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Odd page header Chapter 15 Atmospheric Channel Effects and the Impact on Optical Communications Sub-Editor: Abstract: Date of last update 15-Oct Last updated by JF Technical completion % Technical validation % References complete Yes Cross references complete Yes General formatting % 90% Images clear Figure copyright Number of pages 56 Comments/residual actions List of authors needed below. Abstract needed. List of Authors: Odd page footer Page number i Even page header 7Even page footer Page number ii Odd page header Table of Contents Chapter 15 Atmospheric Channel Effects and the Impact on Optical CommunicationsFormel-Kapitel 1 Abschnitt 1 ................................................... i 15. Atmospheric Channel Effects and the Impact on Optical Communication ..................................................................................................... 4 15.1. Introduction .......................................................................................... 4 15.2. Theoretic Description of Atmospheric Turbulence .............................. 7 15.3. Numerical Simulation of Atmospheric Turbulence ............................ 23 15.3.1. Introduction .............................................................................. 23 15.3.2. Method ...................................................................................... 24 15.3.3. Sampling ................................................................................... 27 15.4. Aircraft Boundary Layer Effects ........................................................ 28 15.5. Link Availability ................................................................................ 36 15.5.1. Attenuation in Fogs................................................................... 36 15.5.1.. Physical Characteristics of Fog ............................................ 36 15.5.1.. Attenuation Due to Fog ........................................................ 37 15.5.1.. Experimental Results ........................................................... 38 15.5.2. 15.5.2.. Attenuation in Clouds and Downlink Availability.................... 45 Attenuation of Clouds .......................................................... 45 15.5.2.. .................................................................................................... 49 15.5.2.. Cloud Coverage Statistics .................................................... 49 15.5.2.. Link Availability Estimated from Cloud Coverage Statistics50 15.5.2.. Availability of Ground Station Diversity Systems ............... 52 15.5.2.. Conclusion ........................................................................... 54 Odd page footer Page number iii Even page header 15. Atmospheric Channel Effects and the Impact on Optical Communication M. Knapek, F. Fidler, M. Grabner, V. Kvičera, R. Mackey, F. Moll, F. Stathopoulos Abstract: Atmospheric index-of-refraction turbulence has a strong impact on optical communication links due the short wavelengths used in these applications. This chapter presents in detail the atmospheric effects to be expected in HAP-toground links and in inter-HAP scenarios. Links to ground stations will suffer more significantly from the atmosphere, as the atmospheric density is much higher than in inter-HAP scenarios. Standard atmospheric models, theoretic formulas, and simulation results are provided. The boundary layer around moving aerial vehicles is investigated and their influence on laser communication discussed. The influence of clouds and fogs on optical links is investigated and availability statistics are given. 15.1. Introduction The communication channel refers to the medium used to transport information from the transmitter to the receiver, which in our case is air (in the Earth's atmosphere) as well as vacuum (in space in the case of HAP-to-satellite communication). Each channel shares characteristics, which allow using a common channel model on how the channel affects the transmitted signal. The optical communication channel through the atmosphere between HAPs or between HAP and satellite can be modeled by attenuation of the transmitted signal where the random part is known as fading. The attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The Earth's atmosphere extends approximately 700 km above the surface and consists of several distinct layers [1]. Pronounced density is found within the lowest 20 km [2], still influencing HAP-to-satellite or inter-HAP links. When a laser beam propagates through a turbulent medium like the atmosphere, one observes several disturbances [2]: the laser light is scattered or absorbed (atmospheric attenuation), the beam divergence is larger than in the diffraction-limited case (beam spread), the beam is displaced (beam wander), and the phase front is distorted (phase fluctuations). 7Even page footer Page number 4 Odd page header These phenomena result in loss of power and (the latter two) in intensity fluctuations at the receiver (fading) and - in the worst case - may lead to a link failure. Absorption and scattering: Absorption occurs when the optical field transfers energy to the molecular constituents of the atmosphere. It exhibits a strong dependence on wavelength [2,3]. Atmospheric scattering due to molecular sized particles is called Rayleigh scattering. For objects large compared to the wavelength, Mie scattering occurs. Rayleigh scattering is dominant for clear sky conditions and - being proportional to λ-4 - for short wavelengths, while Mie scattering does not depend on the wavelength that strongly [2, 3]. When transmitting an optical signal on a vertical path through the atmosphere, some 1 to 2 dB of atmospheric loss have to be expected for example for clear skies at zenith. Much stronger absorption with more than 10 dB have to be expected at low elevation angles (<20 degrees). Different weather conditions can also cause variations of the atmospheric loss by several orders of magnitude. Usually all weather phenomena (and thus also cloud coverage) happen inside the troposphere, which extends up to a height of 11 km. In reference [4] the maximum cirrus altitude is given with approximately 19 km. The influence of the atmosphere on an optical link from a HAP at 20 km height to a satellite is therefore much smaller than it is for a link from ground station to satellite. Fading: Variations of the received signal intensity due to interferometric effects and beam wander are usually called fading, and are caused by changes in the characteristics of the propagation path with time or space: Turbulent motion of the atmosphere in the presence of temperature and pressure gradients causes disturbances in the atmosphere's refractive index in the form of eddies, acting as random optical lenses which refract the propagating light. One may distinguish between two main effects causing fluctuations in received intensity (and thus fades): 1. Because of random deflections during propagation through turbulent atmosphere, the beam profile moves randomly off the line-of-sight (LOS) between transmitter and receiver. The instantaneous center of the beam, i.e. the point of maximum intensity, is randomly displaced in the receiver plane, which is commonly called beam wander (cf. Fig. 15.1 (a)). Beam wander is caused mainly by large-scale turbulence near the transmitter and therefore can typically be neglected for downlink scenarios [2]. 2. The effect caused by small random index-of-refraction fluctuations is commonly described as scintillation (cf. Fig. 15.1 (b)). It leads to both the temporal variation in received intensity and the spatial variation within a receiver aperture. Beam spread loss: Atmospheric turbulence causes beam spread (cf. Fig. 15.1 (c)) beyond the diffraction limited divergence θDL, leading to a larger effective divergence angle, θeff, which causes a degradation of the mean received optical power by a factor (θeff/θDL)2. Odd page footer Page number 5 Even page header Fig. 15.1 (a) Beam wander: Displacement of the center of the beam due to large-scale turbulence. (b) Scintillation: Intensity profile fluctuations due to interference effects within the beam. (c) Beam spread: Intensity distribution of a propagating laser beam (solid lines...beam spread due to diffraction, dashed lines...beam spread due to diffraction and turbulence). Phase-front distortions: When a laser beam propagates through the atmosphere its phase-front gets perturbed (cf. Fig. 15.2 (a)), which reduces the coupling efficiency into a single-mode fiber [5, 6]. Turbulent eddies, which are relatively small compared to the beam diameter lead to noticeable phase-front distortions within the receiving aperture. This is the case for example in a satellite-to-HAP downlink (cf. Fig. 15.2 (b)). In the uplink case the turbulent eddies are right in front of the transmitter and comparatively large relative to the optical beam. This leads to a large beam spread causing the phase-front disturbance to be negligible within the small receiving aperture at a satellite (cf. Fig. 15.2(c)). Fig. 15.2 (a) Coupling geometry: A thin lens focuses the incident field E, which is assumed to have a constant amplitude but a statistically disturbed phase, onto the bare end of a single- mode fiber. (b) Downlink: Negligible beam spread, large phase-front disturbance over receiving aperture. (c) Uplink: Negligible phase-front disturbance, large beam spreading. In order to assess the performance of an optical communication link, it is important to find quantitative expressions for all degradations caused by the atmos- 7Even page footer Page number 6 Odd page header phere. While some measured data and mathematical models are available in literature [2, 3, 7] for ground-to-satellite links or for horizontal links near ground, such information is scarce or even non-existent for optical links from or to HAPs. In the following sections we are going to discuss each degrading effect in detail. Then we will present analytical, numerical, and empirical methods for the quantitative estimation of losses and power fluctuations caused by the atmosphere including several weather phenomena like clouds or fog. 15.2. Theoretic Description of Atmospheric Turbulence Various phenomena associated with an optical wave propagating through statistically dependent random inhomogeneities of the atmosphere have been studied for many years (e.g. [2, 8, 9, 10, 11, 12, 13]). Based on those analytical methods and formulas, we develop methods to calculate parameters which help to describe the atmospheric impact on laser beam propagation in communication scenarios from or to HAPs. Table 15.1 shows a set of important input parameters together with typical default values for optical communication scenarios. Table 15.2 gives an overview of the output parameters which can be calculated using the analytical models we will address within this section. We assume a Gaussian beam shape together with the atmospheric turbulence spectrums described by Andrews [2] as basis for the theoretical calculation of, e.g., the scintillation, the fade statistics, beam wander, or the coupling loss into a single-mode fiber. The lowest-order transverse electromagnetic Gaussian beam is a solution of the paraxial Helmholtz equation 2 E k 2 E 0, (15.1) where E is the transversal field of the wave and k = 2π/λ is the wave number related to the wavelength λ. Under the assumption that the change in field distribution is negligible with propagation distance z, the field of a Gaussian wave can be described as [2] w r2 kr 2 exp jkz ( z ) 0 , E (r , z ) E0 exp 2 exp j 2 R ( z ) W ( z) W ( z ) (15.2) where we can identify the amplitude r2 A0 E0 exp 2 , W ( z) Odd page footer Page number (15.3) 7 Even page header the phase kr 2 0 j kz ( z ) , 2 R( z ) (15.4) and a normalization factor w0/W(z) which assures that the total power of the beam along the propagation path z stays constant. The time factor exp (-jωt) of the field is usually omitted in wave propagation studies [2]. In equation Error! Reference source not found., r denotes the radial distance from the center line of the beam (i.e. from the z-axis), w0 is the radius at which the field amplitude falls to 1/e of that on the beam axis in the plane z = 0, W(z) is the beam radius in a distance z = L and can be calculated according to [12] 2 z , W ( z ) w0 1 w0 (15.5) R(z) is the phase-front curvature 2 w2 R( z ) z 1 0 , z (15.6) and Φ(z) is the phase term z ( z ) arctan 2 . w0 7Even page footer Page number (15.7) 8 Odd page header Table 15.1 Default input parameter set for optical communication scenario from/to HAPs Parameter HAP altitude Symbol hHAP Default value 17 – 20 km Satellite altitude hSAT 35786 km (LEO) HAP telescope diameter DHAP < 30 cm Satellite telescope diameter DSAT < 30 cm HAP velocity vHAP 0 – 11 km/min Geodetic latitude geo - (GEO), Zenith angle ζ 0 - 70° Normalized pointing error αn - Communication wavelength λ 850 – 1550 nm Fading threshold FT - Surge threshold ST - Structure constant at ground 2 1.7·10-14 m-2/3 Wind speed at ground Cn (0) vwind 3 m/s Wind speed at tropopause vT 30 m/s Selection uplink/downlink - - Selection untracked/tip-tiltcorr./tracked beam - tracked Odd page footer Page number 9 400 km Even page header Table 15.2 Default output parameter set for optical communication scenario from/to HAPs. Parameter Fried parameter Symbol r0 Unit [m] Beam spread loss abs [dB] Coupling loss into SMF aco [dB] Power coupling efficiency into SMF η [-] 2 Scintillation index σI [-] Probability of fade P(F>FT) [-] Probability of surge P(S>ST) [-] Expected number of fades per unit time ‹n(FT)› [-] Mean fade time ‹tf› [s] Angular pointing error α [rad] Mean-square phase variations σφ 2 [-] Effective divergence angle θeff [rad] The structure parameter, Cn2(h), represents the total amount of energy contained in the stochastic field of the refractive index fluctuations [2]. It is a measure of turbulence strength, required for the calculation of important fading related parameters like the scintillation index or the Fried parameter, and varies as a function of height h above ground. For the calculation of Cn2(h) the Hufnagel-Valley model, 2 v h h h h 16 2 Cn2 (h) 5.94 103 m 8/ 3 s 2 RMS 5 exp 2.7 10 exp Cn (0) exp 1000m 1500m 100m 27 10 m 10 (15.8) is one of the most used models in the field [1], which requires the structure constant at ground, Cn2(0), as an input parameter. As shown in Fig. 15.3 (b), nearground levels may range from 10-17 m-2/3 (during night and weak turbulence conditions) to 10-13 m-2/3 (during day and strong turbulence conditions). The rms wind speed, vRMS, is required as an input parameter for the HufnagelValley model. It is calculated by the Bufton wind model [2, 14, 15], which we write as vRMS 1 15 103 1/ 2 20103 5103 2 h h 2 T vwind vT exp dh d T 7Even page footer Page number 10 . (15.9) Odd page header The quantity h is the height, vwind is the ground wind speed, vT is the wind speed at the tropopause, hT is the height of the tropopause, and dT its thickness. Fig. 15.3 (a) shows a typical wind speed profile vs. height, calculated using the Bufton wind model, which is in good accordance with measured data given in [16, 17]. It reveals the relatively mild wind at HAP altitudes between 17 and 22 km, leading to reduced turbulence, i.e. a small structure parameter (cf. Fig. 15.3 (b)). When calculating temporal statistics (like the number of fades per second or the mean fading time), the mean wind speed transverse to the optical beam is required: hh T vt (h) vmov (h) vwind vT exp dT 2 . (15.10) The height-dependent velocity term vmov(h) is caused by the HAP movement relative to the satellite which for example in the case of a GEO can be calculated as v mov (h) S hSAT rEarth 2 rEarth h 2 sin 2 (rEarth h) cos , cos (15.11) where rEarth is the Earth's radius and ωS is a height-independent angular velocity of the laser beam derived from the HAP moving speed (cf. Fig. 15.4): S v HAP cos . L Odd page footer Page number (15.12) 11 Even page header Fig. 15.3 (a) Wind-speed profile vs. height, calculated using the Bufton wind model. (b) Structure parameter vs. height, calculated using the Hufnagel-Valley model. (dashed-dotted...vwind = 0 m/s, Cn2(0) = 10-17 m-2/3, solid...vwind = 3 m/s, Cn2(0) = 1.7·10-14 m-2/3, dashed...vwind = 20 m/s, Cn2(0) = 10-13 m-2/3) Fig. 15.4 HAP moving speed vHAP and angular velocity of laser beam ωs in a HAP-from/tosatellite (or HAP) communication scenario (L...link length, hHAP...HAP altitude, hSAT...satellite (or second HAP) altitude, rEarth...Earth's radius, ζ = 90-γ...zenith angle, vn...HAP speed component normal to LOS). 7Even page footer Page number 12 Odd page header The Fried parameter (or atmospheric coherence diameter), r0 in [m], is an important quantity used to describe the influence of atmospheric turbulence on a propagating beam [10]. Two common physical interpretations are: 1. The Fried parameter corresponds to the diameter of an aperture over which there is 1 rad of rms phase distortion [13]. 2. It equals a diffraction limited aperture with diameter r0 which produces the same divergence angle as atmospheric turbulence would add to the diffraction limited divergence angle of a telescope with diameter D, resulting in an effective divergence angle θeff = [(λ/D)2+(λ/r0)2] 1/2 [18]. In accordance with [2, 8] one can calculate the Fried parameter as hSAT r0 0.423k 2 sec( ) Cn2 (h) dh hHAP 3 / 5 (15.13) , using the optical wave number k in [rad/m], the zenith angle ζ in [rad], the HAP altitude hHAP in [m], the satellite altitude hSAT in [m], and the structure parameter Cn2(h) in [m-2/3] at height h. Fig. 15.5 (a) shows the decrease of the Fried parameter with increasing zenith angle, which corresponds to an increase in phase distortion over a certain aperture, i.e. an increase in turbulence. Very large values of r0, which are of advantage with respect to fading, can be found at high platform altitudes (cf. Fig. 15.5 (c)). While at ground, e.g. at the optical ground station (OGS) in Tenerife, the Fried parameter varies between 20 mm and 200 mm for strong and weak turbulence [18], respectively, the Fried parameter for a HAP to satellite link is larger than 2.5 m even for strong turbulence. Fig. 15.5 (b) illustrates the wavelength dependence of the Fried parameter, showing the advantage of a 1550 nm communication wavelength compared to shorter wavelengths at 850 nm or 1064 nm. With increasing wavelength the beam divergence increases, leading to less phase-front distortions (e.g. the amount of rms phase distortion in the uplink decreases over a certain aperture) and therefore to an increased Fried parameter, to less scintillation, fading, and beam spread loss. Odd page footer Page number 13 Even page header Fig. 15.5 Fried parameter r0 for a satellite-from/to-HAP link vs. (a) zenith angle ζ, (b) wavelength λ, and (c) platform altitude hHAP (calculated according to equation (15.13), dasheddotted...vwind = 0 m/s, Cn2(0) = 10-17 m-2/3, solid... vwind = 3 m/s, Cn2(0) = 1.7·10-14 m-2/3, dashed... vwind = 20 m/s, Cn2(0) = 10-13 m-2/3) A quantitative measure for the temporal effect of atmospheric turbulence is the scintillation index, σI2, i.e. the variance of intensity fluctuations normalized to the square of the mean intensity, I2 I 2 1, I 2 (15.14) where ‹I› is the temporal mean intensity of the optical wave at the receiver [2]. The scintillation index is generally used to characterize the strength of turbulence for an optical link. Such, σI2 ≤ 1 corresponds to weak fluctuations, whereas σI2 > 1 is refereed to as moderate-to-strong fluctuation regime. Simulations using the analytical formulas as given in [2] for vertical paths through the atmosphere show that - contrary to satellite-ground links – the scintillation parameter is typically smaller than 0.025 for HAP-to-satellite scenarios. For horizontal links one distinguishes between the regime of weak and strong turbulence using the criteria given in [2]: R2 1 and R2 5/ 6 1 , weak fluctuation R2 1 and R2 5/ 6 1 , strong fluctuation conditions, conditions, where the Rytov variance σR2 7Even page footer Page number 14 (15.15) Odd page header R2 1.23C n2 k 7 / 6 L11 / 6 (15.16) and the parameter Λ 2L kW 2 (15.17) depend on the structure parameter Cn², on the optical wave number k, on the path length L, and on the diffraction limited 1/e² beam radius at the receiver W. The probability of fade, P(F > FT ), describes the probability that the loss (or fading depth), F, of the instantaneous received intensity, I, with respect to the received mean on-axis intensity is larger than a fade threshold FT. The term “onaxis” is defined as the line-of-sight (LOS) between the centers of transmit and receive telescope. The fade threshold parameter FT, in [dB], corresponds to the difference between the received on-axis mean intensity ‹I(0;L)› after the transmission distance L and a smaller intensity threshold level IT , i.e. I 0, L . FT 10 log IT (15.18) The probability of fade is deduced from mathematical models for the probability density function (PDF), p(I), of the randomly fading irradiance signal [2, 19, 20, 21]. Assuming that the intensity fluctuation is an ergodic process, the probability of fade as a function of the threshold level becomes the cumulative probability of the intensity, i.e. PF FT PI I T IT pI dI . (15.19) 0 In the weak fluctuation regime typical for HAPs, the time-variant intensity of an optical wave is often described by a lognormal PDF [22] Odd page footer Page number 15 Even page header I 2 2 L2 2 2 ln I I (0, L) W 2 2 1 eff , p I exp 2 I2 I 2 I2 (15.20) Fig. 15.6 (a) illustrates the lognormal PDF in the uplink for various HAP altitudes. The received intensity is close to the mean on-axis intensity if the HAP is situated at hHAP = 20 km. The variance of the PDF increases with decreasing HAP altitude, i.e. with increasing atmospheric turbulence, leading to larger fading levels. Also the maximum of the PDF function shifts to a lower value, which means that the instantaneous received intensity is most likely below the mean on-axis intensity. As shown in Fig. 15.6 (b), the variance of the PDF first increases and then decreases with increasing pointing error. This reflects that the influence of beam wander is more severe if the (point) receiver is situated at the slope of the Gaussian beam than at its peak or at its tail. Fig. 15.7 shows the probability for a fading larger than 1 dB as a function of the HAP altitude in the uplink in different turbulence conditions. Below a height of h = 14 km, an untracked beam clearly leads to a higher probability of fade than a tip-tilt corrected beam or a tracked beam. We distinguish between three cases: When speaking of an untracked beam we fully take into account the effects of beam wander. In the case of a tracked beam, we assume the removal of the root-meansquare (rms) beam wander displacement, i.e. a compensation of the movement of the instantaneous center of the beam with a tracking time constant much smaller than the time constant of the atmospheric fluctuations. In the case of tip-tilt correction tracking is performed by means of closedloop beam tilt control via a tiltable mirror at the transmitter, which removes the rms "tilt" displacement from the far-field beam. This tip-tilt corrected case corresponds to the removal of the Zernike polynomials of the 2nd (x-tilt) and 3rd (y-tilt) order. We find that below a height of h = 14 km, an untracked beam clearly leads to a higher probability of fade than a tip-tilt corrected beam or a tracked beam. The often used standard Rytov model [22] approximates the tip-tilt corrected case very well. At typical HAP altitudes - between 17 km and 22 km - the effect of beam wander becomes more and more negligible; the probability of fade for an untracked beam, a tip-tilt corrected beam, and a tracked beam become virtually equal. The term surge denotes the event when the currently received intensity rises above the (temporal) mean of the received intensity [23]. The probability of surge, 7Even page footer Page number 16 Odd page header P(S ≥ ST), describes the probability that the surge (or excess), S, of the instantaneous received intensity with respect to the received mean on-axis intensity after a link distance L is larger than the surge threshold ST . The surge threshold parameter, ST in [dB], giving the difference between the received on-axis mean intensity ‹I(0;L)› at α = 0 and a higher intensity threshold level IT , is defined as I 0, L . ST 10 log IT (15.21) Following the approach for the probability of fade one can write the expression for the probability of surge as PS ST PI IT IT IT 0 pI dI 1 pI dI . (15.22) Fig. 15.6 Normalized lognormal probability density function of the intensity for an untracked uplink beam: (a) for varying HAP altitudes hHAP (αn = 0), (b) for different normalized pointing errors αn = α/θeff (hHAP = 20 km). Odd page footer Page number 17 Even page header Fig. 15.7 Uplink probability of a fading larger than 1 dB vs. HAP altitude for (a) an untracked beam, (b) a tracked beam, (c) a tip-tilt corrected beam, and (d) when using the standard Rytov model for calculation. (dashed-dotted...vwind = 0 m/s, Cn2(0) = 10-17 m-2/3, solid... vwind = 3 m/s, Cn2(0) = 1.7·10-14 m-2/3, dashed... vwind = 20 m/s, Cn2(0) = 10-13 m-2/3) Temporal statistical parameters are, e.g., the expected number of fades per second or the mean fade time. The number of fades per second gives the mean number of crossings per second of the received intensity I below a specific threshold value IT, i.e. the mean number of fades per unit time with a certain fading depth FT. The mean fade time in [s] represents the average time at which the signal stays below a defined threshold FT. It depends on the probability of fade as well as on the expected average number of fades per unit time. When calculating temporal statistics, the turbulent eddies are treated as frozen in space which move across the observation path with an rms wind speed1 5010 1 vt (h) 2 dh 3 50 10 hHAP hHAP 3 vt , RMS 1/ 2 cos( ). (15.23) 1 This assumption and the formula are in good accordance with the Taylor frozen turbulence hypothesis as described in reference [2]. 7Even page footer Page number 18 Odd page header The input parameter vt(h) takes into account the moving speed of the HAP and is calculated according to equation (15.10). The expected number of fades per unit time larger than a specified fading threshold level FT is given by [2] 0.5 2 2 2 L2W 2 0.23F 2 I eff T nFT 0 exp 2 2 I (15.24) in the case of weak turbulence, i.e. when the scintillation index is smaller than 1, the lognormal PDF is used to describe the statistics of the intensity fluctuations. The formula requires the quasi-frequency 0 1 2 BI (15.25) I2 as an input parameter, with BI being the second derivative of the temporal covariance function. The average time at which the fading of the received intensity relative to the mean on-axis intensity is larger than a fading level FT is determined by t f PF FT , nFT (15.26) where P(F > FT ) is the probability of fade and ‹n(FT)› is the expected number of fades per second. Atmospheric turbulence also causes beam spread (cf. Section 15.1) beyond the diffraction limited divergence. For the calculation of this, additional, beam spread loss abs in [dB], we compare the diffraction limited beam radius WDL (determined by the transmit telescope) of a Gaussian beam [12,24] to the effective beam radius [2] Weff D WDL 1 TX r0 5/3 3/ 5 Odd page footer Page number (15.27) 19 Even page header of the same beam but in the presence of turbulence, leading to Weff . abs 20 log 10 W DL (15.28) For downlink paths only high-altitude turbulence – which is weak and relatively far away from the transmitting source in case of a satellite – has an influence on beam broadening. It is found that in the downlink – where turbulent eddies are small compared to the beam diameter – the effective spot size, Weff , is essentially the same as the diffractive spot size, WDL [22]. Hence, beam spread loss is negligible. In the uplink or in HAP-to-HAP scenarios, the size of turbulent eddies situated just in front of the transmitter is large relative to the beam diameter, leading to a noticeable beam spread loss. Fig. 15.8 illustrates the variation in beam spread loss with increasing zenith angle, wavelength, and platform altitude in the case of a HAP-to-satellite uplink and in different turbulence conditions. As expected, the beam spread loss is larger at zenith angles ζ > 40° and small wavelengths, because of a smaller Fried parameter r0 under these conditions. The “plateau” which can be observed in Fig. 15.8 (c) at altitudes between 4 km and 8 km reflects the increasing wind speed at these altitudes (cf. Fig. 15.3 (a)), leading to shear winds and therefore to additional turbulence. Fig. 15.8 Beam spread loss abs for a HAP-to-satellite uplink vs. (a) zenith angle ζ, (b) wavelength λ, and (c) platform altitude hHAP. (dashed-dotted...vwind = 0 m/s, Cn2(0) = 10-17 m-2/3, solid... vwind = 3 m/s, Cn2(0) = 1.7·10-14 m-2/3, dashed... vwind = 20 m/s, Cn2(0) = 10-13 m2/3) For horizontal HAP-to-HAP links and in the case of weak turbulence the beam radius at the receiver is broadened additionally by the presence of the atmosphere and its effective 1/e² radius can be calculated as [2] 7Even page footer Page number 20 Odd page header 1 z Cn2 ( z )1 L 0 L L Weff WDL 1 4.35k 7 / 6 L11/ 6 5 / 6 5/3 (15.29) dz , whereas in the strong turbulence regime it is found to be 12 / 5 Weff WDL 5/ 3 L 1 z 1 4k 7 / 6 L11/ 6 Cn2 ( z )1 dz L0 L . (15.30) For the calculation of the structure parameter Cn²(z) at every point z along the transmission path the curvature of the Earth has to be taken into account because it leads to an increased atmospheric turbulence halfway between the transmitter and the receiver due to a reduced height above ground. When a laser beam propagates through the atmosphere also its phase-front gets perturbed, which reduces the coupling efficiency into a single-mode fiber [5, 6]. The spatial phase-front disturbances after a propagation distance L can be described by the phase structure function [25] D d , L 1 2 , 2 (15.31) where φ1-φ2 denotes the phase difference at two points on the phase front separated by the distance ρd. According to [1] the structure function for downlink channels can be modeled by D d , L 2.914k 2 hSAT 5/3 d sec C n2 h dh, (15.32) hHAP which, in combination with equation (15.12) for the Fried parameter r0, allows to calculate the mean-square phase variation over an aperture of diameter D [13] D 1.0299 r0 2 5/3 (15.33) . Odd page footer Page number 21 Even page header In the receiver, the optical input field E - which is collected by the receive telescope - is focused by a thin, diffraction limited lens to the bare end of a singlemode fiber. The coupling efficiency η is defined as the ratio of the power carried by the fiber mode and the power available in the focal plane. It is possible - and often more convenient - to calculate the coupling efficiency in the aperture plane A [6], i.e. just in front of the coupling lens (cf. Section 15.1). Then η is given by A E r F * r exp jr dA 2 (15.34) where E is the input field normalized to its overall power, and F* is the conjugate complex of the field distribution of the fiber mode, back-propagated to the aperture plane A. A phase function Φ(r) covers any deviations from an ideal plane wavefront of the input field E. The coupling efficiency depends also on the lensto-fiber coupling geometry, which can be taken into account via an additional coupling design parameter ρ/rS, with ρ being the core radius of the fiber and rS being the Airy radius of the beam in the focal plane. The parameter ρ/rS takes into account the properties of the incoming beam and of the coupling optics, while the normalized frequency V 2 , nco2 ncl2 (15.35) with core and cladding refractive indices nco and ncl, determines the characteristics (e.g. the numerical aperture) of the optical fiber. Without loss of generality we assume for the calculations to follow the fiber to be operated at single-mode cutoff (V = 2.405) and the lens-to-fiber geometry to be optimized for maximum coupling efficiency (ρ/rS = 0.5345). In the case of a perfect phase-front, Φ(r) = const, and when approximating the fiber's eigenmode by a Gaussian field distribution, a maximum coupling efficiency of ηmax = 81.5% can be achieved. When using the exact field of the fiber's fundamental mode the maximum coupling efficiency amounts to ηmax = 78.6%, corresponding to a minimum power coupling loss of 1.05 dB [6]. A comparison between the single-mode fiber coupling efficiency in a satellite-toground communication link and a satellite-to-HAP scenario shows the feasibility of using fiber coupled receivers onboard HAPs due to the reduced impact of atmospheric turbulence at high altitudes. (15.9) gives the coupling efficiency as a function of the rms phase-front perturbation, RMSλ, expressed in fractions of the wavelength λ. For the calculations we assumed a wavelength of 1550 nm and a standard (telecommunications) single-mode fiber with a core diameter of 10 μm, a core refractive index of 1.46, and a core/cladding refractive indices difference of 0.3%. As expected, the characteristic shown in Fig. 15.9 is rather flat for small 7Even page footer Page number 22 Odd page header perturbations, but drops dramatically to very small values for large disturbances. For typical satellite-to-HAP communication links (i.e. with hHAP > 17 km and D < 20 cm) the mean coupling loss is always less than 1.2 dB, while for communication links to a ground station it significantly increases to values larger than 7 dB. Fig. 15.9 Mean coupling efficiency η for a standard single-mode fiber as a function of the rms phase-front perturbation RMSλ given in fractions of the wavelength λ. 15.3. Numerical Simulation of Atmospheric Turbulence 15.3.1. Introduction Numerical simulation is a useful tool for investigating the effects of atmospheric turbulence on beam propagation, particularly in the strong fluctuation regime where Rytov theory begins to break down. This occurs for low-elevation Earthsatellite links (<30°), where the increase in the propagation path length through turbulence causes strong fluctuations in phase. In this regime the fluctuations in optical path length can no longer be approximated using a geometrical optics approach; diffraction effects must also be included to account for the refractive scattering of light rays by turbulent cells less than the coherence length, r0 or the Fresnel length, L , whichever is smaller [26]. For many general situations it is often easier to input a set of known physical parameters, such as the Cn2 profile, the propagation distance, and perhaps even the inner scale, into a numerical simulation and to examine the outputs, than to try and find an analytical solution. The drawback of numerical simulation is the amount of time and computer memory that is required to generate an adequately large ensemble of independent realizations to calculate quantities of interest, such as the degree of scintillation, the frequency and duration of signal fades etc. However, while the analytical solutions Odd page footer Page number 23 Even page header for strong fluctuation regime are still being investigated, numerical simulation is a useful method for evaluating the effect of atmospheric turbulence on wave propagation, in particular in the design and simulation of adaptive optics correction systems. 15.3.2. Method To simulate wave propagation through atmospheric turbulence, the Cn2 profile (for example the HV5/7 profile described in Section 15.2) along the propagation path is discretized to form N slabs of turbulence with a constant Cni2 value over a propagation distance zi, as shown schematically in Fig. 15.10. z N 0 i 1 2 2 Cn z dz Cni zi (15.36) The number of discrete layers to use and the layer separation is chosen to ensure that the scintillation that develops during propagation between layers remains within the weak fluctuation regime (i.e. a Rytov value R2<< 1). In weak turbulance scenarios, for example optical links at zenith between ground and satellite, fewer atmospheric layers are required to adequately model the turbulence and the discretization of the Cn2 profile can be optimized to produce fixed layer heights with the correct Cn2 weighting by matching the first 7 moments of the integrated Cn2 profile as described in [27]. The optical path fluctuations over the atmospheric layer thickness of zi are condensed into a ‘thin’ phase screen, where the term thin indicates that the effects of diffraction on propagation through the layer are negligible. The optical path fluctuations are found by integrating the refractive index fluctuations, n1, over the layer thickness z zi z zi i ( x, y, z ) 2 (15.37) n1 ( x, y, z )dz 2 The phase fluctuations within the layer are assumed to have Gaussian statistics and are therefore completely defined by their second moment. The usual method of producing a phase screen is to use the amplitude of the 2D Kolmogorov power spectrum as a filter in the frequency domain to weight white Gaussian noise [28]. The 2D filter, 2D, is found by integrating the 3D Kolmogorov power spectrum over the direction of propagation to give, 7Even page footer Page number 24 Odd page header 2D ( f x , f y ) 0.023k 7 / 6 ( f x2 f y2 )11/ 6 where k = 2/r0 is the atmospheric coherence length, and (15.38) f x and f y are spatial frequencies on the sampled grid with grid spacing f = 1/D, where D is the width of the grid in meters. The infinite term at the origin represents an unimportant piston term that can be removed by setting its amplitude to zero. the range of frequen When representing the power spectrum on a discrete grid cies is limited by the size of the grid and the size of the grid spacing. To increase the range of frequencies, one may start with a large grid with dimensions of the outer scale of turbulence and cut out the central region of the phase map. However, as the outer scale of turbulence may be on the order of 100m and the desired pixel sampling on the order of several mm, this can lead to extremely large grid sizes. An artificial way of introducing low frequencies is with the addition of subharmonics, as described in reference [29] or by using an interpolation algorithm that takes into account the 5/3 scaling of the phase structure function, such as the random mid-point displacement method described in reference [30]. Fig. 15.10 Schematic of the discretization of the Cn2 profile into thin phase screens, Φi, representing atmospheric layers of thickness Δzi. A split-step Fourier method is used to simulate the propagation of light through the atmosphere. The method described here follows that of reference [31]. Each phase screen is positioned at the mid-point of the layer thickness and the optical field (x,y,z), is allowed to propagate through free-space between phase screens. Odd page footer Page number 25 Even page header At the positions of the phase screens the phase perturbation of the screen, (x,y,z) is added to the phase of the complex field to introduce the wavefront aberration due to the atmospheric turbulence. x, y, z' x, y, z exp i x, y, z (15.39) Propagation over a distance of z through free-space between phase screens is simulated by convolving the aberrated field, (x,y,z’), with the Fresnel diffraction kernel [32] ( x, y, z z ) ( x, y, z ') exp ik x 2 y 2 2 z (15.40) where k = 2/ is the wave-number and * denotes a convolution. In the Fourier domain this is equivalent to multiplying the Fourier transform of the aberrated field by the Fresnel transfer function, H f x , f y exp iz f x 2 f y 2 (15.41) where fx and fy are the spatial frequencies. As the beam propagates it expands due to the refractive scattering and diffraction. To try to capture the beam spread within the grid, the grid width is chosen to be much larger than that of the transmit aperture. For long propagation paths and spherical wavefronts it is impossible to sample all scales adequately without using enormous grid sizes. As discussed by Horwath et al. [33], it is necessary to reduce the angular extent of the grid as the propagation path increases and resample the grid following the method of Rubio et al. [34] in order to sample all scintillation scales adequately. As a safety measure, to avoid reflections of the field at the grid boundary, an apodizing mask can be applied to the amplitude of the field at each propagation step. For example, a circular apodizing mask with a flat profile over a diameter of 80% of the grid and with a Gaussian roll-off at the edges could be used. The apodizing mask is chosen to be flat over much of the grid to try to avoid attenuating any part of the field that may contribute to the field in the receiver plane. 7Even page footer Page number 26 Odd page header 15.3.3. Sampling Fresnel propagator: The Fresnel transfer function has a quadratic dependence on spatial frequency, H f x , f y exp iz f x 2 f y 2 (15.42) To ensure the transfer function is well sampled at the highest spatial frequency the change in phase between adjacent pixels must be less than radians. This gives a requirement that for a fixed pixel size, x, and a fixed interscreen propagation distance, z, the number of grid points, N, must be N z x 2 (15.43) Interscreen distance: The maximum interscreen distance is chosen so that the scintillation that develops over that distance remains within the weak fluctuation 2 regime (i.e. that the Rytov variance, R 1 ). To ensure weak scintillation the maximum Rytov value is set at Rytov value is 1.23k C z 2 R 7/6 2 n 11/ 6 R2 0.1. For a plane wave and constant Cn2, the (15.44) and thus the maximum interscreen distance is z k 0.254 7/6 Cn2 (15.45) 6 /11 The spatial coherence length: To ensure adequate sampling of the phase and scintillation scales at the receiver, the pixel size must be much less than the atmospheric coherence length, r0. The coherence length for a plane wave propagating over a path of length L is given by Odd page footer Page number 27 Even page header L 2.91 2 1 r0 k cos Cn2 dz 0 6.88 3/ 5 (15.46) where k = 2/ and is the angle from zenith. 15.4. Aircraft Boundary Layer Effects A challenging issue is to calculate the distortions on the propagated laser beam at the aircraft boundary layer. The distortions are created from the fluctuation of the air properties inside the flow, specifically the density, which consequently affects the refractive index. Via extensive simulations we examine the distortion of the wavefront with regards to various parameters. The main contributions of this work are: (a) we derive the relation between air properties – e.g. density and pressure – and the refractive index, and then quantify the affect of the flow field on the laser beam, (b) we introduce a framework that can be applied in any flying object independently of the kind of flow, (c) using this framework we are able to describe and quantify the aberration of the laser beam wavefront. Assuming that the air properties around the aircraft are known, we introduce a method in order to be able to calculate the wavefront distortions of the laser beam. From the Gladstone – Dale equation [35]: G n 1 or n 1 G (15.47) where G is the Gladstone – Dale constant, we can calculate the refractive index n. The Gladstone-Dale constant depends only on the beam wavelength, according to the equation [36], [37]: 0 . 0 1 7 8 5 0 7 6 4 G 2 . 1 9 2 5 3 9 2 1 0 7Even page footer Page number 28 (15.48) Odd page header Gladstone - Dale const. ( cm3 / g ) Gladstone - Dale constant over wavelength 0.28 0.26 0.24 0.22 0.2 -1 10 0 10 wavelength [µm] 1 10 Fig. 15.11 The Gladstone-Dale constant vs. wavelength It is obvious from Fig. 15.11 that for a specific wavelength we have a constant ratio between the density and the distance of refractive index from the unit, for two different points (A,B) of the medium: A nA 1 B nB 1 (15.49) That shows us that if we know the density ratio between two points, and the refractive index in one of them (it can be at the free-stream area), we can calculate the refractive index at the other point. The optical path length of the laser beam, noted OPL, is related to the refractive index by: y OPL x, y, z n x, y, z dy (15.50) 0 The Optical Path Difference, OPD, shows the configuration of the wavefront and is defined as the minimization of OPL: O P D O P LO P L m in Odd page footer Page number (15.51) 29 Even page header Fig. 15.12 Diagram of the wavefront error calculation method Since we have the OPD we are able to describe the scintillation, aiming to compensate the distortions. In order to get a better aspect of the topic we present the results of extensive simulations. A number of simulations are performed [38] for various flow fields from laminar, steady to turbulent flow as well as for different shapes of an aircraft, trying to reach closer to the aerodynamic shape of a HAP. The wavelength of the laser beam is considered at 1550 nm. pressure coefficient over a sphere pressure coefficient over a sphere -4 -3 0.8 -3 -2 0.4 -1 0.2 0 0 -0.2 1 -0.4 0 0 1 -0.5 -0.6 2 2 -0.8 3 4 -4 0.5 -1 y- axis y- axis 0.6 -2 -1 -1 3 -1.2 -2 0 2 4 x- axis -2 0 x- axis 2 Fig. 15.13 Pressure coefficient around a Fig. 15.14 Pressure coefficient around an sphere, r = 1 m (case A) eclipse, r/R = 1 m/2 m (case B) In both cases the flow is laminar, steady and incompressible. 7Even page footer Page number 30 Odd page header Fig. 15.15 Density around a sphere, R=1 m, Fig. 15.16 Density around a sphere, u=37.5 m/s, STP R=1 m, u=54 m/s, air at 20 km Compressible flows around a sphere (case C) Optical Path Difference [m] at 0° 5 2.5 10 2 15 -6 x 10 3 5 3 aperture size (cm) aperture size (cm) Optical Path Difference [m] at 30° -7 x 10 3.5 1.5 20 2.5 10 2 15 1.5 20 1 1 25 25 0.5 0.5 30 5 10 15 20 25 30 30 0 5 10 15 20 25 30 0 aperture size (cm) aperture size (cm) θ=30° θ =0° Fig. 15.17 OPD for a specific elevation angle, for case A, aperture diameter= 30 cm, air at STP. Odd page footer Page number 31 Even page header Optical Path Difference for elevation angle 0° 40 x 10 35 3.5 30 3 25 2.5 20 2 15 1.5 10 1 -6 0.5 5 5 10 15 20 25 30 35 40 0 θ=0ο θ=90 ο Fig. 15.18 OPD for case B, aperture diameter= 40 cm, STP. θ= 60ο, φ= 90ο θ= 30ο, φ= 90ο Fig. 15.19 OPD for case C, aperture amplitude = 40 cm. Boresight error and mean tilt [Heading??] From the wavefront configuration, OPD(x,y), we are able to calculate the boresight error, a(x,y), through the wavefront phase error, e(x,y) [39]: e ,y kO D ,y x x 0 P (15.52) where K0 is the wave number, and then: 7Even page footer Page number 32 Odd page header a x , y x , y e x , y ( x , y ) 2 ( x , y ) (15.53) Knowing the boresight error, we are able to calculate the mean wavefront tilt along the two coordinates of the wavefront surface (x,y). The mean tilt is the sum of the two coordinates: 2 2 1m ax,y ai and a a x a y mi1 (15.54), (15.55) wavefront tilt over elevation angle 12 wavefront tilt [µrad] 10 8 6 4 2 0 0 20 40 60 elevation angle [°] 80 Fig. 15.20 Wavefront tilt over elevation an- Fig. 15.21 Mean tilt vs the elevation angle, gle, case A. case B. Odd page footer Page number 33 Even page header mean wavefront tilt over velocity (Mach number) mean beam angle fluctuation over height 12 12 0 30 45 80 8 10 mean wavefront tilt [µrad] mean wavefront tilt [µrad] 10 6 4 5 30 45 80 8 6 4 2 2 0 0.1 0.15 0.2 Mach number 0.25 0 0 0.3 10 20 height [km] 30 40 Fig. 15.22 Mean tilt over the Mach number Fig. 15.23 Mean tilt vs height for several ele- for different elevation angles, case A. vation angles, case A. Zernike polynomials [Heading?] An analytical measure used to characterize the fluctuation of the wavelength are the Zernike polynomials. They show us the effect of the corresponding Zernike polynomial making an accurately describing of the wavefront aberrations. In the next five Figures (Fig. 15.24 to Fig. 15.25) is presented the variation of the first six coefficients (each one for the corresponding polynomial) for elevation angles from 0° to 90°. -9 x 10 value of each coefficient value of each coefficient -8 3 2 1 0 -1 0 1 2 3 4 5 zernike polynomial 6 7 15 x 10 9 10 5 0 -5 0 1 θ = 0° θ = 30° Fig. 15.24 The value of the first six Zernike polynomials, case A. 7Even page footer Page number 2 3 4 5 zernike polynomial 34 6 7 Odd page header θ= 60ο, φ= 90ο θ= 30ο, φ= 90ο Fig. 15.25 The value of the first six Zernike polynomials for case C. Root Mean Square OPD and Strehl ratio Another parameter we can research to define the wavefront fluctuations is the difference-Root Mean Square (RMS) of the wavefront, defined as: 2 1 2 O P D O P D O P D d x d y R M S S (15.56) where S is the surface of the aperture. Τhe ratio of the observed peak intensity to the theoretical maximum peak intensity of the beam, called Strehl ratio, is another determinant. For the calculation of Strehl ratio complex mathematic equations are required, thus we use the following equation, accurate for cases with small errors [40]: 2 SR exp K OPD exp f 2 (15.57) where SR is the Strehl ratio, K is the wave number, OPD is optical path length and f is the wavefront phase error. Odd page footer Page number 35 Even page header Fig. 15.26 OPDRMS vs height, case B. Fig. 15.27 Strehl ratio vs height, case B. It is obvious that there is still space for more research on the topic of the aircraft boundary layer effect on the laser beam propagation. A real challenge is to simulate a more realistic scenario of an aircraft and to calculate the distortions of the beam wavefront. The research is getting more interesting as it combines fluid- and air-dynamics with optics. But the most stimulating issue is the implementation of this research for the improvement of optical telecommunications. Furthermore we can compare but also combine optical links with RF links for better telecommunication results. 15.5. Link Availability 15.5.1. Attenuation in Fogs Physical Characteristics of Fog Fog consists of fine water droplets in the atmospheric layer in contact with the ground. According to the international meteorological definition, a fog occurs when the horizontal visibility is reduced below 1000 m and when humidity is close or equal to 100% [41]. The reduction in the visibility depends on the nature of the fog, on the volume concentration and on the size distribution of the droplets. Fogs are classified according to the physical process whereby water vapour is condensed: radiation fog, advection fog, upslope fog, precipitation fog, valley fog, steam fog, ice fog, freezing fog, hail fog, evaporation fog and mixing fog. Advection fog and radiation fog are two main types of fog. More detailed information about different types of fogs can be found in [41], [42]. Meteorologists classify fog in accordance with the visibility V (m). Classification is given in 7Even page footer Page number 36 Odd page header Table 15.3. Odd page footer Page number 37 Even page header Table 15.3 Classification of Fog light fog 500 m < V < 1000 m moderate fog 200 m < V < 500 m thick fog 50 m < V < 200 m dense fog V < 50 m The dependence of the liquid water content LWC (g/m3) on visibility V (km) can be calculated in accordance with the power law type empirical formula (1), e.g. as given in [43] LWC = 0.0165 * V -1.13636 (15.58) Typical liquid water contents range from 0.003 to 3 g/m3 depending on location, height in the atmosphere, and meteorological conditions [44]. The ITU-R recommendation [45] gives the liquid water content of a fog as 0.05 g/m3 for moderate fog (300 m visibility) and 0.5 g/m3 for dense fog (50 m visibility). The radius of fog droplets varies between 0.1 μm and 20 μm [46], [47]. Horizontal atmospheric visibility is usually measured using either a transmissometer or a diffusiometer at airports so it is possible to obtain visibility characteristics in areas where the FSO systems are to be deployed. The visibility measured at airports provides a good estimate for the assessment of fog impairment. The vertical extent of fog usually varies from a few metres to several hundred meters. In sporadic cases, the vertical extent can be up to 2 km, mainly for the advection fogs [48]. The more detailed information is very scarce. In [49] is stated that the vertical extent of fog rarely exceeds 100 m, while fog events up to 140 m in height are reported in [46]. Attenuation Due to Fog The interaction of the atmosphere with light of free space optical (FSO) links produces the impairment by frequency selective absorption, scattering and scintillation. Molecular absorption is a selective phenomenon and can be negligible in the preferred optical transmission windows from 690 nm to 10600 nm. It becomes a serious problem for wavelengths much longer than 10 μm. The effect of scattering is dominant loss mechanism for fog. The type of scattering is determined by the physical size of fog particles with respect to the wavelength used. Rayleigh scattering occurs when the atmospheric particles are much smaller than the wavelength. The effect of Rayleigh scattering on the attenuation is very small. Mie scattering becomes dominant when fog particles are comparable with the wavelength. Mainly smaller fog particles suffer from Mie scattering. Non-selective or geometric scattering occurs when the fog particles are much larger than the wavelength and therefore there is no dependence of attenuation on 7Even page footer Page number 38 Odd page header wavelength. Primarily thick and dense fog, rain droplets, snow, hail, and cloud droplets geometrically scatter laser wavelengths. There is no great variation of attenuation between 500 nm and 10 μm wavelengths. An extensive search of the literature and some full Mie scattering calculations reveal that 785 nm, 850 nm and 1550 nm wavelengths are all in fact equally attenuated in fog with visibility smaller than 500 m [47]. Fog scattering losses can be approximated by four the most used models: Kruse model [50], Kim model [47] and Al Naboulsi models for advection and convection fog [51], [52]. These models relate attenuation to visibility. Experimental Results For the design of FSO links that should meet required availability performance criteria, attenuation statistics has to be obtained from either attenuation or visibility data measured at particular locations where the planned FSO links are to be deployed. The following experiment provides an insight into the influence of different type of hydrometeors besides fog on attenuation and its relation to visibility. Experimental Setup A FSO link at 850 nm has been operated on a path length of about 850 m since August 2004 in Prague, the Czech Republic. Transmitted power is 16 dBm, divergence angle is 9 mrad and optical receiver aperture is 515 cm2. The recording fade margin is about 17 dB. The other experimental FSO link with the wavelength of 830 nm operates on a 100 m long path in the same location. The transmitted optical power is 30 dBm, the diameter of Fresnel lens is 15 cm. A real optical fade margin is about 20 dB. The meteorological system is located near the receiver site and is equipped with VAISALA sensors for the measurement of temperature, humidity and pressure of air, velocity and direction of wind and tipping-bucket rain-gauge for the measurement of rainfall intensities. The VAISALA PWD11 device is used for the measurement of visibility from 2000 m to 50 m. Attenuation and Visibility due to Individual Types of Hydrometeors The 3-year experimental research (August 2004 – July 2007) of attenuation due to hydrometeors at 850 nm measured on an 850 m terrestrial path confirmed that fog is the most significant impairment factor [53]. The obtained cumulative distributions (CDs) of attenuation due to individual types of hydrometeors, i.e. rain (R), rain with hails (RH), rain with snow (RS), snow (S), fog (F), and snow on the shields of lens of the FSO device (SSL) and sun (the experimental link is situated approximately on an east-west axis and therefore the optical receiver oriented towards the sunset was overloaded sometimes during the summer months) for the entire 3-year period are drawn in Fig. 15.28. Odd page footer Page number 39 Even page header 20 all S R F RH SSL RS sun A (dB) 15 10 5 0 0.00001 0.0001 0.001 0.01 0.1 1 10 percentage of time Fig. 15.28 Obtained cumulative distributions of attenuation due to individual types of hydrometeors for the entire 3-year period It can be seen in Fig. 15.28 that the occurrences of fog caused dominant attenuation events. It can be also seen that both the cumulative distribution of attenuation due to snow and the cumulative distribution due to rain with snow are also significant. On the other hand, rain attenuation events, rain with hails attenuation events, the influence of sun and the influence of snow on the shields of lens of the FSO device can be considered to be negligible. The obtained yearly CD of attenuation due to all hydrometeors together was analyzed and the results obtain are given in Fig. 15.29 and Fig. 15.30. 20 all together F FR FS F+FR+FS R RS S S on lens sun A (dB) 15 10 5 0 0.001 0.01 0.1 1 percentage of time 10 100 Fig. 15.29 Yearly CDs of attenuation due to individual type of hydrometeors and other causes 7Even page footer Page number 40 Odd page header 2000 all together F FR visibility (m) 1500 FS F+FR+FS R 1000 RS S 500 0 0.001 0.01 0.1 1 10 100 percentage of time Fig. 15.30 Yearly CDs of visibility due to individual type of hydrometeors It can be seen the reduced visibility due to the occurrence of dense fog, fog with rain, and fog with snow caused the significant attenuation events. Attenuation of fog with rain and fog with snow can be taken as attenuation due to fog without significant error due to the fact that rain intensities and snow intensities respectively, contained in fog were always less than 3 mm/h. This rain intensity can cause attenuation up to about 3 dB on this path [54]. Therefore, only insignificant error can arise when the events of fog with rain and fog with snow are taken as fog events. It is important in the cases when data obtained at airports are processed. Dependence of Specific Attenuation of Fog on Visibility The dependence of specific attenuation on visibility for fog only, obtained on a terrestrial FSO link at 850 nm on an 850 m long path over one-year period (August 2006 – July 2007) [55], was compared with the calculated dependences in accordance with four different models [47], [50] – [52]. The results obtained are shown in Fig. 15.31. The dependence of specific attenuation on visibility for fog alone agrees very well with the calculated dependence in accordance with the Al Naboulsi model for the convection fog [52]. The differences between results of both Al Naboulsi models are very small, of about 0.2 dB. All the fog events that occurred on the experimental path were of the convection types. Odd page footer Page number 41 Even page header 25 Specific attenuation for fog (dB/km) measured Kruse model Kim model 20 Al Naboulsi model - advection fog Al Naboulsi model - convection (radiation) fog 15 10 5 0 500 1000 1500 Visibility (m) 2000 2500 Fig. 15.31 Comparison of measured dependence of specific attenuation on visibility for fog only and the modelled dependences Comparison of Measured Attenuation with Models The CDs of attenuation due to fog were calculated from the measured CDs of visibility due to fog and compared with the measured CDs of attenuation due to fog [56] on FSO link operating at 850 nm wavelength on a path of 850 m. CDs of visibility due to fog measured in October 2004, December 2004, and July 2005, i.e. for the months with long-term and dense fog events, were chosen and four different formulas [50], [47], [51], and [52] were used for calculations. Visibility was varying from 2000 m to 700 m. The results obtained are shown in Fig. 15.32. 20 Oct + Dec + Jul Kruse model A F+FR+FS (dB) 15 Kim model Al Naboulsi model - advection fog Al Naboulsi model - convection fog 10 5 0 1 10 percentage of time Fig. 15.32 Comparison of measured and calculated CDs of attenuation due to fog for 3-month period It was found that the Al Naboulsi model [52] for convection fog was the best suited model with the r.m.s. value of 0.190 for the above mentioned 3-month period. 7Even page footer Page number 42 Odd page header Proposed Empirical Models Based on Experimental Results Two empirical models based on the results of experimental research in Prague are proposed – the power-law model and the inhomogeneous model [57]. In the power-law model the specific attenuation A (dB/km) is calculated using the following equation: A 10 loge aV b (c), (15.59) where V (km) is atmospheric visibility. In the special case (for parameters a = 3 and b = -1) it is reduced to the Kruse model for the wavelength of λ = 550 nm. An additional shift parameter c is used to further improve a model fit (the shifted power-law model). The inhomogeneous model is based on the assumption of the linear spatial dependence of visibility V(x) along the propagation path and is defined as the mean value of specific attenuation along the propagation path: d d 0 0 A (1/ d ) A( x)dx (1/ d ) 10 log(e) (3 / V ( x)) dx V ( x) V0 (aV0 b) x (15.60) with parameters a, b and V0 denoting visibility at one site of the propagation path. Measured time series from 5 dense foggy days (Nov 19, 2006, Dec 28, 2006, Oct 28, 2007, Jan 2, 2008 and Jan 14, 2008) were processed together and the obtained dependence of the specific attenuation due to fog on visibility (scatter plot diagram), the Kruse, Kim, Al Naboulsi models and the proposed models are shown in Fig. 15.33. Odd page footer Page number 43 Even page header Fig. 15.33 Measured data and comparison of visibility vs. attenuation models, non-parameterized models (left) and fitted models (right) The Kruse, Kim and Al Naboulsi models underestimate attenuation values for medium and lower visibilities. The performance of these models is good for visibilities greater than 1 km. The proposed shifted power-law model is the best one with respect to RMS and it performs better mainly in the region of medium visibilities. The resulting parameters of this model are a = 6.861, b = -0.858, c = -10.428. Availability Performances of Simulated 850nm/58GHz and 850nm/93GHz Hybrid Systems The availability performances of the FSO link, the back-up radio frequency (RF) links and the simulated FSO/RF hybrid system can be assessed from the obtained CDs of attenuation due to all hydrometeors together. Availability performance of FSO link is reduced mainly by dense fog events while availability performance of RF link is impaired primarily by heavy rainfall events. Therefore, the RF part of the hybrid system will mitigate fog events and the FSO part will mitigate rain events. The cumulative distributions of attenuation due to all hydrometeors together for the FSO link, the 58 GHz RF link and the simulated 850 nm/58 GHz hybrid system are plotted in Fig. 15.34 [58]. 7Even page footer Page number 44 Odd page header 25 FSO 58 GHz hybrid A all (dB) 20 15 10 5 0 0.00001 0.0001 0.001 0.01 0.1 1 10 percentage of time Fig. 15.34 Obtained CDs of attenuation due to all hydrometeors for 850 nm link, 58 GHz link and simulated 850 nm/58 GHz hybrid system The cumulative distributions of attenuation due to all hydrometeors together for the FSO link, the 93 GHz link and the simulated 850 nm/93 GHz hybrid system are plotted in Fig. 15.35. 30 FSO 93 GHz hybrid A all (dB) 25 20 15 10 5 0 0.00001 0.0001 0.001 0.01 0.1 1 10 percentage of time Fig. 15.35 Obtained CDs of attenuation due to all hydrometeors for 850 nm link, 93 GHz link and simulated 850 nm/93 GHz hybrid system Let us consider a hybrid system where both the FSO link and the RF link have the same fade margin FM = 15 dB. The availability performance (AP) of the simulated FSO/RF hybrid system can be estimated from the CDs shown in Fig. 15.34 and Fig. 15.35. The results obtained are given in Table 15.4. Odd page footer Page number 45 Even page header Table 15.4 Availability performances of FSO, RF, and simulated FSO/RF hybrid systems System 850 nm 58 GHz 93 GHz 850 nm/58 GHz hybrid GHz/850 850 nm/93 GHznm hybrid GHz/850 nm AP (%) 99.4600 99.9793 99.9608 99.9948 99.9965 It can be seen clearly, that the significant improvement of availability performance can be achieved by using FSO/RF hybrid system. Acknowledgments This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the project No. OC093 in the frame of COST Action 297. 15.5.2. Attenuation in Clouds and Downlink Availability Attenuation of Clouds The dependency of clouds is one of the most problematic issues to be solved in optical free-space communications. At times of overcast sky, a vertical link is very likely to be blocked due to the high attenuation over the whole optical spectrum. Only very thin clouds, which are mainly ice clouds at high altitudes, can be handled with an adequate link margin. Generally, clouds are split into four families. Depending on their base height, three families are designated to low, middle and high clouds. The fourth family consists of clouds with high vertical extent. At middle European latitudes low clouds range from ground to 2 km, middle clouds from 2km to 6 km, and high clouds from 6 to 13 km. The third family is mainly ice clouds and bear relatively low attenuation due to low ice water content and thus less scattering and absorbing particles. The first, second and fourth family are mainly the clouds of concern. These have high liquid water content and thus bear higher attenuation. Table 15.5 lists values for the base height, the thickness, and water content of the most frequent cloud types. Therefore, Stratus, Stratocumulus, and Cumulus clouds belong to the family of low clouds. Altostratus clouds are found in the family of middle clouds, Cirrus are high clouds; Nimbostratus clouds have high vertical extent and thus are grouped in the forth family. Table 15.5 Height and thickness of the most frequent cloud types taken from [59] and water content taken from [60]. Cloud type Base height [km] 7Even page footer Page number Vertical extent [km] 46 Water content [g/m3] Odd page header Stratus 0.1 – 0.7 0.2 – 0.8 0.29 Stratocumulus 0.6 – 1.5 0.2 – 0.8 0.15 Nimbostratus 0.1 – 1.0 2-3 0.65 Altostratus 2–6 0.2 - 2 0.41 0.5 – 1.0 0.5 – 5 1.00 6 – 10 1.0 – 2.5 0.064 Cumulus Cirrus For calculation of the wavelength dependent attenuation of a cloud it is necessary to describe this cloud with a proper model. This comprises the particle size distribution of the water drops in the cloud and the respective wavelength dependent complex index of refraction of liquid water or ice water, respectively. The shape of the particles is assumed to be spherical and for simplicity the cloud is considered to be homogenous and not polluted. With these constraints it is possible to set up a simple to use cloud model which can be used to determine the attenuation characteristics with the theory of Mie scattering. In general, this theory is applied for calculating the scattering of an electro-magnetic wave in the presence of particles with spherical shape. To give an example, Fig. 15.36 depicts the particle size distribution of a Stratus and Stratocumulus cloud as they are also applied in the widely spread LOWTRAN (LOW TRANsition code) and FASCODE (Fast Atmospheric Signature CODE) models [60]. The shape of these distributions, i.e. the particle size of maximum occurrence and width of the curve, together with the absolute water content and complex index of refraction determine the attenuation spectra. Odd page footer Page number 47 Even page header Fig. 15.36 Particle size distribution for the Stratus and Stratocumulus cloud type. These distributions are generated with the modified gamma function proposed by Deirmendjian [61] using the parameterization of LOWTRAN and FASCODE [62]. Using the Mie-tool from the LibRadtran simulation suite [63], attenuation spectra in [dB/km] of these two cloud models together with Cumulus, Altostratus, and Nimbostratus were calculated. They are plotted in Fig. 15.37. In general, the attenuation is very high and seems to be far beyond being considered in link budgets. However, there happens to be a local minimum at wavelengths between 10 µm and 12 µm for all considered cloud types due to low absorption and scattering on the water droplets. Eventually, this wavelength interval is worth being considered for further investigations. 7Even page footer Page number 48 Odd page header Fig. 15.37 Calculated attenuation per km of five water cloud types. For parameterization the models proposed in LOWTRAN and FASCODE are used [62]. Since clouds have different vertical extent, the knowledge of attenuation per km is not satisfying. Table 15.5 lists a range of vertical thickness for the respective cloud types. Thus, there is an absolute attenuation range every cloud can come up with. A Cumulus type, for instance, ranges between 500 m and 1000 m which results in attenuation from ca. 290 dB up to 580 dB in the NIR. Even at the local minimum in the spectrum between 10 µm and 12 µm the attenuation is still far above 200 dB for the thin Cumulus (500 m). So, optical communication through this cloud type is quite hopeless. But in times of occurrence of some particular cloud types, like stratus and stratocumulus types, attenuation may be able to be coped with. The attenuation dynamic of these cloud types is shown in Fig. 15.38. Both types vary in thickness between 200 m and 800 m. In cases where these occur, the attenuation amounts between 29 dB and 116 dB for the Stratus at 11.13 µm and between 16 dB and 63 dB for the Stratocumulus at 11.05 µm; thus, these clouds may allow propagation by use of wavelengths in the middle infrared. Odd page footer Page number 49 Even page header Fig. 15.38 Dynamics of absolute attenuation of Stratus and Stratocumulus clouds. The dashed lines stand for the attenuation with vertical thickness of 800 m, the solid lines for 200 m. The local minimum of the Stratus is at 11.13 µm (29 dB), the one of the Stratocumulus at 11.05 µm (16 dB) [62]. Cloud Coverage Statistics Although, there may be a possible wavelength range with lower attenuation than the usually applied ones in the near infrared, the optical link is likely to be blocked in either case. Thus, under the assumption that any cloud occurrence in the line of sight between HAP and ground station blocks the optical link, it is important to estimate future statistical link availability with measurements of cloud amount. This kind of measurements is available in different metrics. Worldwide, trained weather watchers observe the cloud situation at certain locations four to twenty-four times a day and send them, together with a packet of other relevant meteorological parameters, to the national weather services and the WMO (World Meteorological Organization). The coverage is measured in Okta. 1 Okta corresponds to 12.5% cloud amount averaged over the visible hemisphere. This kind of measurement has a relatively good temporal resolution but a low spatial one for the whole field of view of the observer is taken into account. The second kind of available measurements are based on satellite earth observation. Here, data derived from LEO and GEO satellite images are to distinguish. The first usually deliver only one image a day, due to their limited visibility time. Resolution may be in the range of 1 km at nadir view, which is achieved by the AVHRR (Advanced Very High resolution Radiometer) on board of the newer NOAA (National Oceanic and Atmospheric Administration) satellites. The second produce cloud products with higher temporal resolution, like 96 measurements a day, as obtained with the instruments on the MSG (Meteosat Second Generation) satellite. But spatial resolution is lower and amounts around 2.5 km for the MSG. All data, no matter if derived from satellite or ground observations, are projected on the Earth surface. Thus, they contain information about cloud coverage in zenith view and may be used for estimation 7Even page footer Page number 50 Odd page header of availability of optical links between ground stations and corresponding HAPs hovering above them. Among the two types of cloud measurements mentioned above, there are several other kinds applying cameras, thermopiles, etc, but neither of them is widely used and thus not valuable for calculating statistics. It is important to mention that using of different kinds of data may result in deviating results. For instance, cloud coverage happens to be overestimated by ground observations, but in some cases also underestimated. However, comparisons show that deviations between statistics based on ground observations and Earth observation products of cloud amount in the ECC (European Cloud Climatology) project stay within a measurement error of 1 Okta [64], [65]. Link Availability Estimated from Cloud Coverage Statistics For ground stations in Europe, the ECC data is a good source to identify feasible locations. Fig. 15.39 (left) shows the mean cloud coverage of the year based on data from the years 1990/1995/2000/2004/2005. In this figure, one can see the typical north-south decrease of the mean cloud coverage. Hence; the amount of cloud occurrence in higher latitudes is bigger than in lower ones. For instance, the northernmost city in Sweden, Kiruna, has a mean coverage of 74% and the astronomical site on the Calar Alto, Spain, of 38%. Furthermore, geological features like the Alps, the Carpathians, and the Mediterranean Sea have strong influence on the north-south course. Eventually, it comes out that the Mediterranean region is to be examined first if ground station locations are searched for as it is underlined by the graph in Fig. 15.39 (right). It highlights the locations with over 60% availability that covers the Mediterranean region quite well. Fig. 15.39 Mean cloud coverage over Europe derived from ECC data of the years 1990/1995/2000/2004/2005. The right graph shows a binary illustration with a threshold of 60%. The Odd page footer Page number 51 Even page header white area depicts an availability of 60% and more. The gray area corresponds to the availability below 40% [62]. Further important information is the course of availability over the year. It may happen that locations with same year averages of cloud cover bear different variation over the year. So for some time periods a specific location may be feasible, or even extraordinarily good, but for other periods, link availability is just too low. The course of availability for the German Aerospace Center (DLR) site in Oberpfaffenhofen (Germany) is plotted in Fig. 15.40. As expected, cloud cover tends to be less during summertime than in wintertime. The best months give an availability of up to 66%, whereas the worst months drop below 30%. The year mean is 40%, the standard deviation 13%. A good example for a favourable site with high availability is Aix-en-Provence (France) which is chosen here to demonstrate suitable cloud conditions on the mainland with good infrastructural access. Furthermore, this site may fit well into the diversity network presented below. The mean availability amounts to 68% and remains above 50% for all months. The standard deviation is similar to the latter one. Another example is a site on the Calar Alto (Spain). Besides low cloud coverage, this site offers fine seeing conditions. Astronomical facilities are already located here and thus, infrastructure exists. Again, standard deviation is similar which indicates similar variation of all three stations over the year. When using a single ground station for communication links, minimizing this value is preferable. Fig. 15.40 Course of monthly mean cloud cover over Oberpfaffenhofen, Aix-en-Provence, and Calar Alto. This data is averaged over five years. 7Even page footer Page number 52 Odd page header Fig. 15.40 contains statistics averaged over several years. They show the mean course of availability over the year. Since conditions change not only over the seasons but also between distinct or subsequent years, a closer look reveals large variability as can be seen in Fig. 15.41. The five years, whose data is used to calculate the year course of Oberpfaffenhofen (Fig. 15.40), are separated here to illustrate the dynamics. Variations of up to 50% can be observed. This indicates the fact that any availability statistics are long term and are only valid for long term use of a dedicated ground station. Fig. 15.41 Course of cloud cover over the DLR site Oberpfaffenhofen for five different years. Availability of Ground Station Diversity Systems To raise link availability one can set up a system of several ground stations. Using the ECC data, the availability of a ground station diversity system with sites in southern Europe can be estimated. One condition is to choose sites with an overall low cloud cover, which restricts the available locations to the marked region in Fig. 15.39 (right). For weather cells have finite extent and locations close to each other may be located in the same cell and thus correlate, sites should be separated in distance so that this effect is negligible. To obtain an indication for a minimum distance, correlation of cloud condition around Aix-en-Provence was examined in [66]. Fig. 15.42 shows an exponential best-fit curve of the correlation coefficient over distance to Aix-en-Provence. It shows that correlation beyond 900 km can be considered low and thus negligible. Odd page footer Page number 53 Even page header Fig. 15.42 Best-fit curve for correlation over distance around Marseille [66]. Eventually, this minimum distance is another important condition for the ground station network since increasing the number of ground stations is senseless for they always have similar weather conditions if they are to close. What is more, practical matters like infrastructural facilities have to be obeyed. Together with the two sites in France and Spain, the resulting example network then hosts two more sites in Sicilia (Italy) and Crete (Greece). Fig. 15.43 (left) shows the chosen locations. Fig. 15.43 Location of the stations in two example scenarios. On the left side is a scenario in Europe. The stations have a least distance of 1000 km to each other and are assumed to be located in uncorrelated weather cells. On the right is a scenario in Germany. Here, the distance between the stations lies between 300 km and 900 km. Fig. 15.44 shows the course of the resulting mean availability with increasing number of stations of two network setups, the one in southern Europe and one in Germany. Looking at the course of the first one, it comes out that there is not much difference between availability calculation considering and neglecting correlation of weather cells. Thus, the overall availability of the network can be estimated by the pure knowledge of the locations particular mean cloud coverage. The network in Germany reveals different behavior because the sites are spaced closer. Calculation of network availability, with and without treatment of correlation, results in two quite different results. Here, it is illustrated clearly that correlation in- 7Even page footer Page number 54 Odd page header fluences availability calculation significantly and must be taken care of in that case. Fig. 15.44 Increase of availability of ground station diversity systems in Europe and Germany (left). The dashed lines show the availability when correlation between weather cells is neglected, the solid lines when correlation is taken care of [ 62]. Conclusion Cloud attenuation spectra and ground station availability statistics are presented. In most cases, cloud attenuation will be too high, no matter which wavelength is used and a vertical link from HAP to ground station will be blocked. Thus, availability statistics are needed to estimate link outage frequency, no matter if a single ground station or a network of ground stations is applied. An example network of four ground stations in southern Europe is presented and shows that availabilities over 98% are obtained in that case. However, one has to keep in mind that availability statistics are long term and high variability may occur. Odd page footer Page number 55 Even page header References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] Andrews LC (2004) Field guide to atmospheric optics. 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