Radiance fluctuations induced by surface waves can enhance the appearance of

underwater objects

Shai Sabbah,a,* Suzanne M. Gray,a,b and Craig W. Hawryshyn a

a Department of Biology, Queen’s University, Kingston, Ontario, CanadabDepartment of Biology, McGill University, Montreal, Quebec, Canada

Abstract

To examine the effect of wave-induced light fluctuations on the appearance of objects to fish, we recorded thespatial and temporal fluctuations of light reflected from a diffusely reflecting target that served as a simplifiedproxy for the body of a fish, and of light from the water background that a fish might be viewed against.Measurements were repeated at diverse depths, viewing azimuths, distances to the substrate, and sun conditions.Two conditions that are necessary for wave-induced light fluctuations to make objects more apparent to fish weresatisfied. The contrast of light fluctuations reflected from either the object or water background was higher thanthe minimum contrast value that is detected by fish, or, alternatively, the contrast of light fluctuations reflectedfrom both the object and water background was higher than the minimum contrast value detected by fish, butdiffered from one another. Furthermore, the frequency range where most of the power of wave-induced radiancefluctuations matched the frequency range of maximum contrast sensitivity in fish. Thus, light stimuli havingspatial and temporal characteristics similar to those of wave-induced light fluctuations may make objects moreapparent to fish. We suggest that the frequency characteristics of the visual systems of fish were likely shaped bywave-induced light fluctuations in aquatic ecosystems.

Variability is one of the most distinctive and oftenignored features of the underwater light field. Thisvariability in photon flux, directionality, spectra, andpolarization diverges in magnitude and timescale, rangingfrom seasonal, through diurnal, to short-term fluctuationslasting less than a second. In shallow water, surface wavesare the principal cause for short-term variation in theunderwater light (Snyder and Dera 1970; Dera andOlszewski 1978; Zaneveld et al. 2001). This variation arisesas a result of focusing and defocusing of sunlight raysrefracted at the water surface, producing spatial andtemporal light fluctuations (Schenck 1957; Snyder andDera 1970; Stramski and Dera 1988). These fluctuations inunderwater light were suggested to influence the visibilityof submerged objects (McFarland and Loew 1983; Loewand McFarland 1990). However, this possibility has not yetreceived adequate attention.

Contrast sensitivity (CS) is the relative detectionefficiency of contrast between light stimuli as a functionof their frequency of modulation. The contrast betweenlight stimuli is commonly estimated as the Michelsoncontrast (Lmax 2 Lmin)/(Lmax + Lmin), where Lmax and Lmin

are the maximum and minimum radiance in the stimulus,respectively (Michelson 1920). Visual systems have acharacteristic frequency at which spatially or temporallymodulated light stimuli are best detected (Kelly 1972;McFarland and Loew 1983; Douglas and Hawryshyn1990). This is the frequency at which spatial or temporalCS is highest. The frequency of maximum CS depends onthe adaptation state of the eye (i.e., adjustment of the eyesensitivity to the background light), the mean intensity ofthe modulated light stimulus, and the visual angle

subtended by the stimulus beam (Northmore and Dvorak1979; Bilotta and Powers 1991; Bilotta et al. 1998). As themean intensity of the light stimulus decreases, CS decreasesand the frequency of maximum CS shifts to lower values.In goldfish (Carassius auratus), for example, the frequencyof maximum spatial CS was found to be 0.2 cycles degree21

(c degree21) with an intense light stimulus, but only 0.05 cdegree21 with a dim light stimulus (Bilotta and Powers1991). Similarly, the frequency of maximum temporal CSwas found to be 2 Hz with an intense light stimulus, butonly 0.5 Hz with a dim light stimulus (Bilotta et al. 1998).Comparable values of the frequency of maximum CS offish were reported in several other studies (Table 1).Consequently, for a fish to achieve high CS under a rangeof light intensities (e.g., throughout the day), the spatialand temporal frequencies of the stimulus should be lowerthan 0.4 c degree21 and 2 Hz, respectively. Nonetheless, thefrequency of maximum spatial or temporal CS typicallyequals 10–20% of the frequency at which spatially ortemporally modulated light stimuli appear to fuse (North-more and Dvorak 1979; Laughlin 1981; Northmore et al.2007). Thus, frequencies higher than the frequency ofmaximum CS may still provide high enough contrast to beefficiently used by the fish.

Another attribute of visual systems is the minimumcontrast threshold (MCT). MCT (1/CS) is a measure of thejust-detectable contrast value (i.e., the smallest detectabledifference between light stimuli). As the mean intensity ofthe light stimulus decreases, MCT of fish increases (Bilottaand Powers 1991; Bilotta et al. 1998). For light intensities inthe photopic range, MCT was reported to be 0.039 and0.032 for spatial and temporal contrast, respectively(Bilotta and Powers 1991; Bilotta et al. 1995). If thecontrast between light stimuli exceeds MCT, the spatial andtemporal modulation between stimuli would be detected by* Corresponding author: shai.sabbah@queensu.ca

Limnol. Oceanogr., 57(4), 2012, 1025–1041

E 2012, by the Association for the Sciences of Limnology and Oceanography, Inc.doi:10.4319/lo.2012.57.4.1025

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the viewer. That is, an object reflecting radiance with suchmodulation would flicker and show a spatial pattern.

The underwater environment often presents the viewerwith a problem of object detection at low contrast (Lythgoe1979). That is, the radiance contrast between an object andits background is near threshold and the probability ofobject detection is low. Under such conditions, periodicchanges in the retinal image, necessary for perception(Riggs et al. 1953), would render the object more apparent(McFarland and Loew 1983). Underwater, these spatialand temporal periodic changes in the retinal image can begenerated by radiance fluctuations produced by surfacewaves. Specifically, enhancement of object appearancemight occur if the contrast within either the object or thebackground exceeds MCT. Then, the spatial and temporalradiance fluctuations reflected from either the object or thebackground are detected by the viewer (either the object orbackground would appear to flicker and show spatialmodulation). Enhancement of object appearance mightalso occur if both the contrasts within the object and thebackground exceed MCT but differ from one another.Then, an object whose contrast just exceeds thresholdwould be less apparent than an object whose contrastexceeds threshold to a greater extent. Therefore, twoconditions should be satisfied for wave-induced radiancefluctuations to enhance the appearance of objects: Thecontrast of either the object or water background is higherthan the MCT of the fish, or alternatively, the contrast ofboth the object and water background is higher than MCTbut differ from one another; and the frequency range wheremost power of wave-induced radiance fluctuations is foundmatches the frequency range of maximum CS in fish.

Light enters the water through Snell’s window, which,adjacent to a flat water surface, possesses a cone shape of48.6u around the zenith from the perspective of anunderwater observer (Lythgoe 1979). However, due to the

roughness of the water surface, the edges of Snell’s windoware dynamic (Preisendorfer and Mobley 1986). Yet, in thecommon situation where an object is viewed on ahorizontal line of sight, light within Snell’s window (bestrepresented by sideward irradiance) illuminates the object,viewed against the relatively dark background of waterfound outside of the window (best represented by sidewardradiance) (McFarland and Munz 1975; Janssen 1981).Since direct sunlight is better represented within Snell’swindow than outside of it, one would expect that lightfluctuations produced by the focusing phenomenon wouldbe more pronounced within Snell’s window than outside ofit. In the case of a fish viewing another fish (e.g., in thecontext of predation), the prey fish (object) would beilluminated by spatially and temporally modulated lightand viewed against the relatively uniform water back-ground. This expectation was suggested, but not confirmed(Loew and McFarland 1990).

The characteristics of wave-induced temporal fluctua-tions in downward irradiance have been studied extensive-ly. Frequency and intensity of irradiance flashes (exceeding1.5 of time-averaged irradiance) are typically greatest underlight winds (2–5 m s21) (Dera and Stramski 1986; Stramski1986b; Dera et al. 1993), and decrease with increasing solarzenith angle (Stramski 1986b; Dera et al. 1993), diffusenessof celestial irradiance (Stramski 1986a,b; Dera et al. 1993),and depth (Stramski 1986b; You et al. 2010; Gernez et al.2011). The distribution of the duration of these irradianceflashes shifts toward longer values with increasing windspeed (Dera and Stramski 1986; Stramski 1986b) and depth(Stramski and Dera 1988; You et al. 2010). Additionally,the coefficient of variation (CV) of downward irradiancefluctuations is typically greatest under light winds (Gernezand Antoine 2009; Darecki et al. 2011), and decreases withincreasing solar zenith angle (Gernez and Antoine 2009)and depth (Stramska and Dickey 1998; Darecki et al. 2011),

Table 1. Frequency of maximum (A) spatial and (B) temporal contrast sensitivity for fish in the literature.

Species Frequency (c degree21) Contrast threshold* Intensity (cd m22){ Reference

(A) Spatial variation

Bluegill sunfish{ 0.4 0.03 25 Northmore et al. 2007Goldfish1 0.3 0.024 5 Northmore and Dvorak 1979Goldfish 0.2 0.01 10 Bilotta and Powers 1991Goldfish 0.1 0.039 1023 Bilotta and Powers 1991Goldfish 0.05 0.126 1025 Bilotta and Powers 1991Goldfish 0.2 0.005 10 Bilotta et al. 1995

(B) Temporal variation

Frequency (Hz) Contrast threshold Intensity (cd m22) Reference

Goldfish 2 0.011 10 Bilotta et al. 1998Goldfish 2 0.017 1021 Bilotta et al. 1998Goldfish 1 0.032 1023 Bilotta et al. 1998Goldfish 0.5 0.042 1024 Bilotta et al. 1998Goldfish 0.5 0.079 1025 Bilotta et al. 1998

* The just-distinguishable contrast value. Corresponding to the inverse of the peak of the contrast sensitivity function.{ Light intensity under which experiment was conducted. Light intensities greater than 1023 cd m22 are in the photopic or cone-dominated region of

goldfish vision (Bilotta and Powers 1991; Bilotta et al. 1995).{ Bluegill sunfish—Lepomis macrochirus.1 Goldfish—Carassius auratus.

1026 Sabbah et al.

and toward short light wavelengths (Gernez and Antoine2009; Darecki et al. 2011).

On the other hand, the characteristics of temporalfluctuations in radiance were relatively poorly studied thusfar. The frequency of downward radiance fluctuationstypically varies with surface wave characteristics (Niko-layev and Yakubenko 1978b), and viewing zenith andazimuthal angle (Yakubenko et al. 1974; Nikolayev andYakubenko 1978a; Darecki et al. 2011), whereas the CV ofdownward radiance fluctuations varies with viewing zenithangle (Darecki et al. 2011), and decreases with increasingdepth and toward short light wavelengths (Yakubenko andNikolayev 1978; Stramska and Dickey 1998; Sabbah andShashar 2006). Studies examining the wave-induced spatialand temporal radiance fluctuations on a horizontal line ofsight, which might be closely related to the radiancefluctuations experienced by fish that detect visual stimuliacross a restricted visual angle, are lacking (McFarland andLoew 1983; Loew and McFarland 1990; Darecki et al.2011).

In this study, we recorded the spatial and temporalfluctuations of radiance reflected from a diffusely reflectingtarget that served as a simplified proxy for the body of afish, and of radiance from the water background that a fishmight be viewed against. We addressed the followingquestions: (1) What is the frequency and contrast ofradiance fluctuations that are reflected from the body offish and from the water background? (2) How do thefrequency and contrast of these radiance fluctuationschange with water depth, viewing azimuth (azimuthal anglefrom the sun), proximity to substrate, and sun condition(sun visible or obscured)? and (3) What are the implicationsof wave-induced radiance fluctuations for the appearanceof objects? Our results suggest that light stimuli that showspatial and temporal characteristics similar to those of thewave-induced radiance fluctuations could significantlyenhance the appearance of underwater objects.

Methods

Study site—The study was conducted between 18 July2008 and 23 July 2008 at a nearshore site at Cape Maclear,Nankumba Peninsula, Lake Malawi. The sampling site(14u01926.420S, 34u49925.910E) was located on the southernshore of Thumbi West Island. This site is exposed to windand wave action (Ribbink et al. 1983) and has a rock–sandtransition depth of approximately 12 m.

Spatial radiance variation—Measurement setup: A metalframe holding a white Teflon board (60 3 22 3 0.7 cm;henceforth ‘‘target’’) and a still digital camera (PowerShotG9, Canon) was mounted on a 1-m-tall tripod. The camerazoom (focal length 5 9 mm) was adjusted so that the target(1 m away) filled the bottom half of the image and thebackground water filled the top half of the image. Thus,each image included a representation of the wave-inducedspatial patterns reflected from the target and from thewater background on a horizontal line of sight (viewingzenith angle h 5 90u). Thirty images were acquired duringeach measurement set. Measurement sets acquired at

different sampling rates, sun conditions, depths (z), viewingazimuths (W), or distances to the substrate (d) constituted asequence, e.g., a depth sequence. Considering the smalldistance between the camera and the target, the degrada-tion of high spatial frequencies of the reflection pattern andthe attenuation of light through water were assumed to benegligible. Images were taken in ‘‘manual’’ mode with‘‘daylight’’ white balance settings. For each sequence, thecamera was set at the highest possible shutter speed thatallowed for a correct exposure in the dimmest set in asequence (e.g., greatest depth). The aperture (f-number)was adjusted for each set to ensure optimal exposure of theentire image. All aperture settings used (f-number 2.8–8)were capable of diffraction-limited performance of at least22 c degree21 for wavelengths between 400 and 700 nm.Therefore, variation in aperture settings likely had anegligible effect on the spatial frequencies of interest (0.1–0.4 c degree21; Table 1). To eliminate any in-camera imageprocessing, images were captured and saved as uncom-pressed and unprocessed raw image files.

The spatial characteristics of the target reflection patternand the water background were examined with respect tothe following parameters. Sampling rate: shutter speed 1/200, 1/400, 1/800, and 1/1600 s (W 5 180u, z 5 1 m, d 5100 cm); sun condition: with the sun obscured by clouds andwith the sun exposed (W 5 180u, z 5 1 m, d 5 100 cm);distance to substrate: 20 and 100 cm (W 5 180u, z 5 1 m);viewing azimuth: 0u, 90u, 135u, and 180u (z 5 1 m, d 5100 cm); and water depth: 1, 3, and 5 m (W 5 180u, d 5100 cm; depth range limited by the camera sensitivity). Forall measurements, a scuba diver positioned at the tripodoperated the camera. Fig. 1 shows a schematic of themeasurement setup.

Processing experimental reflection images: RGB (red,green, blue) raw color images (3000 3 4000 pixels) wereconverted to tagged image file format without anypostprocessing or filtering and were cropped to eliminatethe metal frame holding the target (resulting in images of2880 3 3606 pixels). RGB images were split into their R, G,and B channels (Fig. 2). For each channel image, a value of0 (black) was assigned to all pixels that exhibited brightnessvalues smaller than 5 or larger than 250. Exclusion of pixelsthat exhibited boundary values (where deviation from thetypical intensity–response relationship may occur) fromfurther analysis served to increase the reliability of theimages for acting as brightness counts.

Using the following equations, every pixel value of eachchannel image was linearized based on the intensity–response relationship of the camera, and pixel values ofthe red and blue channels were equalized relative to theresponse of the green channel (Stevens et al. 2007),

p̂pR~qR aR|krð Þ ð1Þ

p̂pG~aG|kg ð2Þ

p̂pB~qB aB|kb� �

ð3Þ

where qR 5 1.0198 and qB 5 1.023 stand for the equalizingfactors for the R and B channels, respectively; aR 5 16.96,

Surface wave-induced light fluctuations 1027

aG 5 16.49, and aB 5 17.16 stand for the channel-specificconstants for the R, G, and B channels, respectively; k 51.007 is a camera-specific constant; and r, g, and b stand forthe pixel values of the R, G, and B channels, respectively.

Linearized and equalized images included in eachmeasurement sequence were standardized for exposure tocorrect for differences in the aperture settings used.Specifically, the amount of light captured by the cameralens is proportional to the area of the aperture (A) and wascalculated as:

A~pf

2N

� �2

ð4Þ

where f is the focal length of the camera lens and N is the f-number. Thereafter, the exposure of each image wascalculated by dividing the area of the aperture by theshutter speed. Since the camera lens collected light across arestricted acceptance angle, pixel values could be regardedas relative radiance values (Stevens et al. 2007).

For each channel image, a row pixel vector (3606 pixels)was extracted from the top half of the image (representingthe water background radiance) and from the bottom halfof the image (representing the target radiance). These pixelvectors were chosen such that they did not include anypixels of zero value. See Fig. 3A for an example of a spatialpixel vector of radiance reflected from the water back-ground and the target.

Camera intensity–response calibration: To determine theintensity–response curve of the camera, images of agrayscale standard chart (GretagMacbethTM Color-Checker, Edmund Optics) were acquired, and the responseof each of the R, G, and B channels was evaluated. Thechart was placed outdoors, and six images were acquiredwith the chart aligned vertically and facing the sun. Foreach image and grayscale standard (nominal reflectance:0.2, 0.35, 0.5, 0.65, 0.8, and 0.95) pixel values were averagedacross a circular area (radius 5 100 pixels) and recorded foreach of the channels (0–255). Pixel values, averaged acrossthe six images acquired for each grayscale standard, wereplotted as a function of nominal reflectance S and fitted tothe following function (Stevens et al. 2007):

S~a|kp ð5Þ

where a may stand for the red aR, green aG, or blue aB

channel-specific constants; k is a camera-specific constant;and p may stand for the pixel value of the red r, green g, orblue b channels. By definition, each grayscale standardshould produce the same response in all three channels.Thus, since r ? g ? b for the grayscale standard images, thered and blue channels of experimental images wereequalized using qR 5 r : g and qB 5 b : g, respectively(Stevens et al. 2007).

Temporal radiance variation—Measurement setup: Tostudy the temporal radiance fluctuations on a horizontalline of sight (h 5 90u), the radiance reflected from the targetand the water background were recorded at a high rate. Weutilized the same setup that was used for the previoussection; however, an optical fiber head took the place of thestill camera. Each set consisted of a measurement of theradiance reflected from the target (Lt), and then, by takingthe target out of the frame, measurement of sidewardradiance (Lh, water background). Lt and Lh were measuredconsecutively within less than 10 min.

Radiance was measured using a thermoelectricallycooled spectroradiometer (QE65000, Ocean Optics) con-nected to a 30-m optical fiber (ZPK600-30-Ultraviolet-Visibe, Ocean Optics) that was fitted with an acceptanceangle restrictor (forming a 10u acceptance cone). Thespectroradiometer used a 1024 3 58-element square siliconcharge-coupled device array, configured with a 25-mm slitand a variable blaze wavelength grating (HC-1, groovedensity 5 300 mm21, Ocean Optics), resulting in aneffective spectral resolution of 1.9-nm full width at halfmaximum between 200 and 950 nm. The spectroradio-meter’s integration time was set to 25 ms (theoreticalsampling frequency 5 40 Hz) to allow for the highestpossible sampling rate while ensuring sufficiently highsignal-to-noise ratio. In practice, however, because of atime constant between successive readings, the actualsampling frequency was 17.34 Hz. Thus, 3000 measure-ments were saved over 173 s, constituting a measurementtime series. Two time series, representing Lt and Lh,constituted a measurement set. Measurement sets acquiredat different distances to the substrate, viewing azimuths, ordepths constituted a sequence, e.g., a depth sequence. The

Fig. 1. A schematic of the measurement setup of spatial andtemporal radiance fluctuations on a horizontal line of sight (h 590u). For the measurement of spatial radiance fluctuations, acamera (Cm) and a target (T), positioned 1 m apart, were held ona tripod. Each image included a representation of the spatialpatterns reflected from the target and the water background.Measurements were performed at viewing azimuths (W) of 0u, 90u,135u, and 180u, where W stands for the azimuthal angle betweenthe camera and the sun (S). For the measurement of temporalradiance fluctuations, an optical fiber head, positioned at adistance of 0.5 m from the target, replaced the camera. For eachset, the radiance reflected from the target was measured, and then,upon taking the target out of the frame, the sideward radiance ofthe water background was measured.

1028 Sabbah et al.

spectroradiometer setup was calibrated for absolute radi-ance before each measurement day using a calibratedhalogen–deuterium dual light source (200–1000 nm, DH-2000-CAL, Ocean Optics).

The temporal characteristics of radiance fluctuations ofthe target reflection pattern and the water background wereexamined with respect to the following parameters.Viewing azimuth: 0u, 90u, 135u, and 180u (z 5 1 m, d 5100 cm); water depth: 1, 2, 4, 6, and 10 m (W 5 180u, d 5100 cm); and distance to substrate: 20 and 100 cm (W 5180u, z 5 1 m). To evaluate the temporal characteristics ofradiance reflected from natural vertical formations, whichmay correspond to the background of fish that inhabit andhold territories in between rocks, we measured the radiancereflected from a vertical rock (h 5 90u). In this case,measurements were taken with the optical fiber headmounted on the tripod and pointing at a vertical rockformation from a distance of 0.5 m. A scuba diverconfigured the tripod for each measurement sequence,and readings were saved on a laptop computer placed on aboat. To prevent shading, the boat was positioned as far aspossible from the target and never between the target andthe sun.

We also studied the temporal characteristics of sidewardirradiance (Eh) at the solar azimuth (h 5 90u). Sidewardirradiance illuminates any submerged object that is viewed

on a horizontal line of sight, and also adapts the eye of theobserver, resulting in adjustment of the observer’s visualsensitivity. Eh was measured with a cosine corrector(diameter 5 3.9 mm; CC-3-Ultraviolet, Ocean Optics)fitted to the optical fiber head. This diameter of the cosinecorrector is expected to accurately capture the irradiancefluctuations at near-surface depths. However, we cannotexclude the possibility of miscapturing fluctuations of smallspatial scale, typically encountered at z , 1 m (Dareckiet al. 2011).

To standardize the 3000 readings included in each series,the noise level (measured with the opening of the opticalfiber blocked) was subtracted from each spectrometerreading, and the resulting reading in relative counts wasconverted into photon radiance or irradiance. Wavelengthsat which radiance or irradiance was lower than 3 3 1011

photons cm22 sr21 s21 nm21 or photons cm22 s21 nm21,respectively, were designated as unreliable and removedfrom further analysis. See Fig. 3B for an example of timeseries of radiance reflected from the water background andthe target.

Analysis of radiance variation—To estimate the contrastcreated by radiance fluctuations either within the target orthe water background, the root-mean-square contrast ofeach pixel vector (spatial variation) and of each radiance

Fig. 2. Spatial pattern produced by surface waves. An example of a RGB image split into blue, green, and red channels. This imagewas acquired at a depth z 5 1 m with the target oriented vertically and facing the solar azimuth (W 5 180u). The target shows a distinctspatial pattern, whereas the water background appears spatially uniform.

Surface wave-induced light fluctuations 1029

time series (temporal variation) was calculated followingPavel et al. (1987):

C~1

n{1ð Þ�xx2

Xn

i~1

xi{�xxð Þ2" #1=2

, ð6Þ

where n represents the number of pixels in each pixel vector orthe number of elements in each radiance time series, xi

represents the radiance of each pixel or element, and x̄represents the mean radiance across a pixel vector or a timeseries. Since C accounts for the mean radiance, the derivedcontrast estimate is independent of the mean radiance as wellas the spectral reflectance of the target. C is identical to, andshould be technically termed as, the CV (Moulden et al. 1990;Deakin and Kildea 1999), which is commonly used indescribing the variation in irradiance and radiance (Stramskaand Dickey 1998; Gernez and Antoine 2009; Darecki et al.2011). Nonetheless, we have chosen to use C rather than CVbecause it is the standard measure in image processing(Tiippana et al. 1994; Bex and Makous 2002; Frazor andGeisler 2006), and to emphasize the relationship between thecontrast of radiance fluctuations and the contrast sensitivityof fish. Acting as a diffusive reflector across a broad spectralrange, the target served as a simplified proxy for the flank of afish (McFarland and Loew 1983). Thus, the radiance contrastof the target might simulate the contrast perceived by a fishwhen viewing another fish from a distance of 0.5–1 m. Thecontrast of sideward radiance might simulate the contrastperceived by a fish when viewing the water background at ahorizontal line of sight.

To study the frequency characteristics of wave-inducedradiance fluctuations, we calculated the power spectrum of

spatial frequencies for each pixel vector, and the powerspectrum of temporal frequencies for each radiance timeseries at a light wavelength resolution of 1 nm. Specifically,the discrete Fourier transform (DFT) was calculated foreach pixel vector or time series by using the fast Fouriertransform algorithm, and while applying a Hammingfrequency window that is appropriate for analyzing closelyspaced sine waves (Oppenheim and Schafer 1999). Asindices of the distribution of power across frequencies, wecalculated the fP50, fP90, and fP99, which stand for thefrequencies that correspond to 50%, 90%, and 99% of thecumulative power. Although dependent on the frequencyrange examined, the fP indices describe the modulationsexperienced by an observer reasonably well (McFarlandand Loew 1983). Contrast and frequency calculations wereperformed using Matlab R2009a (Mathworks).

Statistical analysis—To assess the effect of sampling rate(camera shutter speed) on spatial contrast, we used arepeated-measures ANOVA. Sampling rate was a between-subject factor because it represents measurements ondifferent subjects (images), and object (target vs. waterbackground) was a within-subject factor because theradiance fluctuations of the target and the water back-ground were generated by the same surface waves (sameimage). The sphericity assumption was not met; thus, thedegree to which the variance–covariance matrix departedfrom compound symmetry and sphericity was estimatedusing the Greenhouse–Geisser method, and the degrees offreedom were adjusted accordingly (Quinn and Keough2002).

To study the effect of sun condition and distance tosubstrate (independent measures) on the target and waterbackground spatial contrast (dependent measures), we usedsix t-tests for independent samples: two objects (target andwater background) 3 three colors (R, G, and B). Multiplet-tests were performed where an experimentwise error rateof 5% was corrected to 0.83% following the Bonferronicorrection (Quinn and Keough 2002). Normality of datawas confirmed (Kolmogorov–Smirnov test) and homoge-neity of variance was examined (Cochran’s C-test). Therequirement for homogeneity of variance was not met;consequently, t-tests were performed while correcting thedegrees of freedom for unequal variances (Welch 1938).

To study the effect of object (target vs. water back-ground) on spatial contrast, we used multiple paired t-tests.The contrast of the target and the water background arepaired measures, since they were generated by the samesurface waves (same image). This was repeated for fourmeasurement sequences looking at the independent effectsof sun condition, distance to substrate, viewing azimuth,and depth. For the measurement sequences looking at theeffect of sun condition and distance to substrate, six t-testswere used to test the effect of object: two sun conditions(exposed and obscured) 3 three colors and two distances tosubstrate 3 three colors, respectively. For the measurementsequence looking at the effect of depth, nine t-tests wereused to test the effect of object: three depths 3 three colors.For the measurement sequence looking at the effect ofviewing azimuth, 12 t-tests were used to test the effect of

Fig. 3. Example of (A) spatial (green channel) and (B)temporal (550 nm) series of radiance reflected from the waterbackground and the target (W 5 180u, z 5 1 m). For temporalvariation, each radiance value (photons cm22 sr21 s21 nm21) wasdivided by 1013 for readability. The spatial and temporal series ofradiance reflected from the target exhibit larger variability thanthose of the water background.

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object: four azimuths 3 three colors. Following theBonferroni correction, multiple t-tests were performedwhere an experimentwise error rate of 5% was correctedto 0.83% for the effect of sun condition and distance tosubstrate, 0.55% for the effect of depth, and 0.41% for theeffect of azimuth. Since short-term radiance fluctuationsare a result of light being focused by surface waves, a timeinterval of 10 s between consecutive images ensured that thespatial pattern in each image was produced by distinctsurface waves. Surface waves are chaotic and largelyindependent of one another (the characteristics of a givenwave do not depend on the characteristics of the precedingwave) (Denny 1988). Consequently, successive images weretreated as independent. Statistical analysis was performedusing the Statistica software (Statsoft). No statisticalanalysis was performed on the temporal contrast datasince only one time series of radiance was acquired underany given condition.

Surface waves, solar, and celestial conditions—As anindirect measure of surface waves, the wind speed anddirection were measured on the research boat using a hand-held anemometer at a 0.03 m s21 resolution (Kestrel 1000,Kestrel Meters). Solar zenith and azimuthal angles weretaken from the U.S. Navy website (http://aa.usno.navy.mil/data/docs/AltAz.php). All measurements were conductedaround noon, corresponding to a solar zenith angle rangingbetween 36u and 52u. Exceptions to this rule were theimaging and radiometric measurements across viewingazimuth, during which solar zenith angle ranged 54–70uand 60–68u, respectively. Table 2 summarizes the environ-mental conditions during measurements. Unless specified,all measurements were conducted under clear blue sky.

Results

Contrast of fluctuations—Spatial contrast: Differentimaging sequences were acquired at different sampling rates.

To study the effect of sampling rate on the spatial contrast ofthe target (CSt) and the water background (CSw), wecompared images that were taken at camera shutter speedsof 1/200, 1/400, 1/800, and 1/1600 s (W 5 180u, z 5 1 m).Neither CSt nor CSw differed significantly across samplingrates (repeated-measures ANOVA, F3,110 5 0.03, p . 0.993for red R, green G, and blue B). Thus, the contrast ofimaging sequences acquired at different sampling rates wascomparable. Moreover, CSt was significantly higher thanCSw across all sampling rates (repeated-measures ANOVA,F1,110 5 991.92, p , 0.0001 for all colors) and no interactionbetween sampling rate and object (target vs. water back-ground) was evident (repeated-measures ANOVA, F3,110 50.224, p . 0.879 for all colors).

To examine the effect of sun condition on spatial contrast,we compared images that were acquired with the sunexposed (visible) and with the sun obscured by clouds (W5 180u; z 5 1 m). CSt was significantly higher with exposedthan with obscured sun (t-test: R: t 5 10.93, df 5 28.2, p 51.21 3 10211; G: t 5 10.50, df 5 28.5, p 5 2.63 3 10211; B: t5 10.15, df 5 28.8, p 5 5.01 3 10211). However, CSw

typically did not differ significantly between the two sunconditions (t-test: R: t 5 25.62, df 5 47.3, p 5 9.74 3 1027;G: t 5 1.21, df 5 55.9, p 5 0.228; B: t 5 0.56, df 5 52.7, p 50.573) (Fig. 4A). Thus, in general, the spatial pattern seen onthe target, but not in the water column, depended on the suncondition; suggesting a role for the focusing of directsunlight in generating the reflection pattern of the target.Moreover, with the sun exposed, CSt was significantly higherthan CSw for all color ranges (Table 3A). Contrast variedwith color only slightly. Thus, unless contrast of differentcolors behaved differently across treatments (sun conditionin this case), here and throughout this section, contrast datafor all colors were pooled for concise graphic presentation.

To study the effect of distance to the substrate on spatialcontrast, we compared images that were taken at 20 and100 cm above the substrate (W 5 180u, z 5 1 m). NeitherCSt (t-test: R: t 5 1.27, df 5 53.0, p 5 0.206; G: t 5 20.12,

Table 2. Date, wind speed, wind direction (from the north), local time, and solar zenith angle (SZA) during the various measurementsequences. Unless specified, the effect of the various factors on the variation in radiance was examined.

Effect Date

Wind

Local time (h) SZA (u)speed (m s21) Direction (u)

(A) Spatial variation

Depth 13 July 1.8–4.4 90–130 11:14–12:14 36–37Viewing azimuth 15 July 2.6–5.7 105–150 07:39–08:57 54–70Distance to

substrate 15 July 2.4–3.4 90–95 11:26–11:54 36–37Sun condition 15 July 1.6–3.5 90–110 11:26–12:32 36–37Sampling rate 13 July 1.7–3.4 95–110 12:24–13:02 37–40

(B) Temporal variation

Depth 18 July 2.9–4.7 20–110 12:17–14:27 36–51Viewing azimuth 19 July 0.7–2.1 90–140 07:55–08:31 60–68Distance to

substrate 19 July 4.2–4.9 200–210 09:09–09:16 51–52Background type 21 July 1.9–4.2 230–246 12:28–13:34 36–43Depth (sideward

irradiance) 21 July 1.8 235 13:54–14:09 46–50

Surface wave-induced light fluctuations 1031

df 5 50.8, p 5 0.909; B: t 5 0.51, df 5 52.7, p 5 0.609) norCSw (R: t 5 1.56, df 5 28.2, p 5 0.129; G: t 5 2.58, df 527.5, p 5 0.015; B: t 5 2.31, df 5 27.6, p 5 0.028) differedsignificantly across distances to the substrate (Fig. 4B).That is, CSt was significantly higher than CSw regardless ofthe distance to the substrate (Table 3B). To study the effectof viewing azimuth on spatial contrast, we comparedimages that were taken at viewing azimuths of 0u, 90u, 135u,and 180u (z 5 1 m, d 5 100 cm). CSt differed significantlyfrom CSw across all azimuths (Table 3C). However, therelationship between the objects (target vs. water back-ground) varied across azimuth. At a viewing azimuth of 0u,CSt was significantly lower than CSw, whereas at viewingazimuths of 90u, 135u, and 180u, CSt was significantlyhigher than CSw (Fig. 4C). To study the effect of depth onspatial contrast, we compared images that were taken at 1-,3-, and 5-m depth (W 5 180u, d 5 100 cm). CSt and CSw

decreased and converged on one another with increasing

depth (Fig. 4D). CSt was significantly higher than CSw

across all depths, with two exceptions: CSt and CSw in theblue region at a depth of 5 m did not differ significantly,and CSw in the red region at a depth of 5 m wassignificantly higher than CSt (Table 3D).

Either CSt or CSw was typically higher than the MCT offish (Table 3). In general, CSt, but not CSw, was higher thanthe MCT of fish. Additionally, in cases where both CSt andCSw were higher than the MCT, CSt and CSw differedsignificantly. A notable exception to this trend, however,was the contrast at a viewing azimuth of 0u, where CSw, butnot CSt, was higher than the MCT. Taken together, thetarget spatial contrast generally differed from that of thewater background regardless of the sampling rate anddistance to the substrate, across viewing azimuths exam-ined, and down to 5-m depth.

Temporal contrast: To study the effect of viewingazimuth on the temporal contrast of the target (CTt) and

Fig. 4. Effect of (A) sun condition, (B) distance to substrate, (C) viewing azimuth, and (D) depth on the spatial contrast of the targetand water background. (A) Target contrast was higher with the sun exposed than with the sun obscured. (B) Distance to substrate did notaffect the relationship of contrast between the target and the water background. (C) Target contrast was lower than the water contrast ata viewing azimuth of 0u, but higher than the water contrast at viewing azimuths of 90u, 135u, and 180u (see Fig. 1 for angular namingconventions). (D) The effect of depth on spatial contrast was measured for the blue, green, and red spectral regions (W 5 180u). In general,spatial contrast of both target and water background decreased with increasing depth (but see the contrast at 5-m depth in the red region).Target and water background contrast became similar with increasing depth. Error bars represent 0.99 confidence intervals.

1032 Sabbah et al.

the water background (CTw), radiance was measured atviewing azimuths of 0u, 90u, 135u, and 180u (z 5 1 m, d 5100 cm). CTt was higher than CTw at viewing azimuths of90u, 135u, and 180u, but not at a viewing azimuth of 0u(Fig. 5A, Table 4A). Therefore, the target flickered againsta relatively uniform background at viewing azimuths of90u, 135u, and 180u, but against an equally flickeringbackground at a viewing azimuth of 0u. To study the effectof water depth on temporal contrast, radiance wasmeasured at depths of 1, 2, 4, 6, and 10 m (W 5 180u, d5 100 cm). CTt was higher than CTw across all depths(Fig. 5B, Table 4B). Both CTt and CTw decreased withdepth, and increased toward longer light wavelengths. Thedifference between CTt and CTw also decreased with depth,approaching zero at a depth of 10 m. Thus, the targetflickered against a relatively temporally uniform back-ground down to a depth of 10 m. To study the effect ofdistance to the substrate on temporal contrast, radiancewas measured at 20 and 100 cm above the substrate (W 5180u, z 5 1 m). CTt was higher than CTw regardless of thedistance to the substrate and both increased toward longerlight wavelengths (Fig. 6A, Table 4C). To study thetemporal characteristics of radiance reflected off a naturalsubstrate, the contrast of radiance reflected off a verticalrock formation was compared with that of sidewardradiance (CTw). Rock contrast was higher and showed adifferent spectral shape than CTw; however, both increasedtoward longer light wavelengths (Fig. 6B, Table 4D).Finally, to study the effect of water depth on the temporalcontrast of sideward irradiance (Eh), irradiance wasmeasured at depths of 1, 2, 4, 6, and 10 m at the solarazimuth (h 5 90u). The mean and contrast of Eh decreased

with depth, with the contrast increasing toward longer lightwavelengths (Fig. 7).

As was found for spatial contrast, either CTt or CTw washigher than the MCT of fish (contrast averaged across thespectrum). Additionally, in cases where both CTt and CTw

were higher than the MCT, CTt was considerably higherthan CTw (Table 4). A notable exception to this trend,however, was the contrast at a viewing azimuth of 0u, whereCTt and CTw were comparable. Taken together, the targetgenerally flickered against a relatively uniform backgroundregardless of the distance to the substrate, at viewingazimuths of 90u, 135u, 180u, and down to a depth of 10 m.The temporal contrast of a vertical rock formation washigher than that of the water background, and the contrastof sideward irradiance decreased with increasing depth, andincreased toward longer light wavelengths.

Frequency of fluctuations—Spatial frequency: To studythe spectral power distribution of the frequencies of spatialfluctuations, we calculated the fP50, fP90, and fP99 values,representing the frequencies at 50%, 90%, and 99% of totalpower, respectively. For instances where CSt or CSw waslower than approximately 0.075, the DFT detected verysmall brightness differences between adjacent pixels (likelyproduced by electrical noise in the camera detector). Thisresulted in unrealistically high power at high spatialfrequencies, not reflecting the power distribution of thewave-induced spatial pattern. Thus, power distributions arereported only for instances where the contrast was higher than0.075. To reduce sensitivity to sporadic fluctuations of extremespatial frequencies, the median and the 1st and 3rd quartiles offP values were calculated for each measurement set.

Table 3. Summary of paired t-test results for the comparison of the spatial contrast of the target and water background. The effectsof (A) sun condition (W 5 180u, z 5 1 m), (B) distance to substrate (W 5 180u, z 5 1 m), (C) viewing azimuth (z 5 1 m), and (D) depth (W5 180u) were tested.

Spatial contrast{

t df p*Target Water

(A) Sun condition

Exposed 0.116, 0.131, 0.155 0.024, 0.020, 0.020 12.2, 12.7, 12.4 30 ,1310212

Obscured 0.060, 0.064, 0.055 0.034, 0.032, 0.034 17.1, 22.2, 16.6 28 ,1310215

(B) Distance to substrate (cm)

20 0.124, 0.132, 0.174 0.039, 0.036, 0.025 8.8, 9.8, 12.5 27 ,131028

100 0.116, 0.131, 0.154 0.024, 0.021, 0.021 12.2, 12.8, 12.9 30 ,1310213

(C) Viewing azimuth (u)0 0.025, 0.021, 0.021 0.067, 0.069, 0.071 218.5, 218.9, 223.5 27 ,1310216

90 0.068, 0.079, 0.087 0.021, 0.017, 0.017 8.1, 9.4, 8.5 29 ,131028

135 0.099, 0.111, 0.115 0.020, 0.017, 0.018 10.3, 10.2, 9.9 29 ,1310210

180 0.088, 0.099, 0.100 0.022, 0.016, 0.016 12.2, 13.1, 12.6 32 ,1310212

(D) Depth (m)

1 0.161, 0.178, 0.201 0.048, 0.046, 0.036 13.3, 14.9, 19.4 29 ,1310213

3 0.059, 0.072, 0.074 0.024, 0.018, 0.021 10.4, 14.4, 12.1 30 ,1310210

5{ 0.026, 0.028, 0.038 0.024, 0.019, 0.074 2.3, 5.2, 211.2 35 ,131025

* p-Values for treatment pairs that differed significantly in contrast are marked in bold. Following Bonferroni correction, multiple t-tests were performedwhere an experimentwise error rate of 5% was corrected to 0.83% for 6 hypothesis tests (a 5 0.0083; effect of sun condition and distance to substrate),0.55% for 9 hypothesis tests (a 5 0.0055; effect of depth), and 0.41% for 12 hypothesis tests (a 5 0.0041; effect of azimuth).

{ Mean target contrast and mean water contrast values are given for the blue, green, and red regions (left to right). Absolute spatial contrast values largerthan the minimum contrast threshold of fish under the photic conditions encountered in this study (0.039) are marked in bold.

{ Target and water contrast did not differ significantly for the blue region (p 5 0.024).

Surface wave-induced light fluctuations 1033

Fifty percent (fP50), 90% (fP90), and 99% (fP99) of thepower was evident at spatial frequencies lower than 0–0.054, 0.054–0.34, and 0.953–28.434 c degree21, respective-ly, for median fP values for all measurement sequences(Table 5). The power distribution of spatial radiancefluctuations of the target varied with distance to substrate(W 5 180u, z 5 1 m). Ninety percent of the power wasevident at spatial frequencies lower than 0.136–0.163 cdegree21 away from the substrate, but at frequencies lowerthan 0.272–0.313 c degree21 close to the substrate(Table 5A). Additionally, the power distribution of spatialradiance fluctuations of the target varied with viewingazimuth (z 5 1 m). Ninety percent of the power was evidentat spatial frequencies lower than 0.082–0.34 c degree21 at W5 90u, at frequencies lower than 0.123–0.259 c degree21 atW 5 135u, and at frequencies lower than 0.054–0.109 cdegree21 at W 5 180u (Table 5B). Importantly, thefrequency range where maximum spatial contrast sensitiv-ity in fish is achieved (0.05–0.4 c degree21, Table 1)corresponded with the frequencies of the spatial patternsbelow which 90% of the power of wave-induced radiancefluctuation was found (Fig. 8A).

Temporal frequency: Fifty percent (fP50), 90% (fP90),and 99% (fP99) of the power was evident at temporalfrequencies lower than 0.992, 2.815, and 8.207 Hz, respec-

tively, for mean fP values (W 5 180u, z 5 1 m) (Table 6A).The power distribution of radiance fluctuations varied withviewing azimuth (z 5 1 m). fP values for both target andwater background at viewing azimuths of 0u and 90u weretypically lower than those at viewing azimuths of 135u and180u (Table 6A). The power distribution of radiancefluctuations varied with depth (W 5 180u). fP values forboth target and water background generally decreased withincreasing water depth, representing a decrease in high-frequency power produced by light focusing by the smallestsurface waves (Table 6B; Fig. 9). Furthermore, fP valuesfor the water background, but not for the target, decreasedcloser to the substrate (Table 6C), whereas fP values for thetarget and a vertical rock formation were found to becomparable (Table 6D). Finally, the frequency range wheremaximum temporal contrast sensitivity in fish is achieved(0.5–2 Hz) corresponded with the temporal frequenciesbelow which at least 50% of power of wave-inducedradiance fluctuations was found (Fig. 8B).

Discussion

Overview—The two conditions necessary for wave-induced radiance fluctuations to enhance the appearanceof objects and to provide fish with an optimal detection

Fig. 5. Effect of (A) viewing azimuth (z 5 1 m) and (B) depth (W 5 180u) on temporal contrast of the target and water background.(A) Target contrast was comparable with the water contrast at W 5 0u, but higher than the water contrast at W of 90u, 135u, and 180u (seeFig. 1 for angular naming conventions). (B) Target contrast and water contrast became similar with increasing depth. Deeper in the watercolumn, the radiance at both ends of the spectrum was too low to be considered reliable (see Methods for the criteria for excluding datapoints). Therefore, the spectral range presented narrows with depth.

1034 Sabbah et al.

environment were found to be satisfied. We found thatwhen an object (i.e., the target) was viewed on a horizontalline of sight, it appeared to flicker against a temporallyuniform water background and showed spatial contrastagainst a spatially uniform background. This observationholds regardless of the proximity to the substrate, forviewing azimuths of 90u, 135u, and 180u, and down to 5-mand 10-m depth for spatial and temporal contrast,respectively. Additionally, when this object was viewed atthe solar azimuth and at a depth of 1 m, the radiance of the

object was spatially uniform, whereas the water back-ground showed spatial contrast (see discussion of thetemporal contrast at the solar azimuth). We also found thatthe power distribution of the spatial and temporal radiancefluctuations coincided with the frequency range of maxi-mum CS of fish. Specifically, most radiance power wasfound at spatial and temporal frequencies lower than 0.4 cdegree21 and 2 Hz, respectively. Thus, we conclude thatwave-induced radiance fluctuations may enhance theappearance of underwater objects when viewed by fish ona horizontal line of sight at depths down to 5 to 10 m. Thisraises the possibility that fish have evolved contrastsensitivity characteristics that allow them to best utilizelight stimuli that show the spatial and temporal radiancefluctuations produced by surface waves. However, toconclusively confirm that wave-induced radiance fluctua-tions can make objects more apparent, the ability of fish tobehaviorally respond to objects under radiance fluctuationsdiffering in spatial and temporal frequencies should beassessed. This study provides important information for thedesign of such behavioral experiments. The properties ofwave-induced radiance fluctuations, their dependence onthe environmental factors studied, and their biologicalrelevance are discussed below.

Effect of cloud cover—When the sun was obscured byclouds and no direct sun rays refracted at the water surface,the contrast of radiance reflected from the target was lowerthan when the sun was visible. It would be interesting to seewhether fish behavior, such as predator avoidance or visualforaging, would change as a result of reduced objectcontrast when the sun is obscured by clouds or below thehorizon. For example, the number of juvenile Atlanticsalmon (Salmo salar) actively foraging was shown todecrease with an increase in cloud cover (Girard et al.2003). However, it remains unclear whether the observedbehavioral change was related to a reduction in radiancecontrast or simply a reduction in light intensity that allowsefficient foraging.

Fig. 6. Effect of (A) distance to substrate and (B) background type on temporal radiancecontrast. (A) The difference between the contrast of the target and the water background atdistance to substrate d 5 100 cm (thin lines) was larger than that at d 5 20 cm (thick lines).However, target contrast was still higher than the water contrast. (B) The contrast of radiancereflected from a vertical rock formation was higher than that of the water background.

Table 4. Temporal contrast of the target and waterbackground for the effect of (A) viewing azimuth (z 5 1 m), (B)depth (W 5 180u), (C) distance to substrate (W 5 180u, z 5 1 m),and (D) background type (W 5 180u, z 5 1 m).

Temporal contrast*

Target Water

(A) Viewing azimuth (u)0 0.22860.082 0.22660.06090 0.13860.036 0.02660.005135 0.34260.082 0.03660.013180 0.30160.063 0.02360.010

(B) Depth (m)

1 0.22260.038 0.10660.0522 0.19960.042 0.07760.0374 0.14660.042 0.03360.0126 0.07360.027 0.02660.00610 0.04360.012 0.02860.003

(C) Distance to substrate (cm)

20 0.25860.044 0.10960.025100 0.30160.063 0.02360.010

(D) Background type

Rock 0.12760.035 0.14760.042Water 0.12760.035 0.04960.033

* Target and water contrast (mean6SD across the spectrum) are given.Absolute temporal contrast values larger than the minimum contrastthreshold of fish under the photic conditions encountered in this study(0.032) are marked in bold.

Surface wave-induced light fluctuations 1035

Effect of distance to the substrate—The spatial andtemporal contrast of the target was higher than that of thewater background regardless of the proximity to thesubstrate. The power distribution of radiance fluctuationsof the target and the water background varied with distanceto substrate in a complex manner. However, regardless ofthe proximity to the substrate, the frequencies below which50–90% of power was found coincided with the frequencyrange of maximum spatial and temporal CS of fish. Thissuggests that fish residing either in the water column orclose to the substrate would likely show spatially modulat-ed patterns and appear to flicker against a spatially andtemporally uniform water background. Consequently,wave-induced radiance fluctuations may enhance theappearance of underwater objects both in the water columnand close to the substrate. In this regard, it would beinteresting to examine whether different substrates thatdiffer in reflection properties would show different rela-tionships between the contrast of objects and the waterbackground, and thus affect the appearance of objects.

Effect of viewing azimuth—The spatial and temporalcontrast of the target was higher than that of the waterbackground at viewing azimuths of 90u, 135u, and 180u. Atthe solar azimuth, however, the spatial and temporalcontrasts behaved differently. The temporal contrast of thetarget was similar to that of the water background, whereasthe spatial contrast of the target was lower than that of thewater background. The latter observation is supported byour visual inspection of the raw images of spatial patternthat clearly show shafts of light transmitted through thewater just behind the practically uniformly bright target.Without further measurements, we cannot explain thesimilarity in the temporal contrast of the target and thewater background at the solar azimuth. Thus, at this time,our results suggest that the contrasts of the target and waterbackground differ for viewing azimuths of 90u, 135u, and180u, and possibly also for others. Therefore, wave-inducedradiance fluctuations may enhance the appearance ofunderwater objects at diverse viewing azimuths.

Effect of water depth—The spatial and temporal contrastof the target and the water background decreased andconverged with increasing depth. The depth at which thecontrast of the target and water background becomesimilar (‘‘convergence depth’’) is likely dependent on theoptical properties of water. Light scattering degrades thelight-focusing effect and reduces the contrast of the targetand the water background. Thus, a decrease in scatteringwould be expected to result in greater convergence depths.Lake Malawi is generally regarded as a clear, oligotrophicsystem but based on the downward diffuse attenuationcoefficient, the littoral zone corresponds to Jerlov’s coastalwater type 1 or 2 (Sabbah et al. 2011). In comparison, coralreef water is typically type 1 or clearer (Marshall et al.2003), whereas open ocean water is generally extremelyclear (Jerlov’s oceanic water types I–III) (McFarland andMunz 1975; Jerlov 1976). These clearer aquatic ecosystemswould be expected to have appreciably greater convergencedepths, and, consequently, greater depth ranges over whichan object would reflect heterogeneous spatial patterns on aspatially uniform water background and appear to flickeragainst a temporally uniform water background.

Effect of background type—The temporal contrast ofradiance reflected from a vertical rock was found to becomparable with that reflected from the target, both beinghigher than the contrast of the water background (thespatial contrast of radiance reflected from a vertical rockwas not assessed). Thus, when viewed against the waterbackground, an object would flicker against a temporallyuniform background. On the other hand, when viewedagainst a natural reflective substrate such as a vertical rock,the object would flicker against an equally flickeringbackground. Consequently, the appearance of fish thatinhabit and hold territories in between rocks or coralswould probably be reduced. This reduction in appearanceis expected to reduce the visibility of fish to predators butnot to interfere with visual communication tasks such asmate choice and intraspecific competition, since in thesetasks, recognition (of color and shape) rather than

Fig. 7. Effect of depth on (A) mean spectral sidewardirradiance Eh and (B) contrast of temporal fluctuations in Eh

measured at the solar azimuth. Mean and temporal contrast of Eh

decreased with increasing depth, with temporal contrast increas-ing toward long wavelengths.

1036 Sabbah et al.

detection capabilities are more likely to play a role(Marshall 2000; Marshall et al. 2006).

Effect of color—The spatial contrast of the target and thetemporal contrast of the target and the water backgroundincreased toward longer light wavelengths regardless ofdepth and viewing azimuth (the spatial contrast of the waterbackground did not show clear dependence on color).Similar increase in temporal contrast toward long wave-lengths was previously demonstrated in downward irradi-ance (Darecki et al. 2011) and upward radiance (Stramskaand Dickey 1998). The variation in contrast across the lightspectrum can be explained by variation in the diffusenessof light at different wavelengths. Scattering at short

wavelengths in the atmosphere and in water is generallymore effective than at long wavelengths. This makes light atshort wavelengths relatively more diffused and less affectedby the wave-focusing phenomenon than light at longwavelengths. Consequently, the contrast of radiance reflect-ed from objects, which depends on the focusing phenome-non, increases toward longer light wavelengths.

Experimental considerations—Sampling frequency: Toevaluate the possible effect of radiance fluctuations on theappearance of underwater objects, we focused on charac-terization of radiance fluctuations at time and space scalescorresponding to the maximum CS of fish (i.e., up to 2 Hzfor temporal variation). This frequency range coincides

Fig. 8. Cumulative power values of the target (A) spatial and (B) temporal radiancefluctuations produced by surface waves and their relation to the spatial and temporal frequenciesof maximum contrast sensitivity reported for fish. Horizontal dashed lines bound the frequencyrange where contrast sensitivity of fish is maximal. The frequency range where maximum spatialcontrast sensitivity is achieved coincided with the spatial frequencies below which 90% of powerof wave-induced radiance fluctuation was found. The frequency range where maximum temporalcontrast sensitivity is achieved coincided with the temporal frequencies below which at least 50%(in many cases even 90%) of power of wave-induced radiance fluctuation was found. This figureincludes the fP50 and fP90 values summarized in Table 5 (spatial frequency) and Table 6(temporal frequency) for different distances to the substrates, viewing azimuths, and depths.

Table 5. Median cumulative power values for the spatial radiance fluctuations of the target (fP50, fP90, and fP99) for the effect of (A)distance to substrate, (B) viewing azimuth, and (C) water depth.

Cumulative power index (c degree21)*

fP50 fP90{ fP99

(A) Distance to substrate (cm)

20 0.054, 0.054, 0.054 0.272, 0.272, 0.313 2.872, 1.361, 1.402100 0.027, 0.027, 0.027 0.136, 0.136, 0.163 3.049, 0.953, 3.770

(B) Viewing azimuth (u)90 0.000, 0.000, 0.000 0.340, 0.082, 0.286 28.434, 23.153, 19.464135 0.000, 0.000, 0.000 0.177, 0.123, 0.259 20.866, 18.361, 17.640180 0.000, 0.000, 0.000 0.082, 0.054, 0.109 16.633, 13.666, 15.163

(C) Depth (m)

1 0.027, 0.027, 0.027 0.313, 0.299, 0.313 1.470, 1.075, 1.402

* Cumulative power values are given for the blue, green, and red spectral regions (left to right). The table lists fP values only for instances where thecontrast was higher than 0.075, and could be considered reliable.

{ Ninety percent of the power in the blue (0.082–0.34 c degree21) and red (0.109–0.313 c degree21) regions was evident at slightly higher spatial frequenciesthan in the green region (0.054–0.299 c degree21). That is, the power distribution in the blue and red regions was slightly shifted to higher frequencies.

Surface wave-induced light fluctuations 1037

with the dominant frequency of downward irradiancefluctuations at near-surface depths, e.g., 1.2 to 2.1 Hz atdepths of 0.86 to 2.84 m with a sampling frequency of 1 kHz(You et al. 2010), and 0.3 to 1.7 Hz for various near-surfacedepths (within Gernez and Antoine 2009). Additionally, thepower of irradiance fluctuations typically declines steeplywith increasing frequency. For example, the power ofirradiance fluctuations at a frequency of 8.67 Hz (ourfrequency limit considering a sampling frequency of17.34 Hz) was reported to be approximately 5- to 200-foldsmaller than that at the dominant frequency at depths of0.86 to 2.84 m (You et al. 2010). To fully capture thehighest-frequency irradiance fluctuations, it would benecessary to use a high-rate (e.g., 1 kHz) radiometricmeasurement system (Darecki et al. 2011). However, therelatively low frequency of maximum CS in fish as well asthe steep decline of irradiance fluctuations’ power withincreasing frequency suggest a limited effect of high-frequency irradiance fluctuations on the appearance ofobjects. Additionally, the shortest-duration light flashes,which also show the highest amplitudes, are rare (Dera andOlszewski 1978; Dera and Stramski 1986; Stramski 1986b).Therefore, their contribution to the total power ofirradiance is small, making them hard to detect using theFourier spectral analysis (Dera and Olszewski 1978).Consequently, our spectral analysis, the basis on whichthe fP indices were calculated, might misrepresent thehighest-amplitude, shortest-duration light flashes. Howev-er, considering their rarity (e.g., 0.1 min21 for light flashes

exceeding 7 to 13 times the time-averaged irradiance;Darecki et al. 2011), these light flashes would likely havelittle effect on the appearance of objects.

Averaging temporal radiance fluctuations across space:Temporal radiance fluctuations from the target wereaveraged across a circle 8.75 cm in diameter (acceptancecone of optical fiber 5 10u; distance between target andoptical fiber head 5 0.5 m), whereas the temporal radiancefluctuations from the water background were averagedacross an imaginary circle whose diameter depends on thewater’s optical properties. Such averaging across space mayresult in averaging of high-frequency and high-amplitudeflashes, potentially leading to inaccurate estimation of thefrequency of flashes and the contrast they produce. Note,however, that this averaging across space, by definition, isunavoidable and inherent in every radiance measurement.

Wind speed: Wind speed influences the roughness of thewater surface and alters the characteristics of wave-inducedirradiance fluctuations. The frequency and intensity (Deraand Stramski 1986; Stramski 1986b; Dera et al. 1993), as wellas the contrast (also CV) of downward irradiance fluctuations(Gernez and Antoine 2009; Darecki et al. 2011), are typically

Fig. 9. Effect of depth on the cumulative power of temporalradiance fluctuations (W 5 180u). In general, (A) fP50, (B) fP90,and (C) fP99 of both the target and the water backgrounddecreased with increasing depth, representing a decrease in thepower of high-frequency fluctuations with growing depth. Thepower distribution of temporal radiance fluctuations from thewater background was slightly shifted toward higher frequencies.

Table 6. Cumulative power values for temporal radiancefluctuations (fP50, fP90, and fP99) for the effect of (A) viewingazimuth (z 5 1 m), (B) depth (W 5 180u), (C) distance to substrate(W 5 180u, z 5 1 m), and (D) background type (W 5 180u, z 51 m).

Cumulative power index (Hz)*

Target Water

fP50 fP90 fP99 fP50 fP90 fP99

(A) Viewing azimuth (u)0 0.023 1.445 5.596 0.105 1.350 5.41390 0.013 0.185 1.568 0.266 1.246 5.741135 1.115 3.723 8.024 0.343 1.899 6.402180 0.992 2.815 8.207 0.446 1.815 5.352

(B) Depth (m)

1 1.082 2.314 5.968 1.063 2.827 7.3642 0.845 1.783 5.295 0.855 2.105 5.9444 0.886 1.901 5.602 0.765 2.322 7.2036 0.704 1.441 5.089 0.651 1.951 6.93610 0.569 1.204 5.092 0.011 0.951 6.776

(C) Distance to substrate (cm)

20 1.167 3.066 7.286 0.038 1.184 3.968100 0.992 2.815 8.207 0.528 2.427 7.420

(D) Background type

Rock 1.785 2.732 6.302 1.093 2.497 6.506Water 1.785 2.732 6.302 2.075 6.334 9.602

* fP values were calculated at a spectral resolution of 1 nm. For concisedescription, however, the cross-spectrum mean of the fP values are given.

1038 Sabbah et al.

greatest under light winds (2–5 m s21). These light winds areoptimal for efficient focusing of light by surface waves. In thisstudy, wind speed typically corresponded to the optimal speedrange for efficient light focusing and varied only slightlythroughout measurement sequences (Table 2). Yet, we cannotexclude the possibility that variation in wind speed through-out measurement sequences (e.g., across depths) haveintroduced additional variation into the measurement.Nevertheless, the temporal radiance fluctuations of the targetand water background were measured consecutively withinless than 10 min, during which time considerable change inwind speed is unlikely. Furthermore, the spatial radiancefluctuations of the target and water background weremeasured simultaneously (within the same image), and thus,also under the same wind conditions. Therefore, thedifferences observed between the radiance fluctuations ofthe target and water background, which are crucial forenhancement of the appearance of objects, are likely valid.

Minimum contrast threshold and contrast sensitivityconsiderations—To evaluate the feasibility of wave-inducedradiance fluctuations in enhancing the appearance of objectswhen viewed by fish, MCT of fish was taken as 0.039 and0.032 for spatial and temporal contrast, respectively. TheseMCT values correspond to light intensities within thephotopic range of goldfish (1023 cd m22) (Bilotta andPowers 1991; Bilotta et al. 1995). The intensity of lightstimuli during these MCT measurements was given inphotometric units, which cannot be directly compared withthe irradiance spectra we recorded underwater. Nonetheless,in this study, we characterized the radiance fluctuationsdown to a depth of 10 m, where spectral irradiance ranged1011–1013 photons cm22 s21 nm21 (Fig. 7). These irradiancevalues are well within the photopic range of many fish, e.g.,cyprinids (Demarco and Powers 1991), salmonids (Hawry-shyn et al. 2010), and cichlids (Sabbah et al. 2010). Thus, forthe lowest irradiance level encountered in this study, thespatial and temporal contrast of the stimulus should behigher than 0.039 and 0.032 to be detected by a fish,respectively. We used these conservative criteria to estimatethe feasibility of contrast detection.

Furthermore, we compared the frequency of underwaterradiance fluctuations with the frequency of maximum CSreported for fish. For these comparisons, we used dataavailable in the literature for goldfish and bluegill sunfish(Table 1). Both species are found naturally in shallowwaters of temperate ponds and lakes (Page and Burr 1991).It would be beneficial to compare the characteristics ofwave-induced radiance fluctuations with those of the visualsystem of other species. For example, since the contrast andfrequency of radiance fluctuations decrease with waterdepth, it would be interesting to see whether the MCT andfrequency of maximum CS in deep-water fish differ fromthose of the two shallow-water species studied thus far.

Generality of findings and spatiotemporal interactionsin vision—The radiance fluctuations reflected from the targetcan serve only as an approximation for the radiancefluctuations reflected from the body of fish, which are typicallythree-dimensional, patterned, colored, and dynamic. (1) The

radiance reflected from our two-dimensional target repre-sented mainly sideward irradiance incident on the target, withsome contribution from downward and upward irradiance.Conversely, radiance reflected from a three-dimensional objectwould likely represent a composite of irradiance from alldirections, each showing different spatial and temporalcharacteristics. Such a divergence in reflection pattern wasreported for the reflection from a three-dimensional polyvinylchloride pipe (Loew and McFarland 1990). (2) Our targetwas a diffusely reflecting white board, whereas theradiance reflected from the body of fish likely arises fromboth diffuse and specular reflections. Additionally, manyfish show spatial body markings that may include colorfulvertical bars, horizontal stripes, or spots of various shapes.Thus, in nature, wave-induced reflection patterns may besuperimposed on the spatial patterns exhibited by fish tocreate a rather complex pattern of varying frequencies anddepths of modulation. Interestingly, the body markings insome cephalopods and fish resemble the spatial reflectionpattern produced by waves, and were suggested to makethe animals less visible (Loew and McFarland 1990). (3)Our target was static, whereas fish in their naturalenvironment typically move. Thus, in nature, the wave-induced reflection patterns, the viewer, and the objectsviewed continuously move with respect to one another.Currently, an accurate description of such a highlydynamic multidimensional system is not feasible. Addi-tionally, CS and MCT of fish for spatiotemporallymodulated stimuli might differ from those obtained forspatially or temporally modulated stimuli alone (Kelly1972). In this study, however, we provide an accuratedescription of the patterns reflected toward the eye of theviewer across space at a given moment (spatial variation)and over time across a given space (temporal variation)from a stationary, flat target. This first comprehensivequantification of spatial and temporal reflection patternspermits a better understanding of the baseline visualenvironment experienced by fish.

AcknowledgmentsWe thank the University of Malawi and the personnel at the

Mbuna Research Station, Cape Maclear, Malawi, Thomas Croninfor providing us the GretagMacbethTM ColorChecker, Tom Kocherand Karen Carleton for suggestions regarding the study site selection,and Tice Post, Ron Kerr, and Rob Snetsinger for help in fabricatingthe metal frame and various adaptors to hold the test board.

This research was supported by a Natural Sciences andEngineering Research Council of Canada (NSERC) DiscoveryGrant and NSERC Research Tools and Instrumentation Grant,Canada Foundation for Innovation, Ontario Innovation Trust, andthe Canada Research Chair Program to C.W.H. S.S. was supportedby a Vanier Canada Graduate Scholarship from NSERC. S.M.G.was supported by a NSERC Postdoctoral Fellowship.

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Associate editor: Dariusz Stramski

Received: 25 August 2011Accepted: 27 February 2012

Amended: 22 March 2012

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