The Underwater Optical Channel
Laura J. Johnson
Department of Engineering
University of Warwick
February 27, 2012
Abstract
An essay on the underwater wireless optical communication channel is presented. There is
a discussion of the major causes of absorption and scattering. This paper suggests optimum
wavelengths for transmission in both open ocean and coastal areas to be chosen by absorption,
these are blue-green and yellow-green respectively. It is found that open oceans are limited by
pure water absorption whilst coastal regions are dominated by large particle scattering.
1
Motivation
Free-space optics (FSO) is a branch of optical communications that uses air as the transmission
medium. There exists a need to modify this technology for high-speed, low-range underwater
applications as current technologies are not suitable; conventional acoustic systems undergo severe
multipath dispersion and therefore cannot support high bandwidths [1] whilst radio frequencies are
subject to extreme signal attenuation underwater [2]. Applying FSO underwater is not a trivial
matter. The underwater environment is far more challenging than air, not only due to increased
channel attenuation, but also significant variability and more sources of communication disruption.
Natural oceans are rich in dissolved and particulate matter, leading to a large range of conditions
that an underwater communication system must satisfy. However, constituent properties and
optical properties are coupled, implying that optical constants can be deduced from the local
water composition. For example, in Figure 1 (a) the clear open ocean is blue in colour, whereas
the productive, particulate-rich coastal water in (b) appears green.
This research essay aims to explore the factors which determine how light propagates underwater and how they might impact on a communication system. The sources of noise which are
specific to the underwater channel are also discussed. By using the detailed underwater optical
channel which is described here, it is hoped that underwater FSO systems can achieve increased
performance and range.
(a) Open ocean
(b) Coastal ocean
Figure 1: Varied optical properties of ocean water due to differing composition [3].
1
∆r
Φs (λ, ψ)
ψ
Φi (λ)
Φa (λ)
-
- Φt (λ)
Figure 2: Geometry of inherent optical properties for a volume ∆V [4]
2
Introduction
Optical properties of water are divided into two mutually exclusive groups: inherent and apparent. Inherent properties describe optical parameters which depend only on the medium, more
specifically the composition and particulate substances present. Apparent properties depend on
both the medium and the geometric structure of illumination, thus is a directional property. Inherent and apparently properties are explored in sections 2.1 and 2.2 respectively.
2.1
Inherent Optical Properties
When a beam of light is sent through a medium there are two reasons that a reduced number
of photons reaches the receiver. The first possibility is that the photon changes direction, this
phenomena is known as scattering. Alternatively, the photon could have its energy converted into
another form, such as heat or chemical, which removes it from the light path completely. This
process is known as absorption. Scattering and absorption are combined to give the overall beam
attenuation. The beam attenuation coefficient, which describes the loss of power per meter, is
derived in the following way:
Begin by considering an elemental volume of water, ∆V , which has thickness ∆r, as shown
in Figure 2. The water is illuminated by a collimated beam of monochromatic light, at a fixed
wavelength λ, of spectral radiant power Φi . A certain amount of the incident power is absorbed by
the water, denoted Φa . Another portion of the power will be scattered, the total scattering power
Φs (λ) is the summation of Φs (ψ, λ) over all angles of ψ. The remaining power, Φt passes through
the water unaffected. Therefore, by conservation of energy, it can be said that;
Φi (λ) = Φa (λ) + Φt (λ) + Φs (λ)
(1)
The critical assumption made here is that no photon re-emittance has occurred, this will be
revisited in section 5.2. The absorbance A is now defined as the fraction between incident power
and absorbed power, as written in equation 2. Scatterance B refers to the ratio between incident
power and scattered power.
A(λ) ≡
Φa (λ)
,
Φi (λ)
B(λ) ≡
Φs (λ)
Φi (λ)
(2)
Although these coefficients accurately describe the inherent optical properties, it is more useful
to define them per unit distance. The subsequent new coefficients are attenuation a and scattering
b. These coefficients are found by taking the limit as the thickness becomes infinitesimally small.
∆A(λ)
dA(λ)
=
(3)
∆r
dr
The scattering and absorption coefficients can be combined to gives the overall beam attenuation c, as required. Superposition may be applied as the coefficient are linear;
a(λ) ≡ lim
∆r→0
a(λ) + b(λ) = c(λ)
2
(4)
Water Type
Clear ocean
Coastal ocean
Harbour water
a(m−1 )
b(m−1 )
c(m−1 )
0.114
0.179
0.366
0.037
0.220
1.829
0.151
0.399
2.195
Figure 3: Typical inherent coefficient values [5]
To calculate the attenuation over many meters, say distance z, the propagation loss factor in
equation 5 should be calculated. This equation shows an exponential decrease in power where the
rate of decay is dictated by the attenuation coefficient.
L(λ, z) = e−c(λ)z
(5)
Inherent optical properties depend on the composition, concentration and morphology of both
particulates and dissolved substances. As will be discussed in section 3, there is a large variation
in the absorption spectra for different substances; concentration also has a profound effect. Section
4 focuses on scattering and shows how particles of various shape and size scatter light differently.
In general, the physical characteristics of seawater composites varies by orders of magnitude and
therefore so do the inherent attenuation coefficients. Figure 3 shows typical values for the attenuation, absorption and scattering coefficients in different locations. Light propagation in turbid
areas such as harbours is much more difficult than open ocean, thus making it more challenging to
design a communication system to work near the shore. The values in figure 3 shall be discussed
further in sections 3.5 and 4.6 but note that open ocean and coastal locations correspond with the
images in figure 1.
2.2
Apparent Optical Properties
Apparent optical properties are those which depend on both the medium and the geometric
structure of illumination [6]. Their existence is due to the difficulty in measuring inherent properties
directly; the common apparent coefficients are radiance, irradiance and reflectance. Apparent
optical properties can only be formed from regular and stable sources of illumination in order
to be a useful descriptor of a body of water. This means, for example, that the downwelling
irradiance from sunlight is not an apparent property because it changes due to cloud cover and
time of day. There are two methods which can be used to transform this into a usable apparent
property; either create a ratio of properties which are equally affects by the environment or use
the normalised derivative. The latter method creates what is known as the diffuse attenuation
coefficient K, the general form of which is written in equation 6.
K(z, λ) = −
1
dE(z, λ)
E(0, λ)
dz
(6)
Where E is the original apparent property such as downwelling irradiance of sunlight. There
are a few important factors to know about K functions [7]: they are all directional; they vary
greatly near the ocean surface; they are not constant with depth, even with homogeneous water;
they can take positive or negative values at boundaries and finally, at certain distances they become
the same as the inherent properties (known as K∞ ). K functions will be revisited in section 5.1
as part of the description of background light sources.
2.3
Ocean Classification
There have been numerous attempts to classify ocean waters by their optical properties in
order to increase generalisation in ocean optics. The most successful schemes are visual colour
3
Figure 4: Jerlov water classifications map for types I-III [8] [9]
matching, Jerlov water types and ternary diagrams [11]. Visual classification with a Secchi disk
was historically the first classification scheme. It used a submerged white disk and grouped ocean
types by what colour the disk appeared to be. As this is very inaccurate, it has since been replaced
by other technologies such as the Forel-Ule scale, which compares the water colour to twenty-two
different coloured chemicals. Visual schemes are qualitative and primarily based on absorption
since scattering has a lesser affect on water colour.
The first quantitative classification scheme was derived by Jerlov [12]. It is based on an apparent
optical property; the downwelling irradiance of sunlight. The Jerlov water classification scheme
splits the ocean into two types; open ocean water and coastal water. Open ocean is then subdivided
into four categories, IA, IB, II and III. Whilst coastal areas are split into groups 1-9, representing
increasing turbidity. The distribution of these waters over the earth’s surface is shown in Figure 4.
This is the most popular of the three schemes discussed here.
Ternary diagrams use inherent optical properties to create a triangle of relative contributions
for each of the main optical components of ocean water. As with colour matching, this method
is focussed on absorption. It is the only scheme which is capable of classifying the ocean below a
depth of 50-200 m.
3
Absorption
Absorption is a highly wavelength dependant process where electromagnetic energy is converted
into other forms, typically heat or chemical. It is significant in a optical communication systems
because it dramatically reduces the photons that reach the detector. Absorption is much more
significant in water than in air, and again more profound in seawater than pure water. The
overall absorption of seawater can be written as the sum of each of the ocean’s optical components
multiplied by their concentration;
a(λ) =
n
X
Ci ai (λ).
(7)
i=0
The optical properties are split into: pure seawater, denoted aw ; elemental marine life, phytoplankton aφ ; gelbstoff ag which is decaying organic matter and finally non-algal materials in
suspension, denoted an . In this section, the contribution from each of these components is explored separately.
a(λ) = Cw aw (λ) + Cφ aφ (λ) + Cg ag (λ) + Cn an (λ)
4
(8)
(a) Pure Water [13]
(b) Phytoplankton [14]
(c) Gelbstoff
(d) Non-algal particles
Figure 5: Typical absorption spectra for different ocean optical components, absorption coefficients
in m−1 .
(a) Open ocean
(b) Coastal region
Figure 6: Combined absorption spectra of different ocean types, absorption coefficients in m−1 .
5
Figure 7: Absorption spectra of different specie of phytoplankton [7].
3.1
Pure Seawater
Seawater comprises mostly of water, the rest being dissolved salts such as NaCl, MgCl2 ,
Na2 SO4 , CaCl2 and KCl [15]. Such a composition gives seawater a complex absorption spectrum.
The absorption coefficient throughout most of the electromagnetic spectrum is high, typically 104
m−1 for infra-red [16], but there is a region in the visible light spectrum (400-700 nm) where it
is significantly reduced. Consequentially, the typical wavelengths used in FSO communications,
which are in the infra-red region, are unsuitable. In figure 5 (a) the absorption spectrum has been
plotted for the visible light region. Red wavelengths of 500 nm or higher are greatly attenuated
by water, leaving primarily blue light to propagate. This is one of the reasons why relatively clear
oceans, such as the one in figure 1 (a) appear a rich blue colour. Indirect methods have been used
to determine a maximum for the water absorption coefficient, given in equation 9 [17].
bw (λ)
(9)
2
Where bw is the scattering coefficient of water and K is the diffuse coefficient, as before. This
formula is useful in worse case calculations for communication systems.
The seawater concentration Cw which appears in equation 8 can be set to unity for most applications. Exceptions to this are where the seawater is mixed with another significantly present liquid.
Examples of where this might occur include at estuaries where there is a a seawater/freshwater
mix and seawater/oil mixes due to pollution.
aw (λ) < K(λ) −
3.2
Phytoplankton
Phytoplankton are photosynthesising, microscopic organisms which form the foundation of the
oceanic food chain and account for roughly half photosynthetic activity on earth [18]. Phytoplankton describes a diverse group of species and the optical properties of each is determined by
their composition and concentration of pigments. Figure 7 shows the visible absorption spectrum
of several types of phytoplankton. Common absorption features shared by all species are; high
absorption in the blue-green 400-500 nm region and a further peak at 670 nm. The reason that
these features are similar is because the absorption behaviour is dominated by a single pigment,
chlorophyll. Chlorophyll is such a significant component that the overall phytoplankton absorption
aφ is often approximated to the chlorophyll absorption spectrum. This spectrum is given in figure
5 (b). As the blue and red wavelengths are absorbed, areas with high phytoplankton appear more
yellow-green in colour, as was shown in the coastal region of figure 1 (b).
The concentration of phytoplankton Cφ is well documented, both across the sea surface and at
different depths. As phytoplankton is a photosynthesising organism, it inhabits only the part of
the ocean where sunlight can propagate, known as the photic zone. This is up to 200 m deep in
clear open ocean waters, 40 m over continental shelves and 15 m in coastal waters [19]. The depth
distribution of these organisms in the photic zone is a skewed Gaussian curve from the surface,
given by the following equation [20]:
6
h
−(z − zmax )2
(10)
Cφ (z) = B0 + Sz + √ exp
2σ 2
σ 2π
Where B0 is the background chlorophyll concentration at surface, S is the vertical gradient of
concentration, h is the total chlorophyll above background levels, z is the depth and finally, σ is the
standard deviation of concentration. The standard deviation is calculated by a further formula:
q
σ = h/ 2π(Cφ(zmax ) − B0 − Szmax )
(11)
The subsequent phytoplankton distributions typically have a maxima at between depths of
20-50 m and decays to a negligible level at 50-200 m depending on the surface phytoplankton
levels. This is significant because it means the attenuation coefficient changes with depth, so
a communication system will give a different performance depending on the depth of water it
propagates through. Ocean surface chlorophyll levels are determined by remote sensors such as the
SeaWiFS (Sea-viewing Wide Field-of-view Sensor) project which uses a colour matching method
[42]. The concentrations have also been linked to Jerlov water types. For example, type IA water
has a typical chlorophyll concentration of 0.1 mg m−3 whereas coastal water type 1 has a chlorophyll
concentration of 9 mg m−3 . In general, coastal and harbour areas have far higher concentrations
of phytoplankton than the open ocean, despite them existing in a more shallow region. Another
method to determine surface chlorophyll concentration is via fluorescence, where phytoplankton
emits light at a longer wavelength and is detected, this shall be discussed in detail in section 5.2.
3.3
Gelbstoff
Gelbstoff has various names; colour dissolved organic material, yellow substance and gilvin. It
is defined operationally as organic material that passes through a filter of nominal pore size 0.2 mm
[21]. It comprises of broken down plant tissue and decaying marine matter. Gelbstoff therefore
contains humic and fulvic fluid as well as CO2 and an inorganic mix of nitrogen, sulphur and
phosphorus, the three main plant nutrients. It is sometimes split into its constituent components
such that:
ag (λ) = ah (λ) + af (λ)
(12)
Where ah and af are the absorption coefficients for fulvic and humic fluids respectfully. Others
substances provide negligible contribution to the absorption and therefore are not included. The
absorption spectrum for gelbstoff in the visible region is given in figure 5 (c). The spectrum is
approximately exponential, where blue-violet wavelengths are highly attenuated so that yellow-red
colours become more dominant. Beer’s law is used to fit the exponential function, as given in
equation 13. The slope of the function Sg is estimated by non-linear regression and the wavelength
measurement is given in nm:
ag (λ) = ag (440) exp[−Sg (λ − 440)]
(13)
Gelbstoff is generally present in low concentrations in open waters and in higher concentrations
in the coastal waters. It is strongly linked to the amount of phytoplankton present and this is
explored in section 3.5.
3.4
Non-Algal Materials
Non-algal materials widely vary in composition but are grouped due to similar absorption
behaviour. It is a composite of living organic particles such as bacteria, zooplankon, detrital organic
matter and suspended inorganic particles such as quartz and clay. The absorption spectrum is given
in figure 5 (d), as with gelbstoff it can be described by an exponential:
an (λ) = an (440) exp[−Sn (λ − 440)]
7
(14)
Where Sn is the exponential slope which typically takes values between 0.006 - 0.013 nm−1 [14]
[22] making it a statistically flatter curve than that of gelbstoff. Despite being optically important,
there are no empirical relations for the concentration of non-algal materials as it is such a diverse
group. They are therefore often omitted from unified channel models, as will be shown in the next
section.
3.5
Unified Absorption Model
Haltrin derived a model which describes the concentration and absorption of each of the ocean
optical components in terms a single parameter; chlorophyll concentration [23]. In the model,
which is given in equation 15, the contribution from non-algal particles has been omitted as there
is currently no known way to predict their concentration and gelbstoff is split into the main
components, as written in equation 12. The model was created by combining in-situ measurements
of inherent optical properties from various researchers and reports.
a(λ) = aw (λ) +
a∗φ (λ)
Cφ
Cφ∗
!0.6
+ a∗f Cf exp [−kf λ] + a∗h Ch exp [−kh λ]
(15)
Where Cφ is the total concentration of chlorophyll in mg m−3 (Cφ∗ = 1 mg m−3 ) and a∗φ is
the specific absorption coefficient of chlorophyll. a∗f and a∗h are the specific absorption coefficients
of fulvic and humic acid respectfully (given as a∗f = 35.96 m2 mg−1 and a∗h = 18.8) with decay
constants of kf = 0.019 nm−1 and kh = 0.011 nm−1 . Finally, Cf and Ch are the concentrations
of fulvic and humic acid. They can be determined from the concentration of chlorophyll by the
following equations:
Cf = 1.74098Cφ exp [0.12327Cφ ]
(16)
Ch = 1.9334Cφ exp [0.12343Cφ ]
(17)
In open oceans, the chlorophyll concentration is low, therefore so too are the concentrations of
humic and fulvic acid. The subsequent absorption spectrum is dominated almost entirely by the
attenuation of pure water which is evident from the shape of the spectrum in figure 6 (a). For
wavelengths of 500 nm and greater, the attenuation coefficient is almost the same as that of pure
water (figure 5 (a)) with only a small absorption increase in the blue region. From this it can be
deduced that the most ideal wavelengths for an optical communication system in open oceans is
450-500 nm, which represents blue-green light.
In coastal regions the chlorophyll concentration can be up to two orders of magnitude higher
than that found in open oceans, leading also to a greater concentration of gelbstoff. In this case, the
total absorption in shorter wavelengths becomes dominated by the combination of phytoplankton
and gelbstoff, as shown in figure 6 (b), and the ideal transmission wavelength is shifted. The lowest
absorption is experienced between 520-570 nm, which means yellow-green light propagates best in
these areas. It is important to note at this point that in an open and still ocean, the behaviour is
influenced mainly by absorption, so the attenuation coefficient is close to the absorption coefficient.
However, in coastal places organic matter also causes great amounts of scattering which induces
more signal losses than absorption. The next section looks in detail at the process of scattering.
4
Scattering
Scattering is a change of direction of electromagnetic energy and there are two reasons why
it is significant for a communication system. Firstly, it reduces the number of photons reaching
the detector, therefore weakening the detected signal. The second reason is the temporal effects
that can occur, this is shown in figure 8. If a photon is scattered away and then later scattered
8
Figure 8: Origin of temporal scattering [24].
back and detected, it has travelled a longer path than a photon moving a straight line. The longer
path takes more time to travel and the time delay between receiving the two photons can cause
inter-symbol interference if the bit rate of the system is not suitably lowered to accommodate for
the temporal scattering.
Scattering is largely independent of wavelength. In fact, it is more dependant on particulates
that are present, thus is dominant in particulate-rich coastal areas. Scattering also occurs in pure
seawater and because of its refractive index changes which can be due to variations in flow, salinity
and temperature. At present, it is not possible to describe a scattering equivalent of equation
8 as little is known about some aspects. Therefore, this section explores the extent of existing
knowledge on scattering. However, before looking in detail at the individual causes, the geometry
of scattering must be defined.
4.1
Volume Scattering Function
The volume scattering function (VSF), β, describes the ratio of the intensity of scattered light
to the incident irradiance, per unit volume; it is often named as an additional inherent optical
property [12]. Before the VSF can be derived, two assumptions must be made about the system.
First, the water is assumed to be isotropic so that its influence on the incident light is the same
in all directions and secondly, the incident light is unpolarised. If these two assumptions are true,
then scattering is azimuthally symmetric and depends only on ψ, the scattering angle (see figure
2). The scatterance, which was first introduced in equation 2, becomes angular dependant and is
consequentially described as fraction of incident scattered power through an angle ψ into a solid
angle ∆Ω. The VSF is the limit of this as the thickness r and solid angle become infinitesimally
small:
∆B(ψ, λ)
(18)
∆r→0 ∆Ω→0 ∆r∆Ω
To convert the VSF into its usual form, the scatterance from equation 2 is substituted in. The
spectral scattered power is rewritten as intensity of scattered power multiplied by the solid angle,
Φs (ψ, λ) = Is (ψ, λ)∆Ω, and the spectral incident power is split into incident irradiance multiplied
over area of incidence Φi (λ) = Ei (λ)∆A. Recalling also that ∆V = ∆r∆A, the VSF can finally
be written as:
β(ψ, λ) ≡ lim
β(ψ, λ) =
lim
dIs (Ω, λ)
1
Ei (0, λ)
dV
(19)
This equation very much fits the description of a volume scattering function; a ratio of scattered
light intensity to incident irradiance, per unit volume. To give the total scattered power per unit
irradiance, i.e. the scattering coefficient, the sum of contributions over all angles is taken.
9
(a) Rayleigh scattering
(b) Mie scattering
(c) Mie scattering (large particle)
Figure 9: Scattering profiles for beam of light moving left to right.
Zπ
Z
b(λ) =
β(ψ, λ) dΩ = 2π
Ξ
β(ψ, λ) sin ψ dψ
(20)
0
Conventionally this equation is split into forward scatter, between angles 0 < ψ < π/2, and
back scatter, π/2 < ψ < π. In a communication system these limits can be adjusted to match
the sending angle to see how much the original signal has scatted. The VSF can be used calculate
the beam spread function (BSF), through radiative transfer theory. The BSF is a model of how
a collimated beam of light spreads due to scattering as it travels through a body of water. The
derivation of the BSF is beyond the scope of this text, however it is covered extensively in Shifrin
[15].
4.2
Pure seawater
Scattering events are physically categorised by the size of the the density fluctuations they
cause; inhomogeneous seawater causes small scale fluctuations ( λ), whilst turbulence induced
fluctuations are very large ( λ). Scattering by organic or inorganic particles (> λ) lies between
these two extremes [25]. Physically small scale density fluctuation scattering occurs because seawater contains a mix of salt ions which vary in concentration and density. Assuming all particles
are spherical, Rayleigh scattering equations can be used to describe the extent of scatter. In the
visible spectrum Rayleigh scattering by seawater, bw , is fairly wavelength invariant, as can be seen
in equation 21 [23] and figure 12.
bw (λ) = 0.005826
400
λ
4.322
(21)
Where λ is given in nm. The typical angular distribution of Rayleigh scattering is given in
figure 9 (a). In an isotropic material the probability of forward and backscattering are equal,
represented in this figure by the scattering to the right and left of the particle, respectively. The
VSF is therefore symmetric, given empirically as [26];
βw (ψ) = 0.06225(1 + 0.835 cos2 ψ)
(22)
In general, scattering by seawater plays only a small part in the total scattering coefficient, as
shown by figure 12. The next section describes scattering by larger suspended substances.
4.3
Suspended Particles
Suspended particles such as phytoplankton, gelbstoff and non-algal particles account for roughly
40-80% of total scattering [9]. The scattering caused by these particles peaks in the forward
direction, suggesting the application of Mie scattering theory [4]. Mie scattering is a solution
to Maxwell’s equation across a refractive index boundary specifically for spherical particles and
10
n
1
2
3
4
5
sn
ln
-2.957x10−2
-1.604
-2.783x10−2
8.158x10−2
1.255x10−3
-2.150x10−3
-2.156x10−5
2.419x10−5
1.357x10−7
-6.579x10−8
Figure 10: Large and small particle coefficients for phase functions of particle scattering [23].
Rayleigh scattering, which is responsible for scattering in pure seawater, is the small particle
approximation of this.
Typically ocean particulates are split into small and large particles, where small is defined
as any particle with a diameter of 1µm or less [10]. This type of scattering varies slightly with
wavelength being marginally higher in the blue-green region, as can be seen from the scattering
coefficients:
400 1.17
bl (λ) = 1.151302
λ
400 0.3
bs (λ) = 0.341074
λ
(23)
(24)
Where bs and bl are the scattering coefficients for small and large particles respectfully. Each
sized particle has a different angular scattering distribution; typical forward dominant scattering
profiles for small and large particles can be seen in figure 9 (b) and (c). The categorisation into
small and large particles is arbitrary and splitting this down further would make the model more
exact. However, angular distribution itself is difficult to calculate, although there are algorithms for
calculating coefficients in single and multi particle systems [27]. The total VSF from particulates
βp is given as [23]:
βp (ψ, λ) = bs (λ)ps (ψ)Cs + bl (λ)pl (ψ)Cl
(25)
Where Cl is the concentration of large particles and Cs is the equivalent for small particles.
ps (ψ) and pl (ψ) represent phase functions for scattering which are given empirically by the following
formulae [23]:
" 5
#
" 5
#
X
X
3n/4
3n/4
ps (ψ) = 5.6175 exp
sn ψ
, pl (ψ) = 188.38 exp
ln ψ
(26)
n=1
n=1
The coefficients of sl and ln are given in figure 10. These phase calculations can be used to plot
two diagrams similar to figure 9 (b) and (c). Both of these specific Mie solutions are symmetric
through the centre and azimuthally symmetric and although both of these scattering regimes are
forward dominant, large particles scatter more to small near-forward angles. In areas of high
turbidity, scattering by suspended particles is known to cause collimated light beams, such as a
lasers, to appear as a diffuse source after a short distance.
4.4
Refractive Index
Controlled laboratory experiments have shown scattering by suspended particles and sea water
molecules to match the theory to a good degree of accuracy [28]. However, scattering of light in true
oceanic environments cannot alone be produced by suspended particles and sea water molecules;
measurements by Petzold showed that the VSF for real ocean water varies by order of magnitude
from the theory [29]. There is a third cause of scattering that is of particular importance for the
oceanic waters. Scattering occurs where water has a change in density or refractive index, this
creates an optical boundary where light is reflected and refracted.
11
(a) Wavelength variation
(b) Temperature variation
(c) Salinity variation
(d) Pressure variation
Figure 11: Seawater refractive index experiments. T = 20o C, λ = 500 nm, = 3.5%, P = 0 kg
cm2 unless otherwise stated [4] [30]
Temperature, salinity and pressure of water and wavelength of incident light are factors which
vary naturally in oceanic environments and cause the refractive index to change. Austin and Halikas
note the extreme values of refractive index to be between 1.32913 and 1.36844 [30]. A boundary
between these two extremes produces a significant amount of backscatter, roughly 1.45 percent
assuming the incident light is monochromatic and perpendicular to the boundary. Temperature,
salinity and pressure are all constants which change throughout the ocean, both laterally and by
depth. Algorithms exist that predict the index of refraction at a given location, for example the
27-term algorithm for pure and sea waters developed by Millard [31]. An in-depth discussion of
these algorithms is beyond the scope of this paper however.
The variation of refractive index ns due wavelength λ, temperature T , salinity and pressure
P is given in figure 11 (a)-(d) respectively. Pressure and salinity vary linearly with refractive index
whilst wavelength and temperature exhibit more complex behaviour. Considering the total range of
each parameter, which represent typical ocean conditions, the index of refraction of seawater is least
sensitive to changes in temperature, then salinity, then wavelength and finally most sensitive to
changes in pressure. Figure 11 shows what happens when ocean water is subject to slow condition
changes, the next chapter looks at what happens in turbulence, where the changes are rapid and
extreme.
4.5
Turbulence
Turbulence is the name given to the event where water experiences rapid changes in refractive
index. In oceanic environments, this is typically due to ocean currents although can also occur at
estuaries and due to ocean vehicles. A sharp change in refractive index due to turbulence is known
as scintillation and can affect deep open waters as much as water in coastal regions. Scintillation is
attributed mainly to fluctuations in the temperature [32]. In laboratory experiments, this type of
12
scattering was even found to be much more significant than scattering by particles for near-forward
angles at short distance (typically under 0.25m) [32].
As of yet, there exists no literature on how scintillation might affect optical communications
and only few sources on how it affects underwater light in general. From FSO communications, it is
known that the magnitude of scintillation is proportional to length scale of turbulence and strength
of turbulence regimes [33]. Models of air-based scintillation are based on normalised variance of
irradiance intensity σ.
hI 2 i − hIi2
(27)
hIi2
Where I is the irradiance intensity and h i denotes a time average. In weak-fluctuation regimes,
where σ 1, the scintillation index is given by the Rytov variance [33] [34];
σI2 =
7
2π 11 11
=
L6
(28)
λ
Where Cn is the turbulence strength parameter for refractive index fluctuations and L is the
path length. Expressions to compute scintillation for strong turbulence regimes include many
more variables and are beyond the scope of this paper. In FSO links there are techniques such as
aperture averaging which compensate the effects of scintillation. A similar approach may need to
be adopted also in underwater applications [35]. Theory has been developed for optical propagation
in lab generated turbulence [36], with equations depending on flow characteristics such as Prandtl
number and also in-situ measurements done for the purpose of imagining [37]. However, the
complexity of measurements and the dynamic nature of events make it difficult to model turbulence
and also the subsequent behaviour of light.
Turbulent flows are also likely to also cause the formation of bubbles. Bubbles can be treated in
the same way as particles from section 4.3, except with a much lower refractive index. It is difficult
to predict their occurrence though typical ocean measurements estimate the bubble number density
to be between 105 - 107 m−3 [38]. If these figures are correct, bubble population would significantly
influence the scattering process in the ocean, especially in chlorophyll-rich waters.
2
σw
4.6
1.23Cn2
Unified Scattering Model
As with absorption, Haltrin derived a one-parameter model for scattering. This model only
includes the contributions from pure seawater and particulate substances; refractive index changes
and turbulence have been omitted. The overall scattering coefficient is given in equation 29.
b(λ) = bw (λ) + Cs bs (λ) + Cl bl (λ)
(29)
The definitions of bw , bl and bs are given in equations 21, 23 and 24 respectively. As with the
concentrations for absorption, the concentrations of small and large particles have been derived in
terms of the chlorophyll concentration.
Cs = 0.01739Cφ exp[0.11631Cφ ]
(30)
Cl = 0.76284Cφ exp[0.03092Cφ ]
(31)
These have been used with the chlorophyll concentration at unity to create figure 12. This figure
shows that scattering is completely dominated by large particles and that all scattering relations
are approximately wavelength invariant. This means that the ideal transmission wavelengths for an
optical communication system are the wavelengths that minimise absorption which, as discussed in
section 3.5, are blue-green for open ocean and green-yellow for coastal and harbour areas. However,
in these turbid areas, scattering is a much more significant contributor in the overall attenuation,
as was first shown in figure 3. Therefore despite having its wavelength optimised of absorption, the
amount of scattering will be the factor limiting how well these communication systems perform.
13
Figure 12: Haltrin scattering model for 1 mg m−3 chlorophyll concentration.
5
Channel Disruption
As with all communication systems, underwater optical wireless systems are prone to noise.
In this section, the discussion is limited to noise that is specific to the underwater channel; there
already exists comprehensive literature on typical FSO noise sources [39]. One of the most significant sources of disruption in the channel is background light, which is caused by sunlight, discussed
in section 5.1, and other organic processes such as bioluminescence and fluorescence, included in
section 5.2. In section 5.3, the factors which lead to beam obscuration by marine life, and how this
can be reduced, are discussed.
5.1
Sunlight
In a simple FSO system, an optical receiver detects incoming light by use of a photodiode. This
photodiode will also detect any background light present in the ocean which will be appear as shot
noise. Sunlight is a profound problem in air but less significant in the ocean as it only propagates
so far down into the ocean. Nevertheless, it is known to be the ultimate limiting noise factor for
underwater wireless optical communications [40].
The ocean is zoned into regions by light intensity because background light has a profound affect
on the marine life residing in an area. The photic zone, which was introduced in section 3.2, is
brightest upper region of the ocean where the intensity is at least that necessary for phytoplankton
growth [41]. The depth of this region for different ocean types is given in figure 13 by intersections
with the III line. The light field from the sun or moon which irradiates the ocean in this region
is described by the intensity of light on the surface and the diffuse attenuation coefficient for
downwelling irradiance Kd . The latter has been calculated empirically to be 0.016-0.018 m−1 for
a light source of λ = 490 nm [42] and this is related to the surface intensity by the propagation
loss factor in equation 5, where the apparent diffuse attenuation coefficient replaces the inherent
attenuation coefficient.
Below the photic zone is the aphotic zone, here plants do not survive because of insufficient
intensities to enable photosynthesis. Deep-sea fish have evolved to cope with the low intensities
through bioluminescence, as discussed in the next section. In the aphotic zone the downwelling
irradiance is no longer a problem, such low light intensities indistinguishable from dark current
noise across the photodiode. At depths below 1500 m it becomes much more difficult to design a
communication system because of the increased pressure on the devices.
14
I
II
III
A
B
200
C
400
600
D
800
1000
bioluminescence
10−12
-
10
10−7
10−5
10−3
10−1
101
Light Intensity (W m−2 )
Figure 13: Attenuation of light in different water types where: I. minimum intensity for vision by
deep-sea fish; II. minimum intensity for vision by man; III. minimum intensity for phytoplankton
growth. A and B show moonlight and sunlight in coastal area respectively, C and D are the open
ocean equivalent [43].
5.2
10−11
10−9
Other Light
As mentioned in the previous section, deep sea fish and other marine life have bioluminescence.
Bioluminescence occurs naturally when energy is released by a chemical reaction in the form of
light. Typically bioluminescent transmission is in the blue region, of wavelength 450-550 nm,
although there are a few cases of far red emissions [44]. An algorithm has been developed to
estimate the spatial location and magnitude of bioluminescent radiation [45] but goes far beyond
the scope of this paper.
Another significant light source in the ocean is fluorescence by phytoplankton. This is the reemittance of absorbed light at another wavelength, typically longer [46] and affects only the photic
zone where phytoplankton grows. Fluorescence was omitted from the original energy balance
model of attenuation in section 2.1. Chlorophyll is the most significant pigment which causes
fluorescence in phytoplankton, it is caused as a by product of photosynthesis. The intensity profile
of fluorescence If can be described with the following equation [47]:
If (λ) = Ic Cφ aφ (λ)µf
(32)
Where Ic is the intensity of light on the cell, Cφ is the concentration of phytoplankton, aφ (λ), as
before, is the absorption coefficient of phytoplankton and µf is the efficiency of the cell or quantum
yield of fluorescence.
5.3
Obscuration
Maintaining line-of-sight is important for any optical wireless communications system. The
chance of obscuration underwater is more significant than air; schools of fish can potentially block
15
much more of the signal than a few birds. It is important to design a system which discourages
marine life from blocking the path of transmission.
Light is currently used underwater both to attract fish, in the case of fishing boats, and to
discourage them, in the case of power plant water pipes. Although all fish have different light
preferences, there are some overriding similarities. Fish that live in open ocean prefer light in
blue-green light wavelengths whilst those in freshwater prefer yellow-green wavelengths [48], unfortunately these are the optimal wavelengths for communication. The preferred intensity depends
much on the background conditions and the time to get used to it, similar to humans. Very bright
light in a dark environment causes immediate avoidance reaction until the eyes have adapted, for
fish this is typically 30-40 minutes as the eyes have to switch between their two receptor types.
This switch is also the limit for when fish forage in schools, a bright light will cause schooling
for increased protection for the fish. After the receptors have adapted, the fish are likely to be
attracted to the light, as long as it appears constant. Fish dislike flashing lights, these also cause
an avoidance reaction although the critical frequency at which a flashing light appears constant
to them is unknown [49]. Because of the significant result changing the transmission wavelength
has, the best way to discourage fish from obstructing communication line-of-sight is to have an
seemingly erratic light signal.
Obscuration by algae growth is another possibility for underwater systems that are more permanent in nature. Increased light availability causes more algae growth, subject to sufficient minerals.
The epicentre of this growth will be at the transmission lens of the communication system which
will need an anti-algal coating or to be cleaned regularly. Also, for a long term system in static
or near-static body of water, such as a lake, it may lead to increased phytoplankton growth which
will degrade the channel by causing the amount of absorption and scattering to increase.
6
Summary
This research essay focused on the underwater optical channel model for use by wireless communication systems. Chapter 2 began by defining inherent and apparent optical properties and
showed how these are used in different ways to classify ocean waters. A clear distinction was made
between water in clear, open oceans and particulate-rich water in harbours and coasts.
Sections 3 and 4 looked at absorption and scattering respectively. Absorption by oceanic waters
is very well understood and a comprehensive model exist which accurately predicts it. This model
is the one-parameter model by Haltrin, it describes all parameters in terms of phytoplankton
concentration which can then be combined with phytoplankton concentration profiles. Scattering
is much more complex because it is ultimately caused by refractive index, or density, changes in
the ocean and these are quite common and not always easy to predict. Turbulence is known have
a significant affect on the overall amount of scattering but currently is not sufficiently modelled to
be able to be included in underwater communication channel models.
This text suggests the optimum wavelengths for transmission in both open ocean and coastal
areas are chosen by absorption to be blue-green and yellow-green respectively. Absorption was
emphasised as it is a highly wavelength dependant process, unlike scattering where altering the
wavelength of transmission has little effect. It is found that the total attenuation in open oceans
is limited by the absorption of pure seawater whilst coastal regions are dominated by scattering
from large particles; these are the factors which will ultimately limit the communication system in
the respective areas.
The underwater environment is rich and varied; disruption and noise from the environment
adds to the complexity of creating an underwater communication system. Chapter 5 concluded
this text by looking at wider issues related to underwater communication systems, specifically
obscuration and background light sources. Overall, it is clear that any underwater optical system
needs to be carefully design to suit its environment, whether it be deep in an open ocean or close
to the surface in particulate-rich coastal areas.
16
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