded by the Edom andilat mountains. At nautical sunrise, the Sun was ob-cured by mountains until it reached a solar zenith anglef 86° –88°. Therefore, the solar azimuthal angle at sun-ise was defined as the one at the moment the Sun peekedver the mountains.

Measurements were taken continuously at 1 min inter-als. Each measurement was recorded along with the cor-esponding solar zenith angle and viewing azimuthalngle (measured at a 1° resolution). Throughout thistudy, over 3000 polarization measurements were ex-cuted and analyzed. To measure the underwater polar-zation at a high temporal resolution (which is of impor-ance at the time of sunrise when rapid changes in theight field occur), the polarization at every zenith and azi-

uthal viewing angle was examined on a single day. Onll measurement days the sky was clear, surface wavesere low (�0.5 m height), and underwater visibility was

stimated to be 20 m. Given the fairly stable meteorologi-al and hydrological conditions, the effects of the solar ze-ith angle and the zenith and azimuthal viewing anglesn the underwater polarization could be investigated.

. Data Processing and Analysis of Underwatereasurementsrior to the measurement, the fibers were cross calibratedy examining an evenly illuminated white defusing fab-ic. Taking into account the cross-calibration factors andark noise measurements, the intensity I, percent polar-zation P, and e-vector orientation � of the light were cal-ulated using a custom-made LABVIEW application. The

alculations were based on the equations of Wolff and An-reou [37], modified by Shashar et al. [35]. For detailedquations, refer to Sabbah and Shashar [36] and Sabbaht al. [15]. Throughout this manuscript, the e-vector ori-ntation is designated between 0° and 180°, with 0° /180°orresponding to horizontal and 90° corresponding to ver-ical orientation. The percent polarization P ranges fromto 100%.

. Measurement Controls and Limitationseveral levels of measurement control were performed.

1) While conducting intensity-controlled polarizationeasurements, the minimum intensity level at which a

eliable polarization measurement could be obtained wasetermined. This minimum intensity level plus its squareoot (approximation of the noise level) was defined as theinimum signal usable for analysis, and lower measure-ents were excluded. (2) Due to the local tide, the detec-

or depth varied by up to 1 m during each measuring day.n a control experiment examining the effect of thishange on the measured underwater polarization, maxi-um standard deviations (SDs) of 4.32% and 4.68° for the

ercent polarization and e-vector orientation, respec-ively, were found (at all examined viewing zenith angles).3) Variation between days was established by performing

series of 30 measurements, 1 min apart, on each ofhree days, with the detector facing viewing zenith anglesf 30° and 90°. On these days, recordings were conductedt similar solar zenith angles and viewing azimuthalngles, yielding 30 sets of three measurements each inhich the solar zenith angle and the viewing azimuthalngle were nearly identical (less than a 1° difference).ithin the 350–700 nm spectral range and at individualavelengths spaced 10 nm apart, the SD between theembers of each trio was calculated. Throughout the ex-

mined spectrum the SDs of the 30 trios did not exceed 5°r 7% for the e-vector orientation and percent polariza-ion, respectively. Thus, measurements taken on differentays were comparable.

. Calculation of Rayleigh-Predicted Polarizationatterns and Comparison between Predictednd Measured Polarization Valuest the study site, water clarity conformed to the Jerlov

ype 1 classification [38], with beam attenuation coeffi-ient �0.2/m and the particulate attenuation coefficient0.15/m at 490–510 nm. For a detailed description of theater properties, refer to Boss [39]. Therefore, water mol-

cules along with other Rayleigh-sized particles wereaken to be the primary scatterers affecting the underwa-er polarization patterns.

Assuming Rayleigh scattering, several researchers for-ulated a model predicting the spatial distribution of thenderwater e-vector orientation outside of Snell’s window3,5,7,9]. In this model the e-vector orientation is calcu-ated based solely on geometrical considerations, and theptical properties of the water are not taken into account:

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2052 J. Opt. Soc. Am. A/Vol. 24, No. 7 /July 2007 S. Sabbah and N. Shashar

tan � =tan �r sin��s − �p�

sin �p − tan �r cos �p cos��s − �p�, �1�

here � represents the e-vector orientation relative to theorizontal (0° /180°; vertical orientation can be assignedalues of ±90°). For a detailed description of the geometri-al parameters, see Fig. 1.

Percent polarization was approximated using a Ray-eigh single-scattering model (e.g., Waterman [10], Water-

an and Westell [5], and Ivanoff [40]) according to theormula

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icular to the incident light flux. The scattering angle �scas related to the zenith and azimuthal angles of the Sunnd the detector by the formula

�sca = arccos�cos��r�cos��p� + sin��r�sin��p�cos��p − �s��.

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heoretically, Pmax equals 1. In practice, Pmax�1 and asuch takes into account inhomogeneities of the shapes ofhe scattering particles [40]. Using the above equations,e calculated the predicted e-vector orientation and per-

ent polarization for each of the measurements. In Eq. (2),max was set to be the highest percent polarization ob-

ained at the viewing zenith angle in which the set ofeasurements was taken.To compare the measured and predicted polarization

alues, the Pearson correlation coefficient was calculated;he results were grouped into two solar zenith angle cat-gories: (1) from actual sunrise ��s=85° –87.7° � until a so-ar zenith angle of 75° and (2) solar zenith angles rangingetween 25° and 35°. Since the solar zenith angle athich a local maximum/minimum in the percent polariza-

ion and e-vector orientation was found to equal 74.2° (av-raged across all examined wavelengths and viewing azi-uthal angles; to be discussed further in Section 3), the

ower limit of the large solar zenith angle category waset to equal 75°. The solar zenith angle categories werehosen such as to provide an approximately similar num-er of measurements in each category �n=45�. Statisticalnalysis was performed using STATISTICA software.

. RESULTSight polarization characteristics at sunrise at differentenith and azimuthal viewing angles are presented inig. 3. Note that while the e-vector orientation and per-ent polarization within Snell’s window do not vary muchith wavelength, they do so outside of Snell’s window

compare Figs. 3(a), 3(b), 3(e), and 3(f) with Figs. 3(c),(d), 3(g), and 3(h)]. Within Snell’s window (viewing ze-ith angle of 30°), the percent polarization varied consid-rably with the viewing azimuthal angle, but not so out-ide of Snell’s window [compare Figs. 3(f) with Figs. 3(g)nd 3(h)]. The percent polarization outside of Snell’s win-

ow generally ranged between 3% and 38%, except for the00 nm measurement at a viewing azimuthal angle of35°, which reached 50%. Within Snell’s window (viewingenith angles 0° and 30°), the percent polarization wasigher, attaining 70% when the zenith was examinedFig. 3(e)].

In agreement with the Rayleigh single-scattering pre-ictions, the percent polarization at a viewing zenithngle of 90° (and at viewing azimuthal angles differentrom 90°) increased toward its maximum value at middaysmall solar zenith angles; Figs. 4(f)–4(j)]. In addition, oneveral occasions a local maximum or minimum in theercent polarization occurred shortly after sunrise [Figs.(f), 4(g), 4(i), and 4(j)]. Local maximum/minimum pointsn the e-vector’s tilt were also evident [Figs. 4(a)–4(d)].he correlations between the Rayleigh single-scatteringredictions for the e-vector orientation and percent polar-zation and the measurements were generally good formall solar zenith angles �25° –35° � and at the viewingenith angle of 90°. For the e-vector orientation [Figs.(a)–4(e)], the Pearson correlation coefficient �r� was.79±0.35 �Avg±SD,n=45�, and, for the percent polariza-ion [Figs. 4(f)–4(j)], it was 0.73±0.47, n=45. At solar ze-ith angles from actual sunrise �85° –87.7° � until a solarenith angle of 75°, however, the theoretical predictions ofhe e-vector orientation and percent polarization wereoorly or negatively correlated with measurements. For-vector orientation [Figs. 4(a)–4(e)], r=−0.02±0.77, n45, and, for percent polarization [Figs. 4(f)–4(j)], r=0.57±0.66, n=45. Therefore, at large solar zenith angles

from sunrise to approximately 75°) the basic theoreticalodel could not describe the underwater polarization pat-

ern very well. Indeed, this difference between small andarge solar zenith angles could be detected in the level oforrelation between the predicted and the observed polar-zation. Coefficient values at small solar zenith anglesere significantly larger than those attained at large so-

ar zenith angles (sign test, n=20, p�0.001; throughouthe examined wavelengths and viewing azimuthalngles).

. DISCUSSIONaterman [3] postulated that when the Sun is near the

orizon it creates a unique polarization pattern under wa-er, different from that attained during the rest of the day.ndeed, outside of Snell’s window (at viewing zenithngles of 70° and 90°), the percent polarization at sunrise,hich generally ranged between 3% and 38%, did not de-end on the viewing azimuthal angle. This is in contrasto the general trend found during the other hours of theay, in which the percent polarization is maximal at aiewing azimuthal angle of 90°, less at 180°, and mini-um at 0° [12]. Additionally, at a viewing zenith angle of

0°, roughly as predicted by Waterman and Westell [5],he e vector tilted strongly off of the horizontal [up to 90°t a viewing azimuthal angle of 90°; Figs. 2 and 3(c)]. Inontrast to these unique polarization features, at sunriset a viewing zenith angle of 90°, the spatial distribution of

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S. Sabbah and N. Shashar Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. A 2053

he e-vector orientation exhibited a trend similar to thatreviously reported [10]. That is, an e-vector orientationquals the critical angle �48.6° � at a viewing azimuthalngle of 90°, is nearly horizontal at viewing azimuthalngles of 0° and 180°, and tilts by an intermediatemount at viewing azimuthal angles of 45° and 135°.According to Ivanoff and Waterman [12], at small solar

enith angles (near midday), the maximal percent polar-zation outside of Snell’s window is attained at both edgesf the examined spectrum, i.e., in the UV/blue350–400 nm� and red �600–650 nm� spectral regionsFigs. 3(g) and 3(h)]. Such a trend was not found to occurt sunrise. The large variation in the e-vector orientationnd percent polarization between wavelengths outside ofnell’s window, but not within it, is another indicator of

ig. 3. Underwater polarization at sunrise as a function of the volarization at viewing zenith angles of 0°, 30°, 70°, and 90°, rresented, whereas, due to low signal-to-noise ratio of the recorde80–650 nm. The average (symbols) and standard deviation (ertarting as the Sun peeked above the mountains (solar zenith an

he existence of two distinct polarization patterns, one in-ide of Snell’s window and the other outside of it [10,14].

At a viewing zenith angle of 90°, i.e., outside of Snell’sindow, the percent polarization at midday was found toe higher than that measured either at twilight or at sun-ise. However, within Snell’s window the percent polariza-ion was maximal at sunrise and reached 70% (at the ze-ith), in agreement with the measurement of Novaleslamarique and Hawryshyn [4] of 67% polarization atunset and a similar viewing zenith angle.

The distributions of the e-vector orientation and per-ent polarization were previously shown to be subjected topatial and temporal variations corresponding to varia-ions in the Sun’s position [4,5,9,10,12,41]. Additionally,abbah et al. [15] found that, despite the effects of refrac-

azimuthal angle: (a)–(d) e-vector orientation and (e)–(h) percentvely. Within Snell’s window, the polarization at 350–700 nm isnsities, outside of Snell’s window the polarization is presented atrs) of ten consequent polarization measurements, 1 min apart,f 85° –87.7°) are depicted.

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2054 J. Opt. Soc. Am. A/Vol. 24, No. 7 /July 2007 S. Sabbah and N. Shashar

ion at the undulating water surface, the skylight polar-zation pattern is well transmitted through the water.onsequently, during daytime, both sunlight and skylight

ig. 4. (a)–(e) Predicted and measured e-vector orientations andion of the solar zenith angle, at a viewing zenith angle of 90°. P50 (gray dots), 550 (gray triangles), and 650 nm (open triangldashed curves). To calculate the predicted percent polarization,he day at the relevant viewing azimuthal angle, measured at 550he solar zenith angle at the actual sunrise. Generally, at large soeasured polarization.

ay contribute to the underwater polarization pattern inhallow waters.

Two main processes may determine the relative contri-

percent polarization at five viewing azimuthal angles as a func-tion values are presented at four wavelengths: 380 (black dots),r each plot, the Rayleigh scattering prediction was calculatedas set as the maximal percent polarization recorded throughoute middle of the examined spectrum). Solid vertical lines indicateith angles ��75° �, the prediction considerably diverged from the

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S. Sabbah and N. Shashar Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. A 2055

utions of sunlight and skylight to the underwater lighteld: refraction and attenuation. According to Fresnel’squations of reflection–refraction, with decreasing solarenith angle, the relative contribution of sunlight to thenderwater light field increases. Second, with decreasingolar zenith angle the attenuation of sunlight decreases,nd, again, a larger contribution of sunlight over skylighto the underwater light field is expected.

At large solar zenith angles, the Rayleigh direct-llumination single-scattering model failed to predict ac-urately the observed e-vector orientation and the percentolarization. The Rayleigh scattering model is based on aoughly collimated light beam, i.e., a beam of direct sun-ight, and does not take into account scattered skylight.part from a significant contribution of skylight to thenderwater polarization at large solar zenith angles, ourndings suggest a switching point at a solar zenith anglef around 75°, at which the dominating factor controllingolarization in shallow waters may change from scatteredkylight illumination to direct sunlight. Outside of Snell’sindow, the relative contributions of sunlight and sky-

ight are quite noticeable in the polarization pattern viahe comparison between the Rayleigh predictions and theeasurements. Inside of Snell’s window, however, such an

valuation is not possible, since a comparison between theredicted and the measured polarization within Snell’sindow is currently unavailable.Apart from skylight polarization, the disagreement be-

ween the observed polarization and the Rayleigh single-cattering model at large solar zenith angles may also beresult of internal reflection processes. At daytime, the

nfluence of internal reflection (producing complete polar-zation at Brewster’s angle, 53° off the vertical) on theverall underwater polarization is generally insignificant3,7,17]. At sunrise, however, since the role of sunlight inhaping the underwater polarization is likely to be rathermall, the impact of internal reflection on the underwaterolarization at shallow depths may increase. In this re-ard, another factor to be taken into account is the refrac-ion of light at the air–water interface. At large solar ze-ith angles, the percent polarization and e-vectorrientation of refracted light vary considerably with anyodification in angularity [14] and thus may contribute

o the disagreement between the observed and the calcu-ated polarization values. Unfortunately, the role of up-elling light, which is reflected internally, and that of

ight refracted into the water in shaping the underwaterolarization at large solar zenith angles are yet to be ex-lored.In summary, when the Sun is near the horizon, the un-

erwater polarization patterns are distinctive and do notollow the simplified Rayleigh relationship. The reason forhis is most likely the relatively high contribution of sky-ight during these periods. With the Sun near the horizon,he underwater polarization pattern outside of Snell’sindow differs from that found during the day in its per-

ent polarization, spatial distribution, and wavelengthependence. These unique polarization characteristicsay provide a polarization-sensitive animal with a dis-

inct cue to be used at these restricted periods of the day.n addition, within Snell’s window the highest percent po-arization is attained at large solar zenith angles. This

ay be utilized by planktivores to enhance the detectionf transparent zooplankton [32,33], possibly corroboratedy the intense feeding of planktivorous fishes at these pe-iods [42].

CKNOWLEDGMENTSe thank R. Goldshmid, S. Einbinder, A. Lerner, and R.ent for underwater and technical help; A. Rivlin forriting LABVIEW applications for polarization calcula-

ions; I. Lerer, M. Ohavia, and E. Sarfati for fabricatinghe detector’s anchoring and rotating apparatuses; R.olzman and M. Kiflawi for statistical advice and helpful

omments; and C. Erlick for enlightening discussions. Were grateful to the Interuniversity Institute of Eilat for lo-istical support. This research was supported by Bina-ional Science Foundation grant 1999040, Israel Scienceoundation grant 550/03, and the Ring Foundation.

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3. T. H. Waterman, “Polarization sensitivity,” in ComparativePhysiology and Evolution of Vision in Invertebrates. B:Invertebrate Visual Centers and Behavior I, H. Autrum, ed.(Springer-Verlag, 1981), pp. 281–469.

4. I. Novales Flamarique and C. W. Hawryshyn, “Is the use ofunderwater polarized light by fish restricted to crepusculartime periods?” Vision Res. 37, 975–989 (1997).

5. T. H. Waterman and W. E. Westell, “Quantitative effect ofthe sun’s position on submarine light polarization,” J. Mar.Res. 15, 149–169 (1956).

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