Underwater light polarization and radiance ... - OSA Publishing

Underwater light polarization and radiance fluctuations induced by surface waves Shai Sabbah and Nadav Shashar

The underwater light field is an ever-changing environment. Surface waves induce variability in the radiance and the light’s polarization. We examined the dependence of the polarization fluctuations associated with diffuse light (not including contribution from direct skylight) on the viewing zenith angle (30°, 70°, and 90°), solar zenith angle (23°–72°), depth of 0.5–3 m, and light wavelength 共380–650 nm兲 while observing within the azimuthal plane in the wind–wave direction. Polarization and radiance fluctuated with time. Light variability (presented by the coefficient of variation calculated over a series of fluctuations in the radiance and percent polarization, and by the standard deviation calculated over a series of fluctuations in the e-vector orientation) was highest at a viewing zenith angle of 70°, depended positively on the solar zenith angle, and decreased with depth at viewing zenith angles of 30° and 70°. Additionally, the variability of the percent polarization was significantly higher than that of the radiance. The temporal light fluctuations offer possibilities, such as enhancing the detection of transparent and reflecting objects; however, they set constraints on the optimal underwater polarization vision by both animals and by the use of instruments. © 2006 Optical Society of America OCIS codes: 260.5430, 350.7420, 120.5410, 010.4450.

1. Introduction

Variability is one of the most distinctive, if often ignored, features of the underwater light field. This variability, in photon flux, directionality, spectra, and polarization, diverges in its magnitude and time scale, ranging from seasonal, through diurnal, to fluctuations lasting less than a second. In shallow depths, surface waves are the principal cause for short-term variation in the underwater light.1 Surface wave-induced light fluctuations arise mainly as a result of two distinct natural processes: (i) changes in the water column’s height above the observer or light detector, and (ii) focusing and defocusing of sunlight rays refracted at the sea surface, caused by variability in surface curvature.2 Irradiance (E) fluctuations induced by surface waves represent fluctuations in the flow of radiant energy in all directions subtending a hemisphere, either when looking upward (downwelling irradiance) or when

The authors are with the Interuniversity Institute for Marine Sciences in Eilat and Department of Evolution, Systematics and Ecology, Hebrew University of Jerusalem, P.O. Box 469, Eilat 88103, Israel. N. Shashar’s e-mail address is [email protected]. Received 24 June 2005; revised 29 December 2005; accepted 4 January 2006; posted 20 January 2006 (Doc. ID 62972). 0003-6935/06/194726-14$15.00/0 © 2006 Optical Society of America 4726

APPLIED OPTICS 兾 Vol. 45, No. 19 兾 1 July 2006

looking downward (upwelling irradiance), or of the entire ambient sphere.3 Under cloudy skies, when no direct Sun rays refract at the sea surface, variability of the water column height is the predominant process; the power spectra of the downwelling irradiance and that of water pressure resemble each other.4 With increasing depth, however, the relative impact of a given change in the light’s path length on the total length, and hence on the induced light fluctuations, is diminished. In contrast, under clear sky conditions, Sun rays are refracted at the sea surface, and the focusing phenomena prevail. Here, the power spectra resulting from the changes in downwelling irradiance at the blue– green wavelengths exhibit their maxima at frequencies of fluctuations higher than the dominant frequencies of water pressure (due to surface waves) fluctuations.4 With increasing depth, the dominant frequency of the downwelling irradiance fluctuations is shifted toward low values until it coincides with that of the principal maximum in the wave spectrum.5,6 This trend was shown to be affected by the solar zenith angle.5–7 Nikolayev and Khulapov,8 and Prokopov et al.6 demonstrated that the coefficient of variation of the downwelling irradiance fluctuations is also related to the surface waves. Several studies on the underwater irradiance fluctuations examined the effects of focusing light by surface waves.9 –12 They found light fluctuations to vary also according to the solar zenith

angle, wind speed, air humidity, and diffuseness of the surface irradiance.3,10 –13 In contrast to irradiance fluctuations induced by surface waves, fluctuations in radiance (L, described as the flow of radiant energy through the detector’s acceptance solid angle, often specified along with the detector’s zenith and azimuthal angles), were up to now inadequately investigated (but see Yakubenko et al.,14 Yakubenko and Nikolayev,15 Nikolayev and Yakubenko,16 and Stramska and Dickey4). In this regard, when measuring radiance, the sampling time interval (integration time) and the relationship between the solar and the viewing directionality are of importance. Measuring underwater radiance fluctuations while using narrow acceptance angle light sensors 共0.5°–2.5°兲, Yakubenko et al.,14 Yakubenko and Nikolayev,15 and Nikolayev and Yakubenko16 reported radiance fluctuations of approximately 0.2– 1 Hz and reaching up to 4 Hz. Nikolayev and Yakubenko,16 found that the coefficient of variation of the radiance fluctuations in the plane of the solar vertical decreases with increasing angle between the solar and the viewing zenith directions. Additionally, when the angle between the solar and the viewing zenith directions was increased, the relative contribution of the high-frequency components of the radiance fluctuations decreased.16 With increasing depth, one encounters a few maxima in the coefficient of variation of the downwelling radiance fluctuations. Each maximum is assumed to arise as a result of the focusing of light by surface waves of a certain frequency.15 This frequency decreases with increasing depth.15,16 Measuring in clear oligotrophic water at 15 and 35 m depth revealed that the coefficient of variation of both downwelling irradiance and upwelling radiance increases toward the red wavelengths.4 Whereas the effects of the surface waves on the underwater radiance and irradiance are relatively known, light possesses an additional quality, polarization. Light, whose electric field preferentially oscillates in a specific plane, is thought to be partially polarized. Underwater, except for elliptical polarization adjacent to Snell’s window at shallow depths,17 partially polarized light is predominantly linear.18 Therefore this paper focuses on linear polarization and refers to it as polarized light. A linearly polarized light beam can be characterized by three parameters: (i) orientation of the light’s electric-field orientation, the e-vector orientation; (ii) the percent polarization (% polarization); and (iii) the radiance. The definitions to be used hereafter for describing the geometric distribution of the underwater polarization are presented in Fig. 1. Sunlight and skylight enter the water through Snell’s window, which, adjacent to a flat water surface, possesses a cone shape of 48.6° around the zenith from the point of the underwater observer.19 Thus at shallow depths there are two distinct polarization patterns, one within Snell’s window and the other outside it.20 Horvath and Varju21 calculated the underwater polarization pattern within Snell’s window to correlate with the celestial polarization pat-

Fig. 1. Definition of the radiance’s directionality. The solar zenith angle (␪s), the vertical angle between the zenith and the Sun as viewed from outside the water, ranging from 0° (when the Sun is at the zenith), at 90° (when the Sun is at the horizon), to angles greater than 90° (when the Sun is below the horizon); the vertical angle between the refracted light beam and the zenith (␪r) ranges from 0° (when the Sun is at the zenith), at 48.6° (when the Sun is at the horizon), to larger angles (when the Sun is below the horizon); the detector zenith angle (␪p; also referred to as the viewing zenith angle), the vertical angle between the zenith and the detector, ranges from 0° (when the detector is facing the zenith), at 90° (when the detector is facing horizontally), to 180° (when the detector is pointing toward the nadir); the solar and the detector azimuthal angles (␸s) and (␸p), the horizontal angles between the direction in which the wind is blowing and the Sun or the detector, respectively [following Mobley (Ref. 3); the azimuthal angles are measured clockwise from the direction of the wind when looking downward]; and the viewing azimuthal angle (␸), the horizontal angle between the two vertical planes containing the Sun and the detector.

tern. However, due to surface waves1,2,22 and light scattering,23 certain distortions in this pattern may occur. The polarization pattern outside of Snell’s window is considerably different. It arises mainly from scattering24 and internal reflections off the water surface.18 Underwater, bottom reflection,25 water turbidity, and proximity to the shoreline26 may diminish the % polarization. Outside Snell’s window the polarization pattern is light wavelength dependent, and during the daytime the % polarization can reach values of up to 40%.27,28 Additionally, considerable theoretical work, using the Stokes vector and Mueller matrices, and regarding the polarization of light in the ocean, has been performed.29 –31 Although it was postulated that ripples and surface waves may distort the Snell’s window polarization pattern,18,21 the effects of surface waves on the underwater polarization patterns have not yet been studied. In this study, we aimed to (i) measure the surface waveinduced underwater radiance and polarization fluctuations of diffuse skylight at different wavelengths, and 1 July 2006 兾 Vol. 45, No. 19 兾 APPLIED OPTICS

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examine their dependence on the viewing zenith angle; and (ii) study how the solar zenith angle and water depth affect the surface wave-induced light fluctuations.

Since the phase ␪ represents the e-vector shift from the vertical, to obtain the absolute e-vector orientation ␣, the following condition was applied: If 共␪ ⬎ 90°兲 ␣ ⫽ ␪ ⫺ 90°, otherwise ␣ ⫽ ␪ ⫹ 90°. (2)

2. Materials and Methods

This study was conducted on a coral reef at the H. Steinitz Marine Biology Laboratory 共29° 30⬘ 020⬙ N, 34° 55⬘ 010⬙ E), Red Sea, Eilat. Measurements were performed under clear blue sky conditions, off the laboratory pier, where the sandy bottom depth was 3.5–4 m (depending on the tide level), and the water clarity fits the Jerlov type 1 classification.3 The beam attenuation coefficient ⬇0.2兾m and the particulate attenuation coefficient ⬇0.15兾m at 490–510 nm. For a detailed description of the water properties, refer to Boss.32 A.

Polarization Measurements

Recordings were conducted using a three-channel spectropolarimeter (Ocean Optics ADC-1000-USB).23 A fiber optic [Ocean Optics transmitting ultraviolet– visible light (UV–VIS), 600 ␮m diameter] with an acceptance angle restrictor of 5° (in situ) was connected to each channel, and on each restrictor a polarizer (Polaroid HNP’B) was mounted. The polarizers were adjusted to three different orientations: 0°, 45°, and 90° from the horizontal. On top of each polarizer, a polarization-neutral, colored filter (Rosco Supergel #02, Bastard amber) was mounted to flatten the natural spectrum. The fibers, along with their polarizers and colored filters, were inserted into a submersible housing that was fixed on a rotating apparatus, attached to a stable vertical pole. When recording radiance at different viewing zenith angles, we encountered a wide range of intensity levels. Thus to attain a high signal-to-noise ratio in our system, when measuring in the spectral range of 350– 650 nm, the spectrophotometer was set to integration times of 50 ms (at a viewing zenith angle of 30°) and 200 ms (at viewing zenith angles of 70° and 90°). Owing to an inherent delay of the spectrophotometer between successive integrations, the actual sampling frequency was 3.2 and 1.7 Hz. All the experiments and controls were performed using these two integration times. Prior to each experimental session and deployment, fibers were cross calibrated by examining an evenly illuminated white defusing fabric. Taking into account the cross-calibration factors and dark noise measurements, we calculated the light polarization parameters using a custom-made LabView application. Polarization analysis was based on the equations of Wolff and Andreou,33 and Shashar et al.,23 where the phase ␪ is given by ␪⫽

冉冊

冉

冊

1 L0 ⫹ L90 ⫺ 2L45 arctan . 2 L90 ⫺ L0

(1)

Then, if (L90 ⬍ L0 [if (L45 ⬍ L0) ␪ ⫽ ␪ ⫹ 90°, otherwise ␪ ⫽ ␪ ⫺ 90°]. 4728


The total radiance is given by L ⫽ L0 ⫹ L90,

(3)

while the % polarization is given by p ⫽ 100

冑共L0 ⫺ L90兲2 ⫹ 共2L45 ⫺ L90 ⫺ L0兲2 L0 ⫹ L90

.

(4)

The e-vector orientation scale ranges between 0° and 180°, with 0° and 180° corresponding to horizontal polarization, and 90° corresponding to a vertical e vector. The polarization ranges between 0% and 100%. B.

Analysis of Surface Waves

To evaluate the surface waves’ significant height (the average height of the one-third highest waves),34 and the period during the polarization measurements, we videotaped waves for 2 min during each session (detector’s direction). Recordings were made out of the water, using a digital video camera. To scale the images of the waves, we attached a measuring tape to the same pole that carried the polarization detector. The waves’ images were examined using a digital VCR (Sony DHR-1000NP) allowing for field-by-field 共50 Hz兲 analysis. For each detector position, 20 waves were analyzed for significant wave height and average period. Since the analysis of ripples and eddies for these parameters is inaccurate when recording on videotape, only waves with heights greater than 10 cm were analyzed. Consequently, waves with heights equal to or lower than 10 cm were defined as baseline waviness, and their significant wave height and period were measured only once by averaging 20 ripples. C. Viewing Zenith Angle-Controlled Polarization Measurements

To examine the dependence of surface wave-induced polarization fluctuations on the viewing zenith angle, we measured polarization at a high sampling rate. Measurements were performed during 12 days in August and October 2003, and February 2004, with the detector facing the direction of the waves’ propagation at four detector viewing zenith angles: 0°, 30°, 70°, and 90°. However, all measurements at a viewing zenith angle of 0° were excluded from further analyses; see Subsection 2.H. At each viewing zenith angle, 5 min recordings were performed. Throughout all the measurements, the detector depth was 2 m 共1.5–2 m above the sea bottom). Zenith and azimuthal solar angles were obtained from the U.S. Navy website (http://aa.usno.navy.mil/data/docs/

Table 1. Data of Hydrological and Meteorological Conditions During the Experimental and Control Setupsa

Surface Waves Measurement Setup Viewing zenith angle-controlled Depth-controlled Day 1 Day 2 Day 3 Integration time-controlled Repeatability Reliability

Significant Height (cm)

Averaged Frequency (Hz)

Solar Zenith Angle (°)

Viewing Azimuthal Angle (°)

Wind Speed (ms⫺1)

Relative Humidity (%)

11.9–16.4

0.4–1.1

23–72

47–178

1.1–10.6

34.5–70.3

27.3–32.3 20.6–27.9 ⬍11.9

0.5–0.6 0.5–0.9 ⬎1.1

39–49

80–134

3.6–7.3

50.4–62.1

18.2–25.3 11.9–27.9

0.6–0.7 1.1–1.4

52–58 57–66 39–49

110–150 70–83 80–134

6.9 0.3 3.6–6.2

57.5 56.4 50.4–59.1

a Wind speed and relative humidity were measured on the experimental pier a few meters away from the underwater light detector. In cases where a single value rather than a range is presented, it denotes the average value of the parameter in question. No data for direct surface waves are available for the integration time-controlled setup; however, the wind speed at the time (serving as a predictor of water surface roughness) (Ref. 10) is well within the range of the experimental setups.

AltAz.html), and the average zenith and azimuthal solar angles during every 5 min recording were calculated (during the 5 min recordings, the zenith and azimuthal solar angles did not change by more than 3°). Given the solar and the detector azimuthal angles, the viewing azimuthal angle was also calculated. During all the measurements, the solar zenith angle ranged from 23° to 72°, and the viewing azimuthal angle from 42° and 178°. Taking into account the 5° acceptance angle of the detector, the maximal waves’ slope (30° off the horizon),35 and the light refraction at the water surface, the maximal angle at which the Sun would still be detectable by the detector was calculated as 45.8°. Since the scope of the current study is to examine the radiance and polarization of diffuse light only, we excluded from further analyses two measurement days (out of 12 days), in which the viewing azimuthal angle was smaller than the above maximal angle. Thus the results presented here represent exposure to diffuse light rather than direct Sun rays. For complete surface waves and meteorological conditions, see Table 1. D. Depth-Controlled Polarization Measurements

To test the dependence of surface wave-induced polarization fluctuations on the detector’s depth, we performed three series of polarization measurements at various depths. Measurements were carried out on three clear sky days during February 2004. While the detector faced a direction parallel to the waves’ propagating direction, we took measurements at four depths: 0.5, 1, 2, and 3.5 m below the sea surface (averaged depths across several waves). At each depth, measurements were performed at three viewing zenith angles: 30°, 70°, and 90°, where at each viewing zenith angle a 5 min recording was taken. Throughout all depths within each of the viewing zenith angles, the difference in the waves’ significant height between depths did not exceed 10%. Theoretically, the observed changes in the polarization with changing detector depth may be attributed to changes in the height of the water column above the detector as well as to changes in the proximity of the

detector to the sea bottom. However, since light measurements were conducted at viewing zenith angles of 90°, 70°, and 30°, any effect of proximity to the sea bottom is likely to be small. E.

Light Measurements Analysis and Statistics

To take into account the extent of light fluctuations of all frequencies (restricted by our measuring frequency) and not only light flashes produced by the focusing phenomena (see Section 1), we used the coefficient of variation (CV; standard deviation兾average).9,10 To quantify the variability in the e-vector orientation, using the CV is ineffectual due to the periodic nature of the angles; hence we used the standard deviation (SD) parameter. To compare the CV and SD of the polarization parameters between different positions of the polarization detector, the number of measurements (n), must be identical (because the calculated values of CV and SD may depend on the number of measurements). At a fixed time period, the longer the integration time, the smaller is the number of measurements. The n at the longest integration time 共200 ms兲 was chosen, and an identical number of samples were randomly taken from the raw measurements performed with the 50 ms integration time. These values of CV and SD will hereafter be referred to as “variability.” Analyses were performed on a total of over 120,000 individual polarization measurements, taken at different zenith and azimuthal solar angles, zenith and azimuthal viewing angles, and depths. The difference between the CV of the % polarization and the radiance from each day was tested using the paired t test.36 To statistically evaluate the effect of the solar zenith angle on the spectral distribution of the variability (CV) in radiance, we calculated the Pearson correlation coefficient36 between all available pairs of CV measurements (n ⫽ 10 measurements; 46 pairs). Then, we classified the data into two categories: (i) small 共n ⫽ 6兲 and (ii) large 共n ⫽ 4兲 solar zenith angles (15 and 6 pairs, respectively), and the correlation coefficient was recalculated separately for each category. Whenever the averaged correlation coefficient between all repetitions was lower than that 1 July 2006 兾 Vol. 45, No. 19 兾 APPLIED OPTICS

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calculated separately on each solar zenith angle category, the spectral distribution of the variability was assumed bimodal. A similar analysis was used to evaluate the effect of solar zenith angle on the spectral distribution of the variability regarding the % polarization and the e-vector orientation. Following Dera and Olszewski,9 and Dera and Stramski,10 we obtained the dominant frequencies of the fluctuations of each parameter at each of the examined viewing zenith angles. The spectral analysis was calculated using a Hamming weighting function,9 followed by a moving average of 50 data points smoothing. To determine the relationship between the features of the fluctuating light parameters and the various environmental conditions (as will be described in Section 3), we assumed linearity; consequently, we applied a series of multiple regression procedures. Whenever only one of the environmental parameters was found to significantly correlate with the variability or the dominant frequency of the light parameter examined, simple regression modules were applied (STATISTICA electronic manual). The residuals of all regression procedures were checked for normality, and homogeneity of variance was confirmed (using ␹2 and Cochran C tests, respectively).37 To determine the effect of depth on the variability of the fluctuating light parameters, we used factorial analysis of variance (ANOVA). Each case was checked for homogeneity of variance using the Cochran C test.37 In cases where this condition was not fulfilled, a quadratic root transformation was applied, which was followed by a factorial ANOVA. However, in cases where homogeneity of variance could not be achieved, the nonparametric Kruskal–Wallis ANOVA was used (analysis was performed on the spectrally averaged values throughout the examined spectrum).37 All statistics were performed using the STATISTICA software. F.

Integration Time-Controlled Measurements

To evaluate the potential impact of integration time on the calculated polarization parameters, we compared the integration time-controlled measurements in a single day. Measurements were taken with the polarization detector positioned parallel to the direction of the waves’ propagation, at a viewing zenith angle of 30°. At this detector position, 15 consecutive sets of measurements were performed; each incorporating a 1 min recording period at the integration times of 50 and 200 ms. This approach was applied to minimize the surface waves’ variability during each measurement set. Five-minute intervals between measurement sets enabled their range to be extended over different solar zenith angles and surface wave levels. For each of the light parameters, a calibration factor (ratio) between the variability at the two integration times was calculated for every wavelength within the range of 380–650 nm. For each light parameter, the last ratio was correlated with the light wavelength 共␭兲 and a conversion function, CV or 4730


SD ⫽ a␭b was obtained (r2 ⬎ 0.94 for all cases). This conversion function was applied to the variability calculated at an integration time of 50 ms (at the 30° viewing zenith angle only). For each integration time, the mean values of each light parameter (calculated out of the 1 min recordings) were averaged over the 15 consecutive sets. For each light parameter, after applying factorial ANOVA, the effect of the integration time on the resulting average values was examined. No significant 共p ⬎ 0.15兲 effect was found regarding the % polarization or e-vector orientation. G.

Repeatability of Polarization Measurements

To confirm the repeatability of the polarization fluctuation measurements, we performed a series of six recording periods of 5 min each. Throughout the series, the detector was parallel to the direction of the waves’ propagation at a viewing zenith angle of 30°. At every single light wavelength (10 nm intervals), the variability was averaged over the six sets. The average variability throughout the spectral range of 350–700 nm was 9.16% for the e-vector orientation, 2.7% for the % polarization, and 4.43% for the radiance, thus validating the repeatability of our method. H.

Verification of the Fluctuations’ Reliability

Theoretically, a light flicker that does not cast simultaneously on the three fibers will result in a false polarization reading. To verify that the measured fluctuations were indeed polarization and radiance fluctuations and not artifacts, we compared the two types of polarization measurements. The first type of measurement is the one applied in all experimental and control measurements previously described. It consisted of a high sampling rate with no averaging; afterward, the polarization parameters for every measurement were calculated and then averaged over 5 min. In this control setup, the radiance readings were averaged by the spectrophotometer itself, and then the polarization parameters were calculated once, using the time averaged values. As a working hypothesis, we postulated that a long sampling time (spectrometer integration time ⫻ number of averaged readings) produces stable readings, unaffected by flicker or other environmental fluctuations. If the average value of any polarization parameter over a period of high-rate measurements equals that obtained from a long-lasting polarization measurement, then the recorded fluctuations do represent the polarization ones. These control measurements were conducted for 2 days. During this time, all viewing zenith angles and depths were examined, and long measurements were performed before and after each 5 min of recording at a high rate. Throughout the spectral range of 350–700 nm, for each light parameter (e-vector orientation, % polarization, and radiance), the ratio between the two long measurements (before and after recording the high rates) was calculated. If the two measurements differed from each other by more than 20%, then they were excluded from the control analysis (17 out of 72

cases, including all measurements at a viewing zenith angle of 0°). Consequently, all measurements at a viewing zenith angle of 0° were excluded from further analyses and discussion. In a linear regression, if a long measurement equals the average of the highrate measurements, then both the slope and r2 are expected to have a value of 1. The slope between the two types of measurement, for all light parameters (throughout all examined detector depths and viewing zenith angles) was 0.97 ⫾ 0.05 (average ⫾ standard deviation; linear regression, r2 ⫽ 0.98 ⫾ 0.04, p ⬍ 0.001). Hence the long-term measurements and the average of the high-rate measurements were statistically identical, thus confirming the accuracy of the high-rate measurements. 3. Results

The radiance, % polarization, and e-vector orientation fluctuated in all viewing zenith angles. An example of a 30 s time series demonstrating deviations exceeding 60° from the time average value of the e-vector orientation and twice the time average value in % polarization is shown in Fig. 2. Polarization averaged 24% at the 70° and 30° viewing zenith angles and 33% at the 90° viewing zenith angle. Spectral effects generated up to 30% difference from the average (n ⫽ 10 days, equal depth measurements). In all viewing zenith angles, the coefficient of variation (CV) of the % polarization was significantly (t test, n ⫽ 10, p ⬍ 0.001) higher than that of the radiance (Fig. 3). Throughout the light spectrum, the variability of the light parameters was maximal at a viewing zenith angle of 70° and minimal at a viewing zenith angle of 90°. Variability of the radiance, the % polarization, and the e-vector orientation ranged between 0.004 and 0.41, 0.007 and 0.95, and 0.344° and 66°, respectively (Fig. 3). A.

Effects of the Light Wavelength

In general, at all viewing zenith angles, the variability of the light parameters varied with the light’s wavelength (Fig. 3). At a viewing zenith angle of 90° the variability of the three light parameters increased with the light’s wavelength [Figs. 4(g)– 4(i)]. At viewing zenith angles of 30° and 70°, an indication for a bimodal (according to the solar zenith angle; but see Section 4 for more details) dependence of the variability of the % polarization and the e-vector orientation on the light wavelength was noted (Figs. 3(b), 3(c), and 3(e); see Section 2 for a description of the statistical bimodal characterization). These two modes were correlated with small and large solar zenith angles: At a viewing zenith angle of 70°, the variability of the % polarization increased with the light wavelength at small solar zenith angles [Fig. 4(e)], whereas at large solar zenith angles, the maximal variability was reached in the vicinity of 500 nm. At a viewing zenith angle of 30°, and at small solar zenith angles, the variability of the % polarization and e-vector orientation [Figs. 4(b) and 4(c)] increased toward both edges of the examined spectrum

Fig. 2. A 30 s time series of high-rate (3.2 Hz) continuous measurements of the (a) raw radiance, (b) % polarization, (c) e-vector orientation. The horizontal line denotes the time averaged value of the parameter in question. The time series was taken at 600 nm, at 2 m depth with the detector facing a viewing zenith angle of 30°, a solar zenith angle of 27°, a viewing azimuthal angle of 178°.

共380–650 nm兲. At large solar zenith angles, however, a weak, if any, wavelength dependence was found. Notably, at all examined viewing zenith angles, the CV of the radiance [Figs. 4(a), 4(d), and 4(g)] increased with the light wavelength. The effects of the lighting and environmental conditions (the solar zenith angle, the viewing azimuthal angle, the significant wave height, and the waves’ dominant frequency) on the light fluctuating parameters were examined using a series of multiple regression procedures. B.

Effects of Sun Position

In all cases the dependence of the light parameters’ variability on the solar zenith angle was positive. That is, the variability increased as the solar zenith angle increased (see Section 4 for further details). At viewing zenith angles of 70° and 90°, the solar zenith angle significantly (p ⬍ 0.05, Table 2) affected the 1 July 2006 兾 Vol. 45, No. 19 兾 APPLIED OPTICS

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Fig. 3. Variability of the radiance, % polarization, and e-vector orientation as a function of the viewing zenith angle (30°, 70°, and 90°) and light wavelength (380 – 650 nm), taken during 10 measurements days.

variability of the radiance and polarization. This holds for six representative light wavelengths (between 400 and 650 nm) as well as the average variability throughout the spectrum. Yet, at a viewing zenith angle of 90°, a significant (p ⬍ 0.05, Table 2) dependence of the radiance CV on the solar zenith angle was found, only in three of the examined wavelengths. Apart from the polarization variability at a light wavelength of 500 nm, at a viewing zenith angle of 30°, no significant dependence of the light variability on the solar zenith angle was found (p ⬎ 0.05, Table 2). C. Effects of the Surface Waves’ Frequency and Significant Wave Height

For all light parameters, whenever a dependency between the average frequency of the surface waves and the dominant frequency of the fluctuations was revealed, it was a positive one (Table 3). More specifically, the dominant frequency of the fluctuating light parameters increased as the frequency of the surface waves increased. At a viewing zenith angle of 70°, the correlation between the dominant frequencies of the fluctuating light parameters and the frequencies of the surface waves was the most striking, and it was spectrally broad (Table 3). At that viewing zenith angle, the ratios between the frequencies of the light fluctuations and the frequencies of the surface waves were smaller than 1 (ranging from 0.32 to 0.46). Hence the frequencies of the light fluctuations were smaller than those of the surface waves. At a viewing zenith angle of 30°, the dominant frequency of the 4732


radiance fluctuations depended on the surface waves’ average frequency, and the ratios between both frequencies were larger than 1 (ranging from 1.79 to 2.95), meaning that the frequencies of the light fluctuations were larger than those of the surface waves. However, at a viewing zenith angle of 30°, the dominant frequency of the polarization fluctuations did not depend on the frequency of the surface waves. At a viewing zenith angle of 90°, the dependence between the frequencies of the light fluctuations and those of the surface waves was not consistent throughout the examined light spectral range (Table 3). Moreover, the variability of radiance fluctuations at a viewing zenith angle of 70° was also found (besides being contingent on the solar zenith angle) to depend on the significant wave height (F2,7 ⫽ 9.45–17.12, p ⬍ 0.01, r2 ⬎ 0.71; for all examined wavelengths, see Table 2). D.

Effects of Depth

At viewing zenith angles of 30° and 70°, the variability of the three light parameters significantly (p ⬍ 0.001, Fig. 5) decreased with the detector’s depth. At the viewing zenith angle of 90°, no significant (p ⬎ 0.05, Fig. 5) effect of the detector’s depth on the CV of the light parameters was found. The latter was true for the cases involving % polarization and radiance; notably a positive and significant 共p ⬍ 0.05兲 dependence between the detector depth and the SD of the e-vector orientation was found. However, when the two longest wavelengths 共600 and 650 nm) were excluded from the analysis, no

Fig. 4. Average (⫾ standard deviation) of the normalized variability of the light parameters as a function of the viewing zenith angle and the light’s wavelength. Repetitions were divided into two groups based on the solar zenith angle. The first group (Œ, n ⫽ 4) incorporated repetitions taken at large solar zenith angles (54°–72°) while the second group (, n ⫽ 6) included repetitions performed at small solar zenith angles (23°– 43°). Variability values were normalized by division to the average calculated throughout the spectrum. In (a), (b), and (e) the dependence on the light’s wavelength was statistically shown to be bimodal (see Section 2 in text).

significant (p ⬎ 0.05, Fig. 5) effect of the detector’s depth on the SD was noted. The surface waves’ amplitude (during the three days of measurement) was 8.49 ⫾ 3.72 cm (average ⫾ standard deviation). 4. Discussion

The radiance, % polarization, and e-vector orientation fluctuated with time. For all light parameters,

the variability of these fluctuations depended on the viewing zenith angle. This was true for the absolute values of the variability (Fig. 3), as well as for the spectral distribution of the light’s variability (Fig. 4). At viewing zenith angles of 30° and 70°, the variability of the light parameters decreased with increasing depth [Figs. 4(a)– 4(f)]. At a viewing zenith angle of 90°, conversely, this variability was depth indepen-

Table 2. Correlation Between the Solar Zenith Angle and the Variability of the Light Parametersa

Parameter Radiance

Percent polarization

e-vector orientation

Viewing Zenith Angle (°)

400 nm

450 nm

500 nm

550 nm

600 nm

650 nm

Average

90 70 30 90 70 30 90 70 30

ns 0.71# * ns ns 0.63 * ns 0.46 * * ns

0.67 * 0.77# * ns 0.63 * 0.77 ** ns 0.38 * 0.72 * ns

ns 0.73# * ns 0.4 * 0.84 ** 0.32 * 0.53 * 0.62 * 0.36 *

0.65 * 0.8# * ns 0.82 ** 0.8 ** ns 0.53 * 0.75 * ns

ns 0.74# ** ns 0.84 ** 0.7 ** ns 0.63 * 0.55 * ns

0.56 * 0.67# * ns 0.82 ** 0.75 * ns 0.59 * 0.69 * ns

0.65 * 0.76# * ns 0.79 ** 0.79 ** ns 0.69 * 0.77 ** ns

a For each parameter, a linear regression was performed for three viewing zenith angles (30°, 70°, and 90°) for the variability at six representative light wavelengths and for the averaged variability throughout the spectrum. The results of a simple regression between the light variability and the solar zenith angle are listed. However, in instances where a multiple regression among the light variability, the solar zenith angle, and the significant wave height value was found to be significant (indicated by #), the corresponding results are given. Numbers indicate the r2, n ⫽ 10 measurement days, p ⬍ 0.05 and p ⬍ 0.001 marked with * and **, respectively; ns, not significant.

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Table 3. Correlation Between the Surface Waves’ Averaged Frequency and the Dominant Frequency of the Fluctuations in Light Parametersa

Parameter Radiance

Percent polarization

e-vector orientation

Viewing Zenith Angle (°) 90 70 30 90 70 30 90 70 30

400 nm ns 0.43 1.79 0.42 0.38 ns 0.42 0.34 ns

* * * * * *

450 nm

500 nm

550 nm

600 nm

650 nm

0.42 ** 0.44 ** 2.68 ** 0.43 * 0.4 * ns ns 0.32 * ns

0.34 * 0.39 * 2.69 ** ns 0.4 * ns ns 0.32 * ns

0.29 * 0.39 * 2.7 ** ns 0.4 * ns ns 0.33 * ns

ns 0.44 * 2.79 ** ns ns ns ns 0.32 * ns

ns 0.46 * 2.95 ** ns ns ns ns 0.32 * ns

a For each parameter, a linear regression was performed for three viewing zenith angles (30°, 70°, and 90°) at six representative light wavelengths. The values in the table represent the slope of the regression line. n ⫽ 10 measurement days, p ⬍ 0.05, and p ⬍ 0.001 marked with * and **, respectively; ns, not significant.

dent [Figs. 4(g)– 4(i)]. Additionally, at viewing zenith angles of 70° and 90°, the variability of the light parameters was affected by the solar zenith angle and was greatest at large solar zenith angles. Yet at a viewing zenith angle of 30°, this variability was independent of the solar zenith angle. At a viewing zenith angle of 70°, the dominant frequency of the light fluctuations was positively affected by the surface waves’ frequencies (Table 3). Additionally, the

dominant frequency of the radiance fluctuations also depended on the waves’ average frequency at a viewing zenith angle of 30°. A.

Limitations of the Experimental Setup

Our system was limited to measuring frequencies of 1.7–3.2 Hz (depending on the radiance levels). It is likely that using faster polarization detectors, future studies will yield better descriptions and insights into

Fig. 5. Effects of water depth on the variability of the radiance, % polarization, and e-vector orientation, as a function of the viewing zenith angle and the light wavelength. Each point represents the average (⫾standard deviation) of the variability of the light parameters during 3 days of measurement at depths of 0.5 m (), 1 m (Œ), 2 m (), and 3 m (ⵜ). At viewing zenith angles of 30° and 70°, variability was negatively correlated with depth (30°, ANOVA for radiance and % polarization, and ANOVA preceded by quadratic root transformation for e- vector orientation, F3,56 ⫽ 9.38, 8.83, and 26.23 for radiance, % polarization, and e-vector orientation, respectively. p ⬍ 0.001 for all cases; 70°, ANOVA preceded by quadratic root transformation, F3,56 ⫽ 14.34, 36.94, and 49.53 for radiance, % polarization, and e-vector orientation, respectively). At a viewing zenith angle of 90° no significant correlation between depth and the variability of the light parameters was found (nonparametric ANOVA, Kruskal–Wallis, H3,12 ⫽ 6.43, 2.07, and 2.69, p ⬎ 0.09, 0.5, and 0.4 for radiance, % polarization, and e-vector orientation after excluding 600 – 650 nm wavelengths, respectively). 4734


the dynamics of the underwater polarized light field. A more sensitive and faster spectrophotometer would be needed to achieve a greater measuring frequency. The measuring and calculation procedures applied in this study may misrepresent the properties of the high-frequency light flashes caused by sunlight focusing at the water surface.12,13 However, the overall variability in the diffuse light field induced by gravity waves (the average frequency of the waves during all measurement days ranged from 0.4 to 1.4 Hz) is indeed adequately represented and described. The maximal contrast sensitivity of many marine animals occurs between the frequencies of 2 to 18 Hz.38 Hence the measuring frequencies applied here are relevant to animal vision, at least for the lower end of their contrast detection frequency range. In our measurement setup, the detector was pointing toward a direction parallel to the waves’ propagation. Hence the solar zenith angle was negatively correlated (Pearson correlation, r ⫽ ⫺0.97, n ⫽ 10) with the solar azimuthal angle. That is, with increasing solar zenith angle, a decrease in the solar azimuthal angle occurred as well. The only way to overcome such a correlation was to neglect the confinement of pointing the detector toward a constant direction relative to the waves, which is certainly undesirable. Therefore our results concerning the dependence of the light variability on the solar zenith angle actually represent the dependence of the light variability on the combined effect of the solar zenith angle and the solar azimuthal angle. B.

Radiance Fluctuations

Since no previous data regarding the fluctuations of the underwater light polarization were available, the findings regarding radiance fluctuations will be discussed first. However, here again current knowledge concerning radiance fluctuations is almost absent. Previous investigations of radiance fluctuations induced by surface waves concentrated mainly on the downwelling and upwelling light fields and were conducted at a fixed solar zenith angle.15,16 Here we compare previous reports on the downwelling radiance and our results at a viewing zenith angle of 30°, and similarly between the upwelling radiance and our results concerning the 90° viewing zenith angle. This comparison is justified since both an upward angle and a viewing zenith angle of 30° are located within Snell’s window, and conversely, both a downward angle and a viewing zenith angle of 90° are constantly outside Snell’s window. Similar to the CV of the upwelling radiance fluctuations,4 the CV of the radiance fluctuations at all examined viewing zenith angles increased with an increase in the light’s wavelength [Figs. 3(a), 3(d), and 3(g)]. The average coefficients of variation (over the 3 days of measurements) of radiance fluctuations at viewing zenith angles of 30° and 70° were found to decrease with depth. However, when examining the dependence of the coefficient of variation on depth during each day separately, one encounters a few maxima in the coefficient of variation of the downwelling radi-

Fig. 6. Coefficient of variation at 500 nm of the radiance fluctuations as a function of detector depth at viewing zenith angles of (a) 30°, (b) 70°, (c) 90°. The surface waves’ averaged frequencies equaled 0.59, 0.56, and 1.12 Hz during days 1, 2, and 3, respectively. During days 1 and 2, when the surface waves’ average frequencies were nearly similar, the coefficient of variation varied with depth similarly. However, during day 3, when the surface waves’ averaged frequency was different, the highest coefficient of variation was attained at different depths.

ance fluctuations (Fig. 6). This is in agreement with Yakubenko and Nikolayev,15 who suggested that each maximum arises as a result of the focusing of light by surface waves of a certain frequency. Measuring at a fixed solar zenith angle, Nikolayev and Yakubenko,16 found the coefficient of variation of the radiance fluctuations in the plane of the solar vertical to decrease with increasing angle between the solar and the viewing zenith directions. This is contrary to our results where, regardless of the solar zenith angle, the highest CV of the radiance was achieved at a viewing zenith angle of 70°. This discrepancy may result from the 1 July 2006 兾 Vol. 45, No. 19 兾 APPLIED OPTICS

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different measuring depths between the current study and Nikolayev and Yakubenko,16 and consequently from the different influence of the motion of Snell’s window on the radiance fluctuations, discussed in detail in Subsection 4.E. Taken together, the agreement between our results and previously reported results supports and reconfirms the measuring procedures used in this study. As previously mentioned, while radiance fluctuations were relatively poorly examined in situ, to date, the polarization fluctuations have not been investigated. C. Polarization Fluctuations

Throughout the day, due to the changing solar zenith angle, the underwater light polarization systematically changes.20,25,39 – 41 At a fixed solar zenith angle, the orientation at which the light ray refracts into the water varies due to the wave-induced curvatures of the water surface. Light scattering that presides over the underwater light polarization18 depends on the orientation of the incoming light. Therefore scattering and polarization are expected to deviate when variations are induced by surface waves. D. Effects of Light Scattering

Light scattering within the water diminishes the extent of the light focusing phenomena and thus reduces the dominant frequency of the induced fluctuations.1,10,12,15,16 Since scattering is a function of the optical path length, as the viewing zenith angle increases, the optical path length and scattering increase. At shallow depths, this scattering effect may account for the low dominant frequency (relative to the surface waves’ averaged frequency) of the light fluctuations at the viewing zenith angle of 70°. At a viewing zenith angle of 90°, where the optical path length approaches effective infinity (where all the light reaching a detector has been scattered at least once), the dominant frequency of the fluctuations of the lights’ parameters is independent of the surface waves’ frequencies. Note that in contrast to the dominant frequencies of the radiance fluctuations that significantly depend on the average frequencies of the surface waves at viewing zenith angles of 70° and 90°, with polarization fluctuations such a dependency was found only with a viewing zenith angle of 70°. This is probably the result of the greater effect of refraction at the water surface and scattering within the water on the light polarization than on the radiance. This may also account for the significant relationship between the significant wave height value and the radiance variability only (Table 2). As we go deeper, the optical path length at smaller viewing zenith angles will approach effective infinity, and the dominant frequency of the fluctuations of the lights’ parameters will become independent of the surface waves’ frequencies as well. Similarly, at viewing zenith angles of 30° and 70°, with increasing depth, the variability of the light fluctuations is reduced. Snyder and Dera,1 Dera and Olszewski,9 Dera et al.,12 and Prokopov et al.6 found a similar trend when examining downwelling irradiance at depths 4736


exceeding 1 m. At a viewing zenith angle of 90°, the variability of the light parameters is independent of the detector’s depth, since the effective optical path length and the scattering are constant. With depth, the variability at the 70° viewing zenith angle is predicted to equal that of the viewing zenith angle of 90°. Using exponential regression and extrapolation of the diminished variability with depth, for each of the light parameters the effective path length in which the light’s variability at the 70° viewing zenith angle equals that of the 90° viewing zenith angle was calculated for the examined light wavelengths. This distance is 11–13 m (3.8–4.5 m deep) for the water conditions under which we worked, where visibility estimated while scuba diving ranged between 10 and 15 m. E. Effects of Internal Reflection and the Motion of Snell’s Window

If the line of sight is located outside the average value of Snell’s window, then internal reflections off the ever-altering water surface increase the variability of the light fluctuations. Since the central axis of Snell’s window is always perpendicular to the water surface, Snell’s window continuously moves along with the motion of the surface waves. Consequently, although fixed in space, the line of sight of a detector and兾or observer may move into and out of Snell’s window. Assuming that the maximum possible slope of surface waves is 30° off the horizon (taking the minimum angle of a wave’s peak to equal 120°),35,42 we can calculate the angular range at which movements into and out of Snell’s window are possible to extend from 18.6° to 78.6° from the zenith. With decreasing viewing zenith angle, the probability of the line of sight to be within Snell’s window increases. This phenomenon may explain the high variability of all light parameters at a viewing zenith angle of 70°, where Snell’s window is rarely looked into, and the low variability at a viewing zenith angle of 30°, which involves mostly examining it. With increasing depth, the light’s path length increases, and both the light’s polarization23 and radiance43 are attenuated, leading to a reduction in the angular diameter of the effective Snell’s window. Furthermore, because of this attenuation, internal reflection outside Snell’s window influences the light’s polarization and radiance only near the water surface.17,18 F. Effects of Absorption and Scattering on the Spectral Distribution of Light Fluctuations

The change in the orientation of a light beam following refraction at the air–water interface may lead to a change in the path length the light propagates within the water until it reaches the light detector. Thus refraction at an undulated air–water interface results in a variation in these path lengths. Along the path the light propagates, it experiences scattering and absorption by molecules and particles of various sizes, shapes, refractive indices, and colors. Therefore variation in the light’s path length may result in varying influences of scattering and absorption. The highest variability of

the radiance fluctuations is expected to occur at the spectral range that is most susceptible to absorption or scattering. Consequently, absorption by seawater that is most intense at the red spectral range43 may explain the increase in the variability of the radiance and polarization fluctuations with wavelength (Fig. 4). The bimodal spectral distribution of the variability of the polarization fluctuations (at viewing zenith angles of 70° and 30°) may probably be explained by the complex relationships between the spectral variations of absorption and scattering. However, to the best of our knowledge, no such mechanism is currently available. G. Effects of the Solar Zenith or Azimuthal Angles

The polarization and radiance fluctuations outside Snell’s window (viewing zenith angles of 70° and 90°) increased with increasing solar zenith angle (Table 2). No detailed mechanism is currently available to explain the relationship between the solar zenith angle and the light variability. However, changes in the solar zenith angle were shown to negatively correlate with the solar azimuthal angle. Changes in these two angles act oppositely on the path length the light propagates within the water. An increase in the solar zenith or azimuthal angles yields an increase in the light’s path, which, due to scattering, is expected to diminish the variability of the radiance and polarization fluctuations. Thus the decrease in the solar azimuthal angle may be coupled with an increase in the solar zenith angle that can lead to an increase in the radiance and polarization variability. Understanding the independence of the variability of light fluctuations within Snell’s window (viewing zenith angle of 30°) on the solar zenith and兾or azimuthal angles awaits future study. H. Implications for Animal Vision

Polarization sensitivity has been demonstrated in numerous marine animals.18,44,45 Using the underwater polarization patterns, polarization-sensitive animals orient themselves,46 –51 escape off shore,26,52,53 break the countershading of light-reflecting silvery fish,54,55 and detect transparent prey.56,57 Marine animals experience an ever-changing light regime. So far, in examining polarization sensitivity, researchers have made great effort to produce a stable polarized light field and to eliminate any fluctuations in it.47,52,55–58 However, fluctuations in light can benefit animals capable of utilizing them. Many organisms search for prey at a horizontal or a somewhat elevated line of sight.19 Therefore when examining predator–prey interactions, the light fluctuations of the quasi-horizontal plane are of importance. Indeed, McFarland and Loew38 found a correlation between the dominant frequencies of wave-induced light fluctuations and the frequencies of maximal contrast sensitivity of many aquatic animals, suggesting that surface waves may enhance the visibility of underwater targets. In the featureless pelagic light field, camouflage is often based on transparency59 or background matching using reflecting surfaces.54 Polariza-

tion sensitivity,55–57 along with UV vision,60,61 was found to be involved in abolishing both types of camouflage. Marine animals can use radiance flicker to enhance the detection of targets.38 Since the variability of the % polarization is greater than that of the radiance, object polarization flicker will be more pronounced than that in radiance. Thus polarization sensitivity can enhance the conspicuousness and detectability of both transparent and reflecting objects. Grass shrimps52,53 and salmonids,50,51 which utilize the underwater polarization in orientation and as a navigational cue, do so in shallow waters, where light fluctuations are high. Since the light’s e-vector orientation fluctuates around its time averaged value, an animal needs to use polarization time averaging in order to obtain a reliable navigational cue. The mechanisms allowing polarization averaging and the specific time scales involved have not yet been identified. We thank R. Goldshmid, S. Einbinder, Y. Belmaker, S. Manor, and R. Kent for underwater and technical help; A. Rivlin for writing LabView applications for polarization calculations; I. Lerer, M. Ohavia, and E. Sarfati for constructing the detector’s anchoring and rotating apparatus; R. Holzman, S. Rickel, A. Genin, M. Kiflawi, and two anonymous reviewers for statistical advice and helpful comments; and E. Boss, C. Erlick, and T. W. Cronin for enlightening discussions. This research was supported by Binational Science Foundation grant 1999040, Israeli Science Foundation grant 550兾03, and the Ring Foundation.

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