Transmission of linearly polarized light in seawater: implications for polarization signaling
1 The Inter University Institute for Marine Sciences in Eilat, PO Box 469,
Eilat 88103, Israel
2 ESE Department, Life Sciences Institute, The Hebrew University, Jerusalem
91904, Israel
3 Department of Biological Sciences, University of Maryland Baltimore
County, 1000 Hilltop Road, Baltimore, MD 21250, USA
* Author for correspondence (e-mail: nadavs{at}huji.ac.il)
Accepted 12 July 2004
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Summary |
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Key words: partial linear polarization, polarization sensitivity, navigation, vision, communication
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Introduction |
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The distribution of polarized light underwater is predominantly affected by
the position of the sun (or the moon) in the sky, the optical properties of
the water, the depth of viewing and reflections from surfaces, such as the sea
floor or the surface of the water (Waterman,
1955,
1988
;
Waterman and Westell, 1956
;
Tyler, 1963
; Timofeeva,
1969
,
1970
;
Novales-Flamarique and Hawryshyn,
1997
; Cronin and Shashar,
2001
). Measurements performed at depths of 56 m by Waterman
(1954
) revealed that
underwater there are two distinct polarization patterns, one inside Snell's
window and one outside it. Generally, the polarization pattern inside Snell's
window down to depths of a few meters is assumed to be determined by the same
factors as those influencing the sky polarization. Therefore, sun position,
amount of overcast, amount of atmospheric dust, the distance of the point
observed from the zenith, multiple scattering, and depolarization due to
anisotropy of air molecules will all influence the polarization pattern within
Snell's window (Waterman,
1981
,
1988
).
Horvath and Varju (1995)
modeled the underwater polarization pattern within Snell's window as it
correlates to the celestial polarization pattern, taking into account
refraction and repolarization of skylight at the airwater interface.
However, due to the focusing and defocusing of sunlight by surface waves
(Schenck, 1957
;
Snyder and Dera, 1970
;
Stramska and Dickey, 1998
;
Maximov, 2000
) and changes in
polarization as the light propagates in water, certain distortions may well
occur. Indeed, Cronin and Shashar
(2001
), measuring polarization
at a depth of 15 m on a coral reef, found only small differences between the
polarization patterns within Snell's window and outside it. Underwater,
factors such as turbidity, bottom reflection
(Ivanoff and Waterman, 1958
)
and proximity to the shore line (Schwind,
1999
) may diminish the percent polarization. In shallow waters,
the percent polarization first decreases with depth
(Ivanoff and Waterman, 1958
)
and then reaches a depth-independent value
(Timofeeva, 1974
). Assuming
primarily Raleigh scattering, Waterman and Westell
(1956
) proposed a model for
the effect of the sun's position on the e-vector orientation outside
Snell's window (see also illustration in
Hawryshyn, 1992
). However, with
increasing depth, the pattern of e-vector orientation simplifies
rapidly, tending to become horizontal everywhere
(Waterman, 1955
;
Tyler, 1963
;
Timofeeva, 1969
). It also
diverges from the predictions of Waterman and Westell's model
(Waterman and Westell, 1956
)
suggesting an effect on polarization of other, non-Raleigh, modes of
scattering and of post-scattering processes. Within this complex partially
polarized light field, animals use polarization sensitivity for a wide range
of tasks.
Polarization imaging, combined with intensity imaging, can increase the
detection range of objects in a scattering medium, including those that
reflect polarized light (Briggs and
Hatcett, 1965; Lythgoe and
Hemming, 1967
; Lythgoe,
1971
; Rowe et al.,
1995
; Tyo et al.,
1996
; Chang et al.,
2003
), transparent objects
(Shashar et al., 1995
) and
non-polarizing objects (Cariou et al., 2003;
Chang et al., 2003
;
Schechner and Karpel, 2004
).
Fish and squid exploit this phenomenon, using polarization vision to improve
the range of detection of transparent prey
(Novales-Flamarique and Browman,
2001
; Shashar et al.,
1998
). Animals such as shrimps, the freshwater branchiopod
Daphnia and possibly fish also use the underwater polarized light
field for navigation or for escaping towards or away from shore
(Goddard and Forward, 1991
;
Ritz, 1991
;
Hawryshyn, 1992
;
Schwind, 1999
).
Some animals produce polarization patterns of reflected light that do not
contain intensity patterns (in other words, they cannot be seen using imaging
devices responding to intensity alone), which are apparently used for
communication. Examples of such animals include stomatopod crustaceans
(Marshall et al., 1999) and
cephalopods (Shashar et al.,
1996
). Polarization signaling has been suggested to serve as a
concealed means of communication used by polarization-sensitive animals that
are preyed upon by polarization-insensitive predators
(Shashar et al., 1996
). Cronin
et al.
(2003a
,b
)
postulated that polarization signals would be especially useful for animals
needing to transfer information at different depths, because spectral signals
will change according to the varying penetration of different wavelengths
through water, while polarization will maintain high signal constancy. We
wished to learn how polarization signals vary when seen from different
distances in water or, more generally, how natural waters affect the
propagation of patterns of polarized light.
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Materials and methods |
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The target was videotaped over a range of distances (0.510 m near LI
and 0.515 m at GBR) with a custom-built underwater imaging polarimeter.
This imaging polarimeter, placed 80100 cm above the sandy bottom (and
thus centered on the target) was based on a Sony VX1000E digital video camera
that used a Polaroid HN38S filter set in front of it, rotating automatically
to 0°, 45° and 90° from horizontal (where 0° represents the
filter being set horizontally). Exposure of the camera was set manually, thus
maintaining constant settings throughout each measurement series, and
measurements were performed near the middle of the camera's exposure range
(Chiao et al., 2000). The
camera and filter were placed inside an underwater housing equipped with a
flat viewing port. Color video images from the three filter settings (i.e.
0°, 45° and 90°) were replayed and captured by computer, reduced
into 8-bit gray-scale images and analyzed according to the equations of Wolff
and Andreou (1995
) to provide
the percent (partial) polarization, orientation of polarization and intensity,
throughout the image, on a single pixel basis
(Fig. 1). The details of these
calculations are provided elsewhere (Wolff
and Andreou, 1995
) but, in short, if I0,
I45 and I90 represent the intensity
values recorded when the polarizing filter was at 0°, 45° and 90°,
respectively, then:
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To measure the rate of decay of polarization at different wavelengths, we used a custom-built rapid spectral polarimeter (Fig. 2). This polarimeter uses three 600 µm-diameter, 10 m-long, UVVis transmitting fiber optics attached to a three-channel ADC1000-USB spectrometer (Ocean Optics, Duendin, FL, USA). The polarimeter allows for reading the spectra of the light arriving from the three fibers nearly simultaneously. The spectrometer was set for an integration time of 150 ms, and 30 spectra were averaged in each measurement. Dark noise correction was performed prior to any calculation. A restrictor providing an acceptance angle of 5° (in water) was attached to each fiber, in series with a linearly polarizing filter (Polaroid HNP'B) set at one of three orientations: 0°, 45° or 90°. The heads of the three fibers, including restrictors and filters, were set in an underwater housing such that they were spatially aligned in parallel. Custom software controlled data acquisition and polarization analysis over the wavelength range of 400700 nm.
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This sensor was placed underwater in front of the center of a 60x50 cm linear sheet polarizer (Polaroid HN38S; water sealed and equipped with a depolarizing filter at its back) producing vertical polarization. Since the fiber optic heads were 7 cm apart, with a 5° acceptance angle per fiber, all three fibers examined the target up to a distance of 5.25 m. Measurements were performed at 0.5 m intervals from 0.5 m to 4 m away from the target. Based on these measurements (eight measurements with three repetitions at each location), the rates of polarization decrease were calculated throughout the 400700 nm spectral range. Due to depth limitations (resulting from the length of the fiber optics), measurements were performed only in shallow waters (46 m deep), on two different days, near Horseshoe Reef, LI. On one of these occasions, a second set of measurements was obtained under nearly identical conditions using the video polarimeter and the 4-part target shown in Fig. 1.
Data were processed and analyzed using Microsoft Excel 2000® and Statistica 6.0® software.
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Results |
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The partial (percent) polarization of light arriving from the polarization filters of the target decreased with distance (Fig. 3), while that coming from the direction of the depolarized section increased (Spearman's correlation test, P>0.8 in all cases, 0.97 for Fig. 3A, 0.81 for Fig. 3B). Eventually, all measurements reached, or were close to (statistically indistinguishable from), the level of the background polarization. The decrease in partial polarization could, in all cases, be described using an exponential function (r2>0.88 in all cases; N=12; composed of two measurement sets, one taken from the vertical and the other from the horizontal polarizing panels of the target, at each of six measurement series performed; each series taken at a different time, place or line of site) following the general equation Pz=P0·eZ·cp, where P0 represents the original partial polarization (in our case postulated to be 100%, except for 90% in one case; i.e. that of the polarizers in the target), Pz represents the partial polarization at a distance of z (here, in meters) from the target, and cp represents the polarization extinction coefficient per meter.
|
The partial polarizations of the horizontally and vertically polarizing targets (after vectorially subtracting the polarization added by the scattering of downwelling light as measured from the depolarizing target) were very similar at each target distance, and so were their polarization extinction coefficients (Fig. 3). cp values were calculated for each of the 12 measurement sets taken from the vertical and horizontal polarizing panels (after correction for polarization in the veiling illumination) and used for further analysis. cp values of horizontal or vertical polarization were not significantly different (for partly turbid waters: cp horizontal = 0.54±0.06 m1; cp vertical = 0.54±0.03 m1; mean ± S.D.; Student's t-test, P>0.5) and hence were grouped together. cp values for sandy bottom areas with medium visibility of approximately 8 m, such as those surrounding LI, were 0.54±0.04 m1 (N=6), while in the very clear waters of the GBR, with visibility estimated at 40 m, cp values were lower, averaging 0.24±0.05 m1 (N=6).
Regarding the polarization orientation, near the targets the observed e-vector angles were those of the filters themselves (i.e. horizontal or vertical), while the orientation of the limited polarization that arose from veiling illumination (as measured in front of the depolarizing standard) was predominantly near the horizontal (e.g. near 160°; Fig. 4). As the partial (percent) polarization of the light coming from the target became lower with distance, and the effect of the veiling illumination became higher, the orientation of polarization of all parts of the target converged onto that of the veiling light (Fig. 4) and therefore also onto that of the background light.
|
cp varied with wavelength
(Fig. 5), with highest values
in the shorter (blue) range and the lowest values in the wavelength range
between 510 and
580 nm.
|
Modeling polarization pattern propagation
The results we obtained in this study encouraged us to formulate a general
model for the formation of polarized light fields in water. Such a model can
be useful for explaining (and predicting) the patterns of polarization seen in
natural waters. Here, we present the model for horizontal lines of sight; with
some effort, it can be, in principle, generalized to any direction of view
outside of Snell's window, with appropriate corrections for the changing
intensities of light at different depths along the line of sight and the
changing scattering angles (between the generally downwelling light and the
line of sight).
Consider the scattering of light perpendicular to a horizontal line of
sight. If the water is homogeneous, at sufficient depth one can assume
illumination to be equivalent at each position along a given line of sight.
This assumption is generally true at depths below the influence of localized
effects caused by the focusing or defocusing of downwelling light by waves
(Schenck, 1957;
McFarland and Loew, 1983
;
Stramska and Dickey, 1998
;
Maximov, 2000
) or by
reflections from objects or the substrate. In such constant conditions of
illumination, the amount of light scattered in each infinitesimally thin
distance plane is identical, and some constant fraction
(Ps) of this light is polarized. Let us designate the
intensity of the scattered light at each point as Io.
Then, the amount of light that is polarized is
IoxPs. As the light travels from
the point of scattering to the viewer, a distance designated by z,
the beam of light is attenuated by water by the standard equation:
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This model allows us to predict the partial polarization in the water along
horizontal lines of sight (P), where there are no
surface effects (e.g. Schenck,
1957
) nor reflection from the bottom (i.e. in midwater), and to
relate it to the inherent optical properties of the beam attenuation
coefficient (c), the polarization induced by side scattering
(Ps) and the polarization attenuation coefficient
(cp) (Fig.
6A). The percent of partial polarization is favored by increases
in c and by decreases in cp and is therefore
primarily dependent on the ratio cp/c; see
Fig. 6B. According to Jerlov
(1976
), beam attenuation in
coastal waters, in the spectral range from 440 to 700 nm, varies from
0.1
to
1.0 m1. As noted above, Ps
ranges from
50% to
80% (Ivanoff
and Waterman, 1958
). In the present study, we measured
cp as
0.3 to 0.5 m1 in fairly clear
coastal waters. Since Ps, cp and
c are all influenced by water clarity and the type of material
suspended in water, they are closely interrelated. However, one should note
that while c and cp are inherent optical
properties of the water, Ps is influenced by the
illumination conditions (such as the orientation of the sun) and should be
considered as an apparent optical property of the water.
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Discussion |
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Scattering creates two interacting effects on polarization propagation. On the one hand, forward scattering gradually depolarizes the original signal. On the other hand, side scattering introduces polarization due to the strong directionality (usually near overhead) of the downwelling light (Fig. 3). Although both processes tend to reduce the original signal, the interactions between them, together with the polarization of the background illumination, determine the polarization contrast level available to a polarization-sensitive animal.
The magnitude of the effects that these processes have on the original
signal depends on the optical path length between the target and the observer.
However, assuming a homogeneous medium, they are not dependent either on the
direction or on the section of the path that is examined. Hence, the
mathematical description of these effects is expected to be exponential in
nature (Lythgoe, 1971). Our
measurements of partial polarization decay indeed follow the exponential
equation
Pz=P0·eZ·cp.
The propagation of partial polarization depends heavily on the scattering of
the medium in which it travels. In the partly turbid waters near LI, which
could be considered as representing moderately clear coastal waters, the decay
was fairly rapid in nature, with nearly half of the partial polarization being
lost with each 1.25 m traveled through water. This decay was lower in the
clear oceanic waters of the GBR; yet even here, 50% polarization loss occurred
at only 3 m or, to put it differently, only 10% of the original polarization
was left after 4.1 and 10 m, respectively, in these two types of water. There
was no difference in the extinction of partial polarization of the different
orientations, with proper accounting for the effects caused by the addition of
low levels of partly polarized veiling light. In our work, the downwelling
light was nearly horizontally polarized, deviating no more than 20° from
the horizontal plane, but different lines of sight would have different
orientations of polarization depending primarily on the sun's position and
visibility within Snell's window and on the water depth
(Waterman and Westell, 1956
;
Waterman, 1988
;
Hawryshyn, 1992
;
Cronin and Shashar, 2001
). It
should be noted that since these measurements were made near the bottom, where
sediment is continuously resuspended by currents and diver activity, they are
probably somewhat greater in value than might be found higher up in the water
column.
Based on these results, it is reasonable to predict that polarization
patterns (including the celestial polarization pattern) will not propagate
very far in water. Novales-Flamarique and Hawryshyn
(1997) found that, even in
shallow waters, the polarization of the light within Snell's window is lower
than in air and that it further decreases with depth. Therefore, underwater
navigation based on the celestial polarization pattern will be limited, at
least near the coast, to shallow water. However, as the polarization
orientation of the background illumination (produced in the water itself) is
dependent on the position of the sun
(Waterman and Westell, 1956
;
Waterman, 1988
;
Cronin and Shashar, 2001
),
animals may be able to use their polarization sensitivity for orientation in
deeper waters. Other visual tasks, such as object detection and communication,
are likely to be much less depth dependent, as the underwater light field is
likely to be partially polarized throughout the photic zone
(Waterman, 1955
;
Tyler, 1963
).
In several cases, a biologically important polarization contrast arises
from an object being less polarized than the background. Such cases may be
reflections off fish (Shashar et al.,
2000) or light passing through transparent objects such as
planktonic organisms (Shashar et al.,
1998
; Novales-Flamarique and
Browman, 2001
). In these cases, the depolarization of the original
signal due to forward scattering will not reduce the polarization contrast
between the target and the background; instead, light from the direction of
the object will become increasingly polarized by the veiling polarization. The
differences between the rates of such increase in polarization vs
polarization loss due to scattering will determine whether such a depolarized
target could be detected at a larger or shorter range than a polarized one.
Hence, a polarization pattern produced by transparent depolarizing objects is
expected to behave differently from that of polarizing objects. The factors
governing the propagation of such a depolarized signal and especially the
effects of the brightness of the depolarizing object need further
examination.
The change in partial polarization of light coming from a small object will
be identical to that of the polarization coming from a large target. Hence,
even in waters of relatively high values of cp,
polarization vision could be used for detecting or examining small objects or
patterns at distances of relevance for the viewing animals (for example, small
fish detecting planktonic prey at distances of centimeters;
Novales-Flamarique and Browman,
2001).
The mathematical model presented here enables us to better understand the
factors governing the partial polarization of the background illumination in
open waters within the optical zone of the sea, distant from bottom effects
and from heterogeneity in illumination at the surface on the ocean. The model
focuses on the processes affecting the polarization following the initial
scattering event. Hence, it is independent of the mode of scattering in the
water (Raleigh vs Mie). One outcome of the model and especially of
equation 7, as well as of work by Timofeeva
(1974), is that in an
optically homogeneous water column with a well-defined light source in a
constant position (such as the conditions occurring in the lower part of the
photic zone, where the patch of brightest light is close to overhead
throughout the entire day; see Jerlov,
1976
), the partial polarization of the background will not vary
with depth. Reports by Ivanoff and Waterman
(1958
) and by Tyler
(1963
) tend to support this
outcome, although information about changes in the solar position between
measurements is not provided. The model predicts that background polarization
(P
) depends on the ratio between
cp and c (Fig.
6B). Timofeeva
(1970
) found that
P
is related to a parameter she designated as
T (also referred to as
;
Timofeeva, 1974
), defined as
the ratio between the scattering attenuation coefficient and the total
(asymptotic) light attenuation coefficient. Hence, T ranges from 0 to
1. Our cp and Timofeeva's
both depend on the
scattering properties of the media, although the two are not equivalent:
cp is an empirical value and
is a theoretical one.
It is reasonable to expect that cp is strongly affected by
scattering, and thus cp and T may well be closely
related. Understanding underwater polarization and its theoretical basis still
requires a thorough understanding of how light is scattered, polarized and
attenuated in natural waters.
Ps, T, cp and c are
wavelength dependent. Not surprisingly, the decrease in partial polarization
with distance was therefore found to vary with wavelength
(Fig. 5), most likely due to
wavelength-dependent scattering and absorption of light in the water. Hence,
it is highly possible that in different water types, such as green or brown
coastal waters (Jerlov types 3 or 9;
Jerlov, 1976), different
wavelengths will best transmit a polarization signal. Our results show that,
in the types of waters we examined, polarization decay is lowest in the
510580 nm range. Ivanoff and Waterman
(1958
) reported little partial
polarization variation with wavelength in the ambient light field, in the
order of 5% out of an approximately 1030% average partial polarization,
with the minimal partial polarization occurring at 450500 nm. Cronin
and Shashar (2001
) reported
similar findings and interpreted these as demonstrating that the ambient
(background) polarization is nearly constant across the visual spectrum. In
cephalopods and stomatopods, polarization vision is based on photoreceptors
with maximal sensitivity around 500 nm. Hence, the polarization sensitivity of
these animals (species of which inhabit the waters we examined) is well suited
for detecting polarization patterns, either for signaling or for target
detection, functioning within the spectral range in which polarization
patterns propagate fairly well, while background and veiling polarization are
relatively low.
Polarization vision, and especially polarization signaling, has the potential to provide polarization-sensitive organisms with information that is concealed from polarization-insensitive animals. The stability of polarization signals with depth offers a potential advantage for polarization sensitivity over color vision, but our results also indicate that these signals are most effective at short range (i.e. no more than a few meters). The conditions in which polarization signals are used, the information they contain and the visual adaptations required for making use of this information require further investigation.
Our model allows one to predict the partial polarization of background illumination in the horizontal plane. This information is important since it sets the stage for polarization contrast functions such as prey detection. It is somewhat counterintuitive to find that the percentage of background polarization is positively correlated with c (Fig. 6A), primarily because greater levels of beam attenuation diminish the effect of polarization decrease by scattering of polarized light arriving from greater distances.
The amount of light that is partially polarized by side scattering (Ps) depends on the amount and type of scattering occurring in the water. It is therefore affected by the concentration, size, shape and heterogeneity of the scatterers in the water. Changes in the downwelling light distribution due to wave action may also change Ps. Our model is limited to the horizontal line of sight and assumes a homogenous medium and constant illumination conditions. Further measurements and calculations are required to verify actual values of the critical parameters in nature (i.e. cp, c and Ps), to extend this model to the whole visual sphere, and to incorporate into it temporal and spatial variation in the illumination field.
Summarizing, we found that polarization patterns propagate to relatively short distances in seawater. Therefore, the visual tasks that make use of such patterns or their details are range-limited as well. Polarization signals will not be seen by distant observers, be they conspecifics or predators. Similarly, navigation, detection of prey and object recognition will be limited to the distances or depths at which the polarization patterns can be seen. This range limitation may be less important to small animals or animals with low visual acuity, but in large predators we suggest that polarization sensitivity will be more useful for ambush predators or for those that are slow moving. Fast-swimming animals, or those who hunt prey at great range, would gain little from using polarization vision to detect objects.
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Acknowledgments |
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References |
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---|
Briggs, R. O. and Hatcett, G. L. (1965). Techniques for improving underwater visibility with video equipment. Ocean Sci. Ocean Eng. 1&2,1284 -1308.
Cariou, J., Jeune, B. L., Lotrian, J. and Guern, Y. (1990). Polarization effects of seawater and underwater targets. Appl. Opt. 29,1689 -1695.
Chang, P. C. Y., Flitton, J. C., Hopcraft, K. I., Jakeman, E., Jordan, D. L. and Walker, J. G. (2003). Improving visibility depth in passive underwater imaging by use of polarization. Appl. Optics. 42,2794 -2803.[Medline]
Chiao, C. C., Osorio, D., Vorobyev, M. and Cronin, T. W. (2000). Characterization of natural illuminants in forests and the use of digital video data to reconstruct illuminant spectra. J. Opt. Soc. Am. A 17,1713 -1721.
Cronin, T. W. and Shashar, N. (2001). The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle. J. Exp. Biol. 204,2461 -2467.[Medline]
Cronin, T. W., Shashar, N., Caldwell, R. L., Marshall, J., Cheroske, A. G. and Chiou, T. H. (2003a). Polarization signals in the marine environment. In Proceedings of SPIE 5158: Polarization Science and Remote Sensing (ed. J. A. Shaw and J. S. Tyo), pp. 85-92. Bellingham, WA: SPIE Press.
Cronin, T. W., Shashar, N., Caldwell, R. L., Marshall, J., Cheroske, A. G. and Chiou, T. H. (2003b). Polarization vision and its role in biological signaling. Int. Comp. Biol. 43,549 -558.
Goddard, S. M. and Forward, R. B. (1991). The role of the underwater polarized-light pattern, in sun compass navigation of the grass shrimp, Palaemonetes vulgaris. J. Comp. Physiol. A 169,479 -491.
Hawryshyn, C. W. (1992). Polarization vision in fish. Am. Sci. 80,164 -175.
Hechet, E. (1998). Optics. Reading, MA: Addison Wesley Longman, Inc.
Horvath, G. and Varju, D. (1995). Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell's window of a flat-water surface. Vision Res. 35,1651 -1666.[CrossRef][Medline]
Ivanoff, A. and Waterman, T. H. (1958). Factors, mainly depth and wavelength, affecting the degree of underwater light polarization. J. Mar. Res. 16,283 -307.
Jerlov, N. G. (1976). Marine Optics. Amsterdam: Elsevier.
Lythgoe, J. N. (1971). Vision. In Underwater Science (ed. J. D. Woods and J. N. Lythgoe), pp. 103-139. London: Oxford University Press.
Lythgoe, J. N. (1979). The Ecology of Vision. London: Oxford University Press.
Lythgoe, J. N. and Hemming, C. C. (1967). Polarized light and underwater vision. Nature 213,893 -894.[Medline]
Marshall, J., Cronin, T. W., Shashar, N. and Land, M. (1999). Behavioural evidence for polarisation vision in stomatopods reveals a potential channel for communication. Curr. Biol. 9,755 -758.[CrossRef][Medline]
Maximov, V. V. (2000). Environmental factors which may have led to the appearance of colour vision. Phil. Trans. R. Soc. Lond. B 355,1239 -1242.[CrossRef][Medline]
McFarland, W. N. and Loew, E. R. (1983). Wave produced changes in underwater light and their relations to vision. Environ. Biol. Fish. 8,173 -184.
Novales-Flamarique, I. and Browman, H. I. (2001). Foraging and prey-search behaviour of small juvenile rainbow trout (Onchorhychus mykiss) under polarized light. J. Exp. Biol. 204,2415 -2422.[Medline]
Novales-Flamarique, I. and Hawryshyn, C. W. (1997). Is the use of underwater polarized light by fish restricted to crepuscular time periods? Vision Res. 37,975 -989.[CrossRef][Medline]
Ritz, D. A. (1991). Polarized-light responses in the shrimp Palaemonetes vulgaris (Say). J. Exp. Mar. Biol. Ecol. 154,245 -250.[CrossRef]
Rowe, M. P., Pugh, E. N., Jr, Tyo, J. S. and Engheta, N. (1995). Polarization difference imaging: a biologically inspired technique for observation through scattering media. Opt. Lett. 20,608 -610.
Schechner, Y. and Karpel, N. (2004). Clear underwater vision. Proc. IEEE Computer Vision and Pattern Recognition 1,5 36-543.
Schenck, H. (1957). On the focusing of sunlight by ocean waves. J. Opt. Soc. Am. 47,653 -657.
Schwind, R. (1999). Daphnia pulex
swims towards the most strongly polarized light a response that leads
to `shore flight'. J. Exp. Biol.
202,3631
-3635.
Shashar, N., Adessi, L. and Cronin, T. W. (1995). Polarization vision as a mechanism for detection of transparent objects. In Ultraviolet Radiation and Coral Reefs. (ed. D. Gulko and P. L. Jokiel), pp.207 -212. Manoa, HI: HIMB and UNIHI-Sea Grant.
Shashar, N., Rutledge, P. S. and Cronin, T. W.
(1996). Polarization vision in cuttlefish a concealed
communication channel? J. Exp. Biol.
199,2077
-2084.
Shashar, N., Hanlon, R. T. and Petz, A. deM. (1998). Polarization vision helps detect transparent prey. Nature 393,222 -223.[CrossRef][Medline]
Shashar, N., Hagan R., Boal, J. G. and Hanlon, R. T. (2000). Cuttlefish use polarization sensitivity in predation on silvery fish. Vision Res. 40, 71-75.[CrossRef][Medline]
Snyder, R. L. and Dera, J. (1970). Wave-induced light-field fluctuations in the sea. J. Opt. Soc. Am. 6,1072 -1079.
Stramska, M. and Dickey, T. D. (1998). Short-term variability of the underwater light field in the oligotrophic ocean in response to surface waves and clouds. Deep Sea Res. I 45,1393 -1410.[CrossRef]
Timofeeva, V. A. (1969). Plane of vibrations of polarized light in turbid media. Izvestiya Atmos. Ocean. Physics 5,603 -607.
Timofeeva, V. A. (1970). The degree of polarization of light in turbid media. Izvestiya Atmos. Ocean. Physics 5,513 -522.
Timofeeva, V. A. (1974). Optics of turbid waters. In Optical Aspects of Oceanography (ed. N. Jerlov and E. Steeman-Nielsen), pp. 177-218. New York: Academic Press.
Tyler, J. E. (1963). Estimation of percent polarization in deep oceanic water. J. Mar. Res. 21,102 -109.
Tyo, J. S., Rowe, M. P., Pugh, E. N., Jr and Engheta, N. (1996). Target detection in optically scattering media by polarization-difference imaging. Appl. Opt. 35,1855 -1870.
Waterman T. H. (1954). Polarization patterns in submarine illumination. Science 120,927 -932.
Waterman, T. H. (1955). Polarization scattered sunlight in deep water. Deep Sea Res. 3(Suppl.),426 -434.
Waterman T. H. (1981). Polarization sensitivity. In Comparative Physiology and Evolution of Vision in Invertebrates (ed. H. Autrum), pp.281 -463. Berlin: Springer-Verlag.
Waterman, T. H. (1988). Polarization of marine light fields and animal orientation. SPIE 925,431 -437.
Waterman, T. H. and Westell, W. E. (1956). Quantitative effects of the sun's position on submarine light polarization. J. Mar. Res. 15,149 -169.
Wolff, L. B. and Andreou, A. G. (1995). Polarization camera sensors. Image Vision Comput. 13,497 -510.[CrossRef]