Paper 060525R received Jul. 9, 2006; revised manuscript received Nov. 7, 2006;accepted for publication Dec. 17, 2006; published online Jun. 20, 2007.
Introduction
ree space optical �FSO� communication is rapidly becom-ng a familiar part of modern urban life. Over the last de-ade, there has been a steady increase in the number ofonsumers using high capacity data transmissions, and theirata rate demands have risen from hundreds of megabitser second to tens of gigabits per second.1 Capacity-hungryommunication applications range from local area networkLAN� systems to the Internet and company intranets. Theigh data rates needed can be attained with optic fiber,hich has been distributed to connect cities and continents.owever, often the “last mile” from the fiber backbone to
he clients’ premises presents a significant problem. It mayot be possible or practical to lay down optic fibers, and its invariably costly and time-consuming. FSOs can bridgehe gap; the idea is to introduce the main advantages ofptical communication in wireless technologies such as theigh data rates, economic efficiency, secure links, and nolectromagnetic interference with other wireless technolo-ies �mainly operating in the license-free and industrialcientific-medical �ISM� bands�.
As in any communication system, the propagation chan-el influences the transmission. For FSO, this channel is thetmosphere and the FSO links are mainly affected and de-ermined by the local weather. At optical frequencies, thenteraction of electromagnetic waves with the atmospheres more pronounced than at microwave frequencies. Theres always a threat of downtime caused by adverse weatheronditions.2 To achieve very high availability in FSOs, fogs the most important limiting factor because it can causeigh attenuations over nonnegligible amounts of time.hus, a better understanding of the phenomenon of fogttenuation is critical for enhancements in the design of
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future terrestrial FSO systems. Because the attenuationcaused by fog can vary from 0.2 dB/km in exceptionalclear sky conditions to more than 450 dB/km in maritimefogs, its affects on link budget and system margins are cru-cial. The phenomenon of fog has been actively researchedfor many decades but with varying aims and for particularaspects.3 Since the late 1990s, when FSO started gatheringmomentum as a potential technology, research in fog at-tenuation revolved mostly around comparing fog attenua-tion for different wavelengths4,5 and proposing better mod-els for relating visibility to fog attenuation.4,6 Fog or otheradverse weather conditions do not effect performance pa-rameters such as the bit error rate �BER� for FSO systemsbecause the BER generally remains very low and the link iseither available or not.7 In recent years, there is a growingtrend to investigate possible modulation and channel cod-ing formats to enhance the capabilities of the FSO links8,9
and, thus, the need to investigate the time-series analysis offog.
In this paper, we take a detailed look at the phenomenonof fog and how it affects the performance of terrestrial FSOlinks, describing and analyzing our measurements done atLa Turbie, near the coast of southern France, for about aweek, and the measurements at the continental city of Graz,Austria for over six months. Our purpose in the currentpaper is not to provide comparisons of fog attenuations atdifferent wavelengths, as it has already been thoroughlyinvestigated and such comparisons appear abundantly inliterature,4,5,10,11 rather we provide insight into efficientFSO design based on the time-series analysis of fog attenu-ations. We start the paper by describing fog and follow itwith a detailed description of our measurement setups. InSec. 4, we present time-series analysis of the fog attenua-
tions, providing a comparison between city and maritime
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og in Sec. 5, validating the different existing fog models inec. 6, and summing up with some conclusions in the lastection.
The Phenomenon of Fogogs are composed of fine droplets of water suspended in
he air near the surface of the earth. The presence of theseroplets acts to scatter the light and thus reduce the visibil-ty near the ground. It is defined in meteorology that theres fog when visibility is reduced to less than 1 km and theelative humidity of the air is brought to the saturation levelclose to 100%�. Eldridge12 defines three generalized typesf shorter visibility weather: fog for visibilities less than00 m, haze for visibilities greater than 1000 m, and a tran-itional zone called mist for visibilities between 500 and000 m. These zones are based on changes in observedarticle size distributions and changes in the wavelengthelectivity of measured attenuation coefficients. Haze is pri-arily composed of microscopic fine dust or salt or small
roplets of a few microns to a few tenths of a micron. Fogccurs during very high relative humidity �greater than5%� when water droplets of a few microns to a few tens oficrons form over the haze particle nucleus. Mist occurs
uring the transition from haze to fog as the humidity in-reases to saturation. This transition is generally quick ashere is a substantial increase in 1- to 2-�m micron dropletshat causes a rapid deterioration of the visibility.
Kinds of fog are characterized by several physical pa-ameters such as liquid water content, particle size distribu-ion, average particle size, and number of particles per airolume. Fog particles are spherical in shape and have radiiarying between 0.01 and 15 �m, depending on geographi-al location. The formation of a fog layer occurs when aoist air mass is cooled to its saturation point �dew point�.his cooling can be the result of radiative processes �radia-
ion fog�, advection of warm air over cold surfaces �advec-ion fog�, evaporation of precipitation �precipitation orrontal fog�, or air being adiabatically cooled while beingorced up a mountain �up-slope fog�. Another type of fog ishe so-called valley fog; this fog forms as a result of aireing radiatively cooled, during the evening, on the slopesf the topographical features. This air becomes denser thants surroundings, starts going down the slope, and results inhe creation of a pool of cold air at the valley floor. If their is cold enough to reach its new dew point, fog formationccurs.
Radiation �convection� and advection �maritime� fog arehe most typically encountered in nature. Radiation fog isenerated by radiative cooling of an air mass during nightadiation when meteorological conditions are favorablei.e., very low speed winds, high humidity, clear sky�. Itppears when the air is sufficiently cool and becomes satu-ated. So this is a fog that generally appears during theight and at the end of the day, particularly in the valleys.article diameters vary weakly around 4 �m, and the liquidater content varies between 0.01 and 0.1 g/m3. Advection
og is formed by the movement of wet and warm air massesbove the colder maritime or terrestrial surfaces. The air inontact with the surface is cooled below its dew point,ausing condensation of water vapor. It is characterized byliquid water content higher than 0.2 g/m3 and a particle
iameter close to 20 �m. Figure 1 shows the fog droplet
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distributions for the cumulus, maritime, and continentalfogs. The vertical axis is droplet distribution in units ofnumber of droplets per cubic centimeter per micron, andthe horizontal axis shows droplets distribution in microns.Because, the fog particles cluster around some typical di-ameters, we use a per micron measure on the vertical axisto harmonize the droplet distributions. As a general rule,fog droplets tend to cluster around 5 to 15�m in diameter.13
The droplet distribution also provides valuable insight intothe scattering caused by fog, because the distributions havea mean on the order of 10�m, so there should not be manychanges in the scattering for 0.85-, 0.95-, or even 1.5-�mwavelengths. They are all much smaller than typical drop-lets, so the percent variation in light scattering would not besignificantly different.
The characteristics of aerosols �i.e., number of particlesconcentration, size distribution, chemical composition�have a large impact on when and where a fog layer willform. Also, due to the strong link between aerosol charac-teristics and fog microphysics, the overall life cycle of afog layer is influenced by these aerosols. Indeed the foglayer liquid water content, drop size distribution, and, thus,visibility will be modified according to the characteristicsof aerosols contained in the air mass. Typical fogs are com-posed of inactivated cloud droplets �haze particles� and ac-tivated cloud condensation nuclei �CCN�. The inactivateddroplets are generally smaller than 2.5 �m in diameter, butactivated droplets are larger than 2.5 �m. So, compared toother cloud types, fog droplets are generally smaller. Intri-cate relationships exist between aerosols and fog. All theoptical characteristics of aerosols and in particular those offog are related to the particle size distribution, which is themost important parameter allowing us to compute the opti-cal properties of a quantity of droplets. Generally, this dis-tribution is represented by analytical functions such aslogarithmic-normal distribution in the case of aerosols andthe modified gamma distribution for fog, which is widelyused to model the various types of fogs and clouds14 and is
Fig. 1 Typical droplet distribution for different kinds of fog.
given by
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�r� = �r�e−br. �1�
n this equation, n�r� gives the number of particles per vol-me unit and per increment unit of the particle radius r; a,, and b are parameters that characterize the particle sizeistribution.
Measurement Setupsn this paper, we will be using results from two differenteasurement campaigns. The first set of measurements was
erformed at the coastal region in southern France at a testacility of France Telecom close to the village La Turbieear Nice, From June 23 to July 1, 2004, and three majorog events were recorded during this week.10 The villageame has the meaning of “bad view,” referring to lowlouds and dense fog, which are often covering this area inhe mountains close to the sea coast. The second set ofeasurements was done at the continental city of Graz,ustria, which provides rather dynamic weather conditionsith thunderstorms in summer, heavy fogs in autumn andinter, as well as drizzle, snow, and haze. The campaign atraz was started on September 27, 2005, and continuedntil March 1, 2006. The considered data span over 156ays and 16 fog events were measured during this period.he real measurement data for a selected day is available atttp://optikom.ibk.tugraz.at/Fog.
The measurement setup in France included a transmis-ometer to measure visibility at a 550-nm center wave-ength, an infrared link for transmission measurement at50 and 950 nm, and a personal computer–based data log-er to record the measured data. In addition, temperature,umidity, and ambient light were recorded. The same setup,xcept for the transmissometer, was used for the measure-ent at Graz, and to capture the weather conditions, a We-
cam was also installed, which took a picture of the linkvery minute.
The link for infrared transmission measurement was de-eloped by our research group Optikom at Graz Universityf Technology. We developed a measurement setup for fogttenuations as similar as possible to practical FSO systemsy modifying our self-developed transmission systems.15
asically, it consists of an optical transmitter and receiverystem, each equipped in a waterproof housing mounted on
tripod with mechanical options for alignment. In theransmitter, two independent light-emitting diode �LED�–ased light sources and optical systems are implemented.ne is operating at 850-nm center wavelength and 50-nm
pectral width at a full angle beam divergence of 2.4 deg,he second one is operating at 950-nm center wavelengthnd 30-nm spectral width at a beam divergence of 0.8 deg.e have used the same transmitter optics for 850 and
50 nm, but different light sources, with different activelight-emitting� areas. This results in different divergencengles. To have approximately the same power for bothavelengths at the receiver, we have used only one LED
L7558-01� at 850 nm, which emits 8-mW average opticalower in total; however, the average emitted power afterhe lens is about 3.5 mW, the rest being radiated in a widerngle. For the 950-nm wavelength, we have used four
EDs �SHF495P�, each emitting 1 mW to produce the
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same average power at the receiver. Thus, for both thewavelengths, the average received optical power after a dis-tance of 30 m is −17 dBm.
Each light source is 100% amplitude-shift key modu-lated by the driver electronics circuit with an individualcarrier frequency provided by a crystal oscillator. Basically,all optical digital transmission systems use this modulationscheme on the physical layer �with very few exceptions�. Asquare wave with 50% duty cycle is used to switch the lightsource on and off. The square wave can be produced easilywith typical FSO transmitter drivers and the receive band-pass filters cut away any higher order harmonics.
For our system, we use 6 MHz for the 950-nm lightsource and 5.5 MHz for the 850-nm light source. This al-lows us to associate the received power of each opticalwavelength with the signal strength of a modulation fre-quency. The choice of the receiver filters was motivated bytwo factors: first, to utilize frequencies that appear in mosttypes of data transmissions �1- to 10-MHz range�, and sec-ond, availability of ceramic bandpass filters. We chosecrystal resonators for the transmitter, at 6 MHz �commer-cially available� and at 5.5 MHz �self-designed� with verysimilar characteristics to avoid any modulation frequency–dependent attenuation effect. Accordingly, the receiver con-sists of a single optical system of a 98-mm lens diameterwith a 1.7-deg full acceptance angle for both wavelengthswithout an optical bandpass filter, a Si-photo-PIN diode�SFH203FA� with a spectral range of 800 to 1000 nm, anda transimpedance amplifier. After the data is received, itgoes throught a rf gain stage, and then the modulation car-rier frequencies are separated by electrical bandpass filters,rectified, and decoupled by a dc amplifier. The resulting dcoutput voltages correspond to the optical power receivedfrom each of the two optical wavelengths. The principle isshown in Fig. 2. To record the measurement data, a con-ventional computer with an analog-to-digital conversioncard �National Instruments PCI-6023E� operating under LA-BVIEW software is used. The card operates at a maximum of200 kilo samples per second and is a 12-bit, 16-inputanalog-to-digital converter. The measured dc voltage valueof every channel is stored as a time series in a table.
Among the advantages of this rf marker transmissionmeasurement concept compared to systems using non-modulated light and optical bandpass filters at the receiveris the point that the same optical system and front end isused for two �or in principle for a number of� optical wave-lengths, and so—except for chromatic aberration �whichmay be neglected�—to have equal optical properties for thewavelengths, it allows excellent suppression of ambientlight and it allows us to measure light transmission undersimilar conditions as used by FSO systems that also operateby on-off keying to modulate the light. Because opticalfilters can be replaced by filters in the electrical domain, thesystem can be built cost-effectively, which may allow awider range of applications.
Before any practical fog measurement was performed,the system was calibrated in the lab to determine the rela-tion between the received optical power and the output dcvoltage level. The crosstalk between the two wavelengthchannels was found to be sufficiently low in the linearrange of the input stage amplifier, resulting in a maximal
output change of 0.19 dB�opt� for both channels in the case
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f a 25-dB difference in the input power. Nonmodulatedmbient light up to 0.1 mW �more than the maximum day-ight receiving power for this system� is completely sup-ressed, resulting in an output power change of less than.005 dB�opt�. The dynamic range of the system exceeds5 dB�opt� for each of the two channels and is limitedostly by the resolution of the data logger and the dc am-
lifier offset.For the two measurement campaigns, the link distance
as selected carefully as a compromise between accuracynd allowable attenuation range, depending on the expectedaximum fog attenuation. Provided a dynamic range of
5 dB for the system at each wavelength, at La Turbie, aink distance of 28.3 m did allow us to measure a specificttenuation of up to 880 dB/km, and at Graz, a link dis-ance of 79.8 m allowed us to measure specific attenuationp to 310 dB/km. The data was processed and evaluatedfter the measurement in MATLAB, resulting in the diagramshown in the following sections.
Time-Series Analysis of Fog Measurementshe time-series analysis of fog can provide interesting in-ights, and lead the way to developing systems that canope better with fog attenuations. For FSO communica-ions, it is of high relevance to consider effects of change inog attenuations during small time intervals. One of theajor aims of the measurement campaign in Graz, in theinter of 2005, was to get better insight into the time do-ain analysis of the fog attenuations for the terrestrial FSO
inks. Earlier in Ref. 10, we had provided some preliminaryotions on the importance of time analysis of fog attenua-ion. The exact, or more compact, analysis of the attenua-ion behavior of fog can lead to the design of better systemsith more throughput capabilities and enhanced perfor-ance. The higher state modulation and channel codes
esign8 for the FSO links also heavily depend on charac-
Fig. 2 Rf marker circuit prin
erizing the fog attenuation in a more detailed manner. In
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this section, we highlight the measurements made and in-dicate their significance in the design of better systems forthe future.
One of the major hurdles in designing efficient modula-tion and channel codes for the FSO links has been the non-availability of relevant data and measurements. Fog attenu-ations done previously have mostly focused on long timedurations to provide availability estimates and attenuationsin terms of decibels per kilometer.16,17 However, character-izing the error behavior of the FSO channel in terms ofrandom or burst errors and to design efficient codingmechanisms based on such a characterization required mea-suring the attenuations at a much better time resolution,preferably at a millisecond interval. Nevertheless, suchmeasurements remained a challenge in themselves becausehandling huge data files and measurement points has neverbeen trivial.
In the measurement campaign, we were able to look atthe attenuation on very small intervals of time, and measur-ing at 100 values per second, we have observed no realchanges in attenuation over the interval of 1 s. To elucidatethe results, we analyze one of the fog events recorded inGraz. Figure 3 shows the complete fog event where a sharpdecline in the specific attenuation is clearly observed duringthe deep fog. In Fig. 4, we magnify 1 min out of the eventafter deep fog has set in and show the specific attenuationthat remains almost constant over at minute. In Fig. 5, weshow 1 s out of 1 min, and it is evident here that the spe-cific attenuation is clearly constant during the second. Asecond is a long enough interval from the perspective ofcoded modulation, and having a constant attenuation overit, the interval indicated a frozen atmospheric model withstrong statistical dependence from symbol to symbol.Looking at these attenuation curves, it can be directly de-duced that once the attenuation is strong enough to disrupta link, there may not be much benefit using any codingschemes in trying to improve the BER performance of the
or transmitter and receiver.
link. Therefore, such stable fog causes a very constant at-
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enuation, which would thus cause burst errors with theengths of the bursts extending to many blocks of symbolata. With complete blocks of data erased, it may not beossible to design any codes, which can combat this attenu-tion. The common approach in code design for tacklingong error bursts is the use of interleavers to spread therrors over many blocks of data. However, this approachay not be feasible in the case of the stable continental fog
ecause the interleaver lengths, which provide considerableerformance enhancement, will be extending to thousandsf symbols �millions of bits� for the traditional On-Offeying modulated data. Such interleavers would introducenacceptable delays in data transmission and reception andery high memory requirements, thus complicating the de-ign much more than enhancing it. On the positive side, thislso means that because the channel state remains constantver pretty long intervals of time, channel estimation might
Fig. 3 A complete fog event measured in Graz.
Fig. 4 One minute magnified out of the Graz fog event.
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yield accurate results. Such estimation algorithms can beuseful in developing successful switch-over techniquesfrom optical to rf links in hybrid systems.
Figure 6 shows the specific attenuation during 1 minrecorded for the maritime fog at Nice, and it indicates adifferent behavior, with the specific attenuation changingrapidly during the minute. The resolution of the measure-ments at Nice do not allow a look at the fog attenuationduring a second, but intuition suggests that it may be pos-sible to see changes in attenuation even during small inter-vals of time. This can lead to significant gains by usingproperly designed channel codes.
5 Comparison of Maritime and City FogAttenuations
Fog remains the major hurdle in establishing FSO linksoperating over long distances with high availability. Fogcan cause high light attenuation and the attenuation charac-teristics depend on the kind of fog and the location of the
Fig. 5 The specific attenuation during 1 s in the Graz fog event.
Fig. 6 Specific attenuation during 1 min of fog at Nice.
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nstallation. We compared and analyzed the fog attenuationharacteristics of the maritime and city fog and found ma-or differences among them. In Graz, the recorded specificttenuation remained up to 120 dB/km, which is a typicalgure for fog attenuation in continental cities. Usually thisog appeared to be stable and with few variations in time.n contrast, the maritime fog was observed up to80 dB/km in the mountainous region at the southern coastf France.
Figure 7 shows the specific attenuation over a scale ofinutes for both Graz and Nice, the differences among the
wo fog types are clear, with the maritime fog havingreater attenuation and faster changes in the attenuation
Fig. 7 Specific attenuation in Graz and Nice over a 1-min scale.
Table 1 Values of specific attenuation and thesentative data set for Nice and Graz.
Nice
No. ofMeasurementValues
SpecificAttenuation
�dB/km�
ChanSpecific A
�dB/
1 12.476
2 13.375 −0.8
3 25.542 −12.
4 12.495 13.0
5 25.726 −13.
6 28.156 −2.4
7 7.7053 20.4
8 6.6075 1.0
9 8.6048 −1.9
10 16.003 −7.3
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levels. To elucidate the different attenuation characteristicsof fog in the two different locations, we decided to look athow the specific attenuation changes from one value to thenext, and Table 1 provides a representative data set of themeasured values and the calculated changes in specific at-tenuation. In Fig. 8, we depict the changes in specific at-tenuation for the two kinds of fog, and the graph shows thatthe Graz fog is pretty stable and has few changes in specificattenuation with low magnitudes; however, for the mari-time fog of Nice; the changes in specific attenuation are fastand have significant values on the magnitude scale. To getbetter insight into the issue, we plot the same changes in
ted changes in specific attenuation for a repre-
Graz
ionSpecific
Attenuation�dB/km�
Change inSpecific Attenuation
�dB/km�
6.1316
6.0304 0.1012
6.0951 −0.0647
6.0716 0.0235
6.0337 0.0379
6.0663 −0.0326
5.983 0.0833
5.9795 0.0035
6.0698 −0.0902
6.144 −0.0742
Fig. 8 Changes in specific attenuation in Graz and Nice over a1-min scale.
calcula
ge inttenuatkm�
982
1680
470
2310
301
510
978
974
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pecific attenuation over 1-s scale in Fig. 9 and observe aery similar behavior to that of Fig. 8. In Fig. 10, we havelotted changes in specific attenuation as a histogram ofvents for both the Nice and Graz fogs. A deeper look at theistograms emphasize our analysis that the fog attenuationn Graz with a mean of 9.0602�10−5, a variance of 0.7307,nd a standard deviation of 0.8548 is stable and has atrong correlation; whereas, the fog attenuation for Niceith a mean of −0.0158, a variance of 1372.3, and a stan-ard deviation of 37.0445 changes very rapidly and, basedn its huge variance, exhibits a totally different behavior.
FSO links operating in the range of gigabit data ratesan have about 50 dB of total system power margin in theptimum case, neglecting losses due to geometrical beampreading. For the case of a continental city like Graz, this
ig. 9 Changes in specific attenuation in Graz and Nice over a 1-scale.
Fig. 10 Histogram of changes in specific attenu
the x axis�.
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would allow link distances up to 400 m to achievie veryhigh availability. As the fog appears to be mostly uniformand stable, coding techniques or space diversity optionssuch as multiple beam transmission have very little effect.On the other hand, provided a sufficient margin, such linkscan offer very high data rates with low latency and allowthe transmission of fast cable protocol standards withoutconversion �different to wireless rf links�. This also allowslarger networks based on segmentation.
For the case of maritime fog or low clouds, high linkavailability would allow FSO link distances of about 100 monly. Even if the mean and averaged attenuation could becompensated by the margin of the installation, still the highvariability of attenuation can cause link disruptions. Thisprovides a chance for improvements by coding techniques.The highest peak-specific attenuation in 1 min was739 dB/km, and the lowest was 366 dB/km. This reflectsconsiderable possible improvement by appropriate channelcoding or protocol techniques, though also resulting in re-duced throughput and increased latency. Except for veryshort links such as street or river crossings, larger networkswill require a hybrid approach for such a location. Theknowledge of a statistical model for the attenuation changeswith time, maybe based on parameters such as wind speedand link distance, can be an important basis for hybrid sys-tems with intelligent switch over between optical and rfmicrowave links. As optical links allow very high data ratescompared to wireless rf links, it might be possible to useshort periods of less attenuation within high average attenu-ation time to transmit data bursts and so to have some datathroughput, if higher latency can be accepted for the type ofservice.
6 Validation of Existing Fog ModelsThe decrease in the power of specular light propagating inthe atmospheric medium can be described in a macroscopic
for Nice and Graz. �Note the different scales of
ation
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ay by the Beer-Lambert law. It gives the transmittance atlight wavelength over a path distance in the homogenousedium.
��,d� =P��,d�P��,0�
= exp�− ����d� , �2�
here � is transmittance �unitless�, � is the light wave-ength �nm�, d is the distance �km�, the P is the power ofight �W�, and � is the extinction coefficient �km−1�.
This decrease is caused by scattering and absorption byhe atmospheric particle constituents—the gas moleculesnd aerosols. For the case of fog, the main contribution tohe extinction coefficient is aerosol scattering caused by themall water droplets that are the constituents of the fog,ollowing a particle size distribution as described in Eq. �1�.s the size of the particles and the wavelength of the con-
idered light are of the same order of magnitude, the scat-ering can be described by the Mie model. ���� is the totalxtinction coefficient per length unit, which represents thettenuation of the light. It is composed of terms for scatter-ng and absorption and is usually denoted as
��� = �m��� + �a��� + �m��� + �a��� � �a��� . �3�
ere �m and �a are the molecular and aerosol absorptionoefficients, and �m and �a are molecular and aerosol scat-ering coefficients. Absorption by gas molecules such as
2O, CO2, and N2, which are constituents of the air, definehe main atmospheric transmission windows used for FSO,here molecular absorption �m is negligible. As the size of
he molecular constituents of air is very small compared tohe wavelengths of visible and infrared light, the contribu-ion of �m acting as Rayleigh scattering is negligible too.
In more technical terms and related to atmospheric dataransmission over a given link distance, the decrease ofower over a certain atmospheric path distance is ratherescribed as attenuation in decibels, which can be calcu-ated from the transmittance or from the extinction coeffi-ient according to Eq. �4�
ABS = 10 log�1
�� =
10
ln�10�����d . �4�
or our figures, we use the specific attenuation, which de-cribes best the channel properties independent of link dis-ance. Specific attenuation can simply be calculated fromhe total attenuation according to Eq. �5�
SPEC = aABS/d , �5�
here aSPEC is the specific attenuation in decibels per kilo-eter, aABS is the total attenuation in decibels for the link,
nd d is the link, distance in kilometers.The specific attenuation, usually given in decibels per
ilometer, is even more appropriate to describe the atmo-pheric loss, as it is independent of a measurement distance
SPEC =10
ln�10����� =
10 log�1/��d
= aABS1
d. �6�
nfortunately, statistics of these well-defined parameters
re not available for different locations and measurements
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over longer times. However, in meteorology and at airports,data records of a related parameter exist, which can be usedin practice. Visibility, or the runway visible range �RVR�takes into account the human eye, which is most sensitiveat the 550-nm wavelength in a range of approximately 380to 780 nm. Visibility gives the distance in a lossy medium,over which the human eye is able to distinguish objects of100% contrast ratio from each other �i.e., sufficiently largeblack and white areas�. Visibility can be expressed by thetransmission or the extinction coefficient �at 550 nm� ac-cording to the Koschmieder formula
V =ln�1/�TH�
���0�=
ln��TH�dln��MEAS�
. �7�
So it is possible to calculate the attenuation out of the vis-ibility distance for �0=550-nm wavelength, and even his-torical data really based on human eyes can be used
aSPEC =log�1/�TH�
V. �8�
Because eyes can be different, two different values for thisthreshold transmittance are defined, one is 2% and the otherone, typically used at airports nowadays, is 5%. So depend-ing on the definition, a visibility of 1 km �also the limit forthe meteorological definition of fog� corresponds to a spe-cific attenuation of approximately either 13 or 17 dB/km at550 nm. In our paper, we follow the 5% threshold.
Because the particle size distributions in the differentfogs are not well-known and may vary, it is not possible togive a definite relation between visibility and the attenua-tion at infrared wavelengths. However, over the years, sev-eral empirical models have been proposed as approxima-tions to predict fog attenuation from visibility statistics fordifferent wavelengths. Kruse,18 Kim et al.,4 Al Naboulsi etal.,16 and Bataille have all proposed models relate fog tovisibility. Pierce et al.13 and, more recently, Ketprom et al.19
have proposed optical depth as an appropriate parameter toestimate fog attenuation. Most of these models use a differ-ent set of parameters, and in our effort to try and validatesome of the existing models for fog attenuation, we arerestricted to only Kruse, Kim et al., and Al Naboulsi et al.�France Telecom� because our measurements provide de-tails with which only these models can be validated. Topredict the attenuation of directed or specular light radia-tion in the atmosphere, we can use the following equation:
�a��� � ���� =ln�1/�TH�
V��/�0�−q. �9�
In the visible and near ir up to approximately 2.5 �m, thisformula shows attenuation to visibility V �in kilometers� fora given wavelength � �in nanometers�. �TH is the transmis-sion threshold over the atmospheric path. The coefficient qhas been the subject of many experimental works and the-oretical investigations. It depends on the scattering par-
18
ticles’ size distributions. The original Kruse approach was
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q
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q
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�
Issiasc
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Muhammad et al.: Characterization of fog attenuation…
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= �1.6 if V � 50 km
1.3 if 6 km V 50 km
0.585 V1/3 if V 6 km
. �10�
his relation indicates less attenuation for longer ir wave-engths for low visibilities in fog. However, our previousnvestigations10 have led us to believe that the modificationo q proposed by Kim et al.4 is more realistic for terrestrialinks, particularly in heavy fog conditions. They had pro-osed the values of q as
=�1.6 if V � 50 km
1.3 if 6 km V 50 km
0.16 V + 0.34 if 1 km V 6 km
V − 0.5 if 0.5 km V 1 km
0 if V 0.5 km
. �11�
Recently, Al Naboulsi �France Telecom�6 has providedis own relations to predict fog attenuations and has char-cterized advection and radiation fog separately and pro-ided the attenuation coefficients as
ADV��� =0.11478� + 3.8367
V, �12�
RAD��� =0.18126�2 + 0.13709� + 3.7502
V. �13�
n Fig. 11, we try to provide the comparison of the mea-ured data points with the models and cannot specify anypecial preference for one model over the other. For betterllustration, Fig. 12 provides a magnified view of a smallerrea of interest, and still the measured data points do noteem to suggest any real reasons for preferring one empiri-
ig. 11 Measurement data points for 950 nm along with differentog models.
al model to the others.
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7 ConclusionsFSO deployments will always remain highly dependent onthe location, and the systems may work better in particularclimatic regions. System design enhancements will have toaccommodate this peculiar weather- and location-dependent behavior of the systems. We have provided de-tailed analysis and comparison for two very different kindsof fog, namely the continental city fog and the maritimefog. The two types of fog behave distinctly different fromeach other with significant impact on the design of opticalwireless systems. Considering in particular, higher statemodulation and channel code design for future FSO sys-tems, our results indicate that for very stable fog conditions�such as those in Graz�, no channel coding mechanism maywork. We have measured fog attenuation with a resolutionof 100 values per second and observed no changes in at-tenuation within 1-s intervals. However, for maritime fog,the availability of the link may be slightly improved byusing appropriate coding schemes, but the attenuations inthese kinds of fog are very high and may not be compen-sated by using higher state modulation mechanisms.
These high changes in attenuation in the maritime fogcan also have an impact on the design of future hybridFSO-rf links. With intelligent switch-over mechanisms, themain data stream maybe moved to the rf link in case ofhigh attenuation, but still the short periods of less attenua-tion within high average attenuation times may be used totransmit data bursts and improve throughput.
We have also tried to validate the existing fog modelsusing our measured data, and it suggests that there is nostrong indication to prefer any existing model for predictingfog attenuations.
References
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3. E. J. McCartney, Optics of the Atmosphere, John Wiley, New York�1977�.
Fig. 12 Magnified view of the 950-nm measurement data fitting.
4. I. Kim, B. McArthur, and E. Korevar, “Comparison of laser beam
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1
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propagation at 785 nm and 1550 nm in fog and haze for opticalwire-less communications,” Proc. SPIE 4214, 38–45 �2001�.
5. E. Korevar, B. McArthur, and I. Kim, “Debunking the recurring mythof a magic wavelength for free space optics,” Proc. SPIE 4873, 155–166 �2002�.
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8. S. Sheikh Muhammad, E. Leitgeb, and O. Koudelka, “Multilevelmodulation and channel codes for terrestrial FSO links,” Presented atIEEE Int. Workshop on Satellite and Space Commun. �IWSSC 2005�,Siena, Italy, 2005.
9. J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic,“Shannon capacities and error correction codes for optical atmo-spheric turbulent channels,” J. Opt. Netw. 4�9�, 586–601 �2005�.
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1. B. Flecker, M. Gebhart, E. Leitgeb, S. Sheikh Muhammad, and C.Chlestil, “Results for attenuation measurements for optical wirelesschannels under dense fog conditions regarding different wave-lengths,” Proc. SPIE 6303, 63030P �2006�.
2. R. G. Eldridge, “Mist—the transition from haze to fog,” Bull. Am.Meteorol. Soc. 50, 422–426 �1969�.
3. P. M. Pierce, J. Ramaprasad, and E. Eisenberg, “Optical attenuationin fog and clouds,” Proc. SPIE 4530, 58–71 �2001�.
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Sajid Sheikh Muhammad received his BSwith honors in electrical engineering in2001, followed by a MS in 2004, both fromthe University of Engineering and Technol-ogy, Lahore, Pakistan. He remained on thefaculty of electrical engineering at the sameuniversity from January 2002 to April 2004.Since May 2004, he has been working to-ward his PhD at the Graz University ofTechnology �TU Graz�, Austria, and hasbeen actively involved in investigating
odulation and code design for FSO systems. He has written 15
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peer reviewed research papers, and his research interests includedigital communications, information theory, and FSO.
Benno Flecker studied electrical engineer-ing at TU Graz with a focus on communica-tions and electronics. His interests includeoptical communications, computer mea-surements, and space sciences. He hasworked with measurements on FSO sys-tems for over two years and has presentedhis work at major conferences in the UnitedStates and Europe.
Erich Leitgeb received his MS in electricalengineering at TU Graz in 1994. In 1994, hestarted research work in optical communi-cations at the Department of Communica-tions and Wave Propagation at TU Graz. InFebruary 1999, he received his PhD withhonors. Since January 2000, he has beenthe project leader of international researchprojects �COST 270, SatNEx� in the field ofoptical wireless communications. He estab-lished and leads the research group for op-
tical communications at TU Graz. He is currently an assistant pro-fessor at the TU Graz. He gives lectures in optical communicationsengineering, antennas and wave propagation, and microwaves. Heis a member of IEEE, SPIE, and WCA. Since 2003, he has been areviewer for IEEE and SPIE conferences and journals and acts asmember of technical committees and chairperson on conferences.
Michael Gebhart studied electrical engi-neering at TU Graz with a focus on commu-nications and electronics and received histo MSc in 1999, and his PhD with honors in2004. He is a member of IEEE and SPIE.His interests include optical communica-tions, wireless technologies, electronic sys-tem development and integration, andspace sciences. From 2000 to 2004, he wasa research assistant in the Department ofCommunications and Wave Propagation
and developed broadband wireless optical communication systemsfor Ethernet connections. He was involved in international projects,such as COST 270 �reliability of optical components and devices incommunications networks and systems� and SatNEx �a network ofexcellence with work package on “clear sky optics”�. Since 2005, hehas been with Philips Austria GmbH Styria working in research anddevelopment on radio frequency identification topics.
