Calculation of Angular Deflection Limits of a Mobile Free-Space Optical Link Beam

Transcription

1 460 J. NĚMEČEK, J. ČIŽMÁ CALCULATION OF ANULAR DEFLECTION LIMITS OF A MOBILE FSO LINK BEAM Calculation of Angula Deflection Limits of a Mobile Fee-Space Optical Link Beam Jiří NĚMEČEK, Jan ČIŽMÁR Dept. of Aeospace Electical Systems, Univesity of Defense, Kounicova 65, Bno, Czech Republic jii.nemecek@unob.cz, jan.cizma@ unob.cz Abstact. This pape descibes the effect of optical beam angula deflection on the powe eceived by the eceive of a mobile fee-space optical (FSO) link. Pemissible fluctuations in the powe eceived wee studied on a steady model of the FSO link. It was assumed that these fluctuations wee caused by oscillations of the optical beam acoss the eceive apetue. The fomula fo beam angula deflection limit was deived fo two diffeent types of optical intensity pofile. The task was solved fo two diffeent types of atmosphee. The fist type of atmosphee was consideed a homogeneous and lossless envionment. In the second type, atmospheic adiation attenuation was included in the calculations. Also, this aticle includes gaphs of dependencies of the angula deflection limits upon the distance between the link stations. Keywods Fee space optical link, steady model, angula deflection of the beam, powe fluctuations, optical intensity pofile, powe budget. 1. Intoduction Fee space-optical (FSO) links ae an altenative solution to adio fequency wieless links. FSO links ae natually esistant to jamming and tapping because of thei low optical beam divegence and thei small eceive field of view. Howeve, these system paametes ae the eason fo high link sensitivity to spatial fluctuations in the link stations. [1] The fluctuations cause angula deflections of both the beam and the eceive field of view that deteioate the powe budget. This esults in link fade if the link magin is depleted. The mentioned featues ae impotant, namely fo diectional mobile FSO links as they ae affected by natual oscillations of the optical beam and the eceive field of view in the equied diection. These oscillations ae caused by pointing eos of the link stations. []. Beam angula deflection limits wee calculated. These deflections ae impotant fo the system contolling the angula position of the FSO link stations. The dependence of the deflection limit upon the distance between the two link stations was studied on a aussian beam and a Top Hat beam. The adiation attenuation caused by absoption and scatteing in the atmosphee was also taken into consideation. The influence of othe phenomena, such as atmospheic tubulence and deflections of the eceive field of view wee not assessed in this aticle.. The Steady Model of a Fee-Space Optical Link The steady model of a fee-space optical link is epesented by a link powe budget used fo calculation of the optical powe P PD eceived by a photodiode. The powe budget povides the basic inputs fo the statistical model that assesses link eliability taking into account its atmospheic inteface. When the span of the equied powe P PD is defined, the steady model povides: Infomation on the value of the powe P PD gained fom the steady model and if it lies in the given span. The link magin fo andom effects. The steady model descibes the powe budget of an ideal link whee additional andom factos affecting the powe eceived ae not consideed..1 The One Channel Aangement of the FSO Link The scheme of the atmospheic pat fo one channel of the FSO link is shown in Fig. 1 [3], whee F is the filte, PD is the photodiode, RW is the eceive window, RXA is the eceive optical system, SR is the souce of adiation, TXA is the tansmitte optical system, TW is the tansmitte window, P SR and P PD ae the optical powe emitted by the souce of adiation and detected by the photodiode, espectively, P is the powe eceived by station No., P t is the powe tansmitted by the station No. 1, R is the distance between the stations, is the optical attenuation, and Θ is the beam divegence. Ciculaly symmetic beams wee used thus divegence is the same acoss all planes.

2 RADIOENINEERIN, VOL. 3, NO. 1, APRIL Knowing both the tansmittance of the individual FSO link elements and the losses caused by linkage impefections, both the adiation attenuation caused at the individual tansmission sections and the total attenuation can be calculated. Afte that, the eceived powe P PD (dbm) can be calculated fom the known tansmitted powe P SR (dbm) and the total attenuation (db). SR Tansmitte of the station 1 SR TXA TW RW RXA F TXA TW Fig. 1. One channel aangement of the FSO link []. The atmosphee is consideed as a homogeneous and lossless tansmission envionment. So called ideal pointing of the link is assumed when the tansmitte optical beam axis and the eceive field of view axis ae identical. To assess the influence of the pointing eos on the fluctuations in the powe eceived, a educed steady model was used. This model expesses the elationship between the output powe P t of station 1 and the adiation incident powe P hitting a eceive window aea of the same size as the eceive apetue size, see Fig. 1. The mathematical educed steady model of a link only takes into account the dependence of the powe eceived on the geometic attenuation α, occuing duing the popagation of the optical signal between the link stations.. The Mathematical Fomula of the Reduced Steady Model If the additional gain of the eceive, esulting fom a specific distibution of the beam s optical intensity, is ignoed, the educed mathematical steady model can be expessed by the following fomula [4], [5]: DRXA P Pt Pt 0 log (1) D Θ R TXA whee D TXA (m) is the diamete of the tansmitte apetue, D RXA (m) is the diamete of the eceive apetue, P t is the tansmitted optical powe, R (m) is the distance between the stations, α is the geometical attenuation, and (ad) is the angula width of the beam. The fomula (1) has to satisfy the following condition [5], [6]: S DRXA Pt 0 log Psat () D Θ R TXA Receive of the station RW RXA P SR P t P P PD R F PD PD whee P sat (dbm) is the maximal pemissible eceived optical powe, and S (dbm) is the eceive sensitivity. The diffeence between the maximum pemissible eceived optical powe P sat and the eceive sensitivity S is the link dynamic ange Δ (db): Δ P sat S. (3) The diffeence between the eceived optical powe P and the eceive sensitivity S is the link magin M (db) M P S. (4) Fo stationay FSO links, M is a constant. Fo mobile FSO links, the link magin depends on the instantaneous distance between the two stations..3 The aphical Repesentation of the Reduced Steady Model In this subsection, a gaphical example of the steady model is shown including its use fo modification of some elevant link paametes with the following components using fomulas (1) and (): tansmitted optical powe P t = dbm, (30 mw), tansmitte apetue diamete D TXA = 0.03 m, eceive apetue diamete D RXA = 0.0 m, eceive sensitivity S = 43 dbm, ( mw), link dynamic ange Δ = 30 db, optical beam divegence = ad, ( 1 ). By enteing the Δ and S into (3), the P sat = dbm, ( mw). Fig. shows a gaphical epesentation of the educed steady link model fo given values of the individual components assuming the distances between the stations ae within the ange of R 100 m, 000 m. Maked is the link magin M = 9.64 db fo the distance R = 1500 m. It is clea fom the gaph that the minimum distance R min is 150 m. It is the shotest link length at which the link can be used. Fo distances whee R < 150 m then P > P sat which does not satisfy the condition (). Howeve, a situation can occu whee the eceived powe, obtained fom the steady model, dops down to the eceive sensitivity level. Then P = S and the distance R = R max0 is the link ange with zeo link magin. Fo R > R max0 the link cannot be used even if the meteoological visibility is at its maximum. If the link is equied to be usable fo the entie span of the distances the powe budget must be adjustable. Assuming two options that eithe only the beam divegence o only the tansmitted optical powe P t can be alteed, then the equied value of both the divegence and the powe P t can be eached using the condition P (R) = P sat,

3 46 J. NĚMEČEK, J. ČIŽMÁ CALCULATION OF ANULAR DEFLECTION LIMITS OF A MOBILE FSO LINK BEAM with R = 100 m. If the divegence is alteed, and the othe paametes emain constant, the limit state is eached fo = 5 mad. If the tansmitted powe P t is alteed, the limit state occus fo P t = dbm (14.7 mw). Fig.. aph of the educed steady model [4]. The link magin M is an impotant esult of the link powe budget and plays a cucial ole in link eliability [4]. It specifies the maximum pemissible value of the eal link s additional powe losses caused by the atmosphee, backgound adiation, pointing eos etc. If the link is to be sufficiently esistant against these influences, the link magin must be as high as possible fo all equied link lengths. Theoetically, the maximum possible link magin is equal to the dynamic ange: M max = Δ. It is clea that fo links with constant paametes, the magin deceases with inceasing distance between the stations. Thus, the link length affects the link sensitivity to undesiable phenomena, showing deteioation of the tansmission chaacteistics and degadation of the link availability. In such a situation, when beam divegence is high and the link is elatively insensitive to pointing eos, it is necessay to ensue compliance with the condition () and povide the eceive with a big dynamic ange Δ. Only that can assue a sufficient link magin. 3. Effect of Beam Deflection on the FSO Received Powe As the eal mobile FSO link suffes fom pointing eos, the link paametes and the paametes of the contol tacking system have to be chosen with egads to the pemissible fluctuations in powe eceived. Received powe fluctuations ae caused by changes in the linea and angula mutual positions of the link stations. These changes ae a natual, pemanent and unavoidable pat of a link opeation envionment, geneally affecting all platfoms and depending on the natue of movement of the specific platfom. The fluctuations in eceived powe depend on the type of platfom and its featues, and on the quality and accuacy of the contol system that povides automatic tacking of opposing link stations. The pointing eos ae: Angula deflection of the eceive field of view fom its ideal position. Angula deflection of the optical beam fom its ideal position. The angula deflection of the eceive causes andom shifts of the adiation footpint fom the sensitive detecto suface. As a esult, some powe losses can occu if the detecto suface is not lage enough. Howeve, mentioned eos ae not the focus of this aticle. This aticle only focuses on losses caused by a shift of the optical beam axis fom the cente of the eceive apetue suface. The angula deflection of the optical beam ba (ad) causes andom linea beam deflections bl (m) at the eceive apetue suface, see Fig. 3. The main equiement fo these deviations is to fulfill the following inequation: DRXA δbl R wr (5) whee w(r) is the beam width at the distance R. The following equations apply to a beam with a small divegence and tiny pointing deflections: w D D Θ R, (6) R. (7) bl Fulfilling the fomula (5) ensues that the optical beam does not miss the eceive apetue totally. In geneal, even if (5) is fulfilled, the link magin could still become zeo (M = 0 db) fo cetain deflection limit bl = blm = bam whee blm, bam ae the beam linea and angula deflection limits, espectively. Howeve, fo deviations bl (R) > w(r) D RXA / the eceived powe could still be sufficient. To assess the effect of pointing eos on fluctuations in the eceived powe P, it is necessay to know the dependence of the optical intensity on the adial distance fom the beam axis. Fo example in the diection of the x-axis, see Fig. 3. Then this dependency can be geneally expessed by a elative optical intensity I (x, R) ( ): ba, R R I x I x, R (8) I whee I(x, R) (W m - ) is the optical intensity, I 0R (R) is the optical intensity on the beam axis at the distance R fom the tansmitte, and x is the adial distance in the diection of the x-axis. As the optical beams ae ciculaly symmetical optical beams, the x coodinate can be substituted by the y 0R

4 RADIOENINEERIN, VOL. 3, NO. 1, APRIL coodinate. The function I (x) influences both the fluctuation amplitude of the eceived powe P and the angula deflection limit of the beam bam. Fig. 3. y Tansmitte apetue C T The coodinate system of the optical beam. Assuming that thee ae two optical intensity distibutions, the aussian beam type and the Top Hat beam type. Then, the definition of the beam edge fo both types is a distance fom the beam axis x = w(r) = whee the optical intensity falls down to the level of I 0R (R)/e. This esults in: = TH =, whee, TH is the divegence of the aussian beam and the Top Hat beam, espectively. It is necessay to define beam edges in the same way fo the analysis of the eceived powe sensitivity to the spatial fluctuations of the individual beams. Taking into consideation the dependency of optical intensity on divegence and distance, the distibution of the elative intensity of the aussian beam can be expessed as follows: - x Θ R I Θ, x e. (9) The elative intensity of the Top Hat beam can be deived fom the Femi-Diac and Supe-aussian appoximations [7], o by using the following fomula: TH c x K - x K 3 ΘR I Θ, x e (10) whee c, K, K 3 ae coefficients. If the condition = TH = is to be fulfilled, one of the paametes K o K 3 has to be dependent on the emaining paametes in (10). Assuming that the coefficient K 3 is dependent, then the following equation deives fom the definition of the beam edge: K c 3 Θ R x K x Enteing x = R into (11) esults in K Line of sight Optical beam x Receive apetue C R. (11) c 3 Θ R Θ R K Θ R R ba z Axis of optical beam and fom that: K Θ c K R. (1) When K 3 fom (1) is substituted into (10), then the elative optical intensity of the Top Hat beam becomes - c [1 KΘR ] ΘR I Θ, x e. (13) TH c x K x 1 Fo example, fo K =.4 and c 1.5, 5, diffeent intensity pofiles can be selected fo the Top Hat beam. Fo c = 1, the pofile is aussian. Fo c = 1.5, the edge beam pofiles can be fomed by changing K within a ange of 1. to.4. Nevetheless, these pofiles ae only slightly simila to eal beams of this type. The behavio of functions (9) and (13) ae gaphically depicted in Fig. 4. The gaphs wee set fo the following vaiables and paametes: = ad, R = 100 m, K =.4, c = 1.5. Fig. 4. Dependency of elative optical intensity on the adial distance x. 3.1 The Deflection Limits of the aussian Beam The optical intensity of the aussian beam can be descibed as [4]: I Θ, Pt ΘR e (14) Θ R whee (m) is the absolute distance fom the beam axis along the eceive apetue plane, 0,. Substituting I 0R fo P t /(Θ R) gives: I - - ΘR Θ, I e 0R. (15)

5 464 J. NĚMEČEK, J. ČIŽMÁ CALCULATION OF ANULAR DEFLECTION LIMITS OF A MOBILE FSO LINK BEAM The quantity I 0R epesents the optical intensity on the axis of the aussian beam at the distance R fom the tansmitte. As a quantitative indicato of the effect of pointing eos on the link eliability, beam angula deflection limit bam can be used. The deflection is then deived fom the fomula expessing the powe popagating though the eceive apetue cente which is located out of the optical beam axis. - P t Θ π DRXA e S Θ R 0. (18) Then fom (18), the analytical equation fo will be S Θ R 0.5 Θ ln. (19) π D P RXA t y RXA Beam Footpint w(r) A bl P t = W, = 0.05 ad Receive apetue C D RXA / x RXA Fig. 5. Misalignment of the beam footpint [8]. The shift of the beam footpint fom the eceive apetue in the eceive coodinate system Cx RXA y RXA, whee C is the cente of the eceive apetue, is depicted in Fig. 5 [8]. If the aea of the eceive apetue A (m ) is compaable with the aea of the beam footpint, the eceived powe P ( bl, Θ, R) should be calculated fom the following geneal equation [8], [9] P δ Θ, R I δ, Θ, R bl, bl A da (16) whee I( - bl, Θ, R) is the optical intensity in the eceive coodinate system, and is the adial vecto fom the beam cente. If D RXA << then the optical intensity at the eceive apetue can be consideed constant and its value depends on the distance between the eceive apetue cente C and the beam axis. Then, the eceived powe can be expessed as a dependency on the angula beam deflection. Fo the aussian beam, the following designation was intoduced: bl = l, ba = a. When is eplaced by bl in (14) and bl is eplaced by (7), then the powe incident on the eceive apetue with the aea of A = π D RXA / 4 will be P a, Θ, R P, Θ, R I, Θ R A a a, 0,185 π D RXA P t Θ R, e a - Θ The condition fo beam angula deflection limit is. (17) P t = W, = ad Fig. 6. Behavio of aussian beam angula deflection limit. Fig. 6 shows gaphs of the aussian beam angula deflection limit fo the two following configuations of the mobile FSO paametes, using the link paametes mentioned in Subsection.3: P t = dbm (14.7 mw), = ad, P t = dbm (30.0 mw), = 0.05 ad. As expected, Fig. 6 confims that, as fa as the sensitivity to pointing eos is concened, it is moe favoable to have a link with a highe divegence, in ou case 0,05 ad. Fo the design of the link it is impotant that the value of deceases with inceasing distance R. Thus, the tacking system should be designed as an adaptive system o should be designed fo the wost case scenaio when the distance R is at its maximum, i.e. 000 m. The coesponding beam angula deflection limits ae 3.0 mad and 16.0 mad, fo = 5.0 mad and = 17.0 mad, espectively. 3. The Deflection Limits of the Top Hat Beam Assuming that the optical intensity distibution of the Top Hat beam is analogically defined as in (15), then

6 RADIOENINEERIN, VOL. 3, NO. 1, APRIL c K c1 [1 KΘR ] ΘR I, Θ, R I e. (0) TH 0RTH Assuming that I 0RTH = I 0R, then the angula deflection limit of the Top Hat beam can be expessed fom the following equation fo elative intensities as: Θ, R I, Θ R I, (1), TH THam whee THam is the angula deflection limit of the Top Hat beam. If x and x ae eplaced by lm = R and THlm = THam R in (9) and (13), then equation (1) will be as follows: e - Θ e c 1 c THam K R THam - c1 [1 K ΘR ] Θ By futhe modifications, we get: THam K D THam. () [1 K c1 c c1 Θ D ] It is clea fom () that the Top Hat beam angula deflection limit has to be solved using an iteative method. The angula deflection limit can be calculated fom () fo seveal distances within the inteval of R 100 m, 000 m and fo gadually changing values of the deflection THam. The esult is the value of THam fo which the following equation is tue: () (19). whee δ () is the angula deflection limit of the aussian beam calculated fom (), δ (19) is the angula deflection limit of the aussian beam calculated fom (19). The divegence and the tansmitted powe fo the aussian beam and the Top Hat beam have to be the same. Fo ou example in Subsection.3, the angula deflection limits of both beams ae aanged in table Tab. 1. Fig. 7 shows these deflections gaphically, depending on distance. Both the table and the pictue wee set fo K =.4, c = 1.5 and the atmosphee was consideed to be a lossless envionment. 3.3 The Consequences of an Optical Beam Powe Dop If a dop in the optical beam powe occus along the tansmission oute, both the powe budget and the angula deflection limits change fo both beam types. Also, the distance fo which the equation THam = is tue changes. The eason fo this could be signal loss due to eithe impuities of the tansmitte o eceive cove windows o due to atmospheic intefeence [1], [10], [11]. The dop in powe can be expessed by additional losses using diffeent expession suited to thei oigin. This aticle focuses only on atmospheic losses such as adiation absoption and scatteing. The losses ae usually expessed eithe by the attenuation α a (db km -1 ) o by the tansmittance τ a ( ), using the extinction coefficient β a (km -1 ). The tansmittance τ a is then used to assess the effect of the powe dop on the angula deflection limit. Assuming that the tansfe path of the length R (km) is homogeneous, then the tansmittance is as follows [1], [10]: R a e. (3) a The actual tansmission oute tansmittance τ a has an equivalent effect on the system as when the tansmitted powe dops down to the level of P t τ a. Then fomula (19) can be expessed as follows: S Θ D 0.5 Θ ln. (4) π D P POS t a R (m) = ad P t = dbm (ad) THam (ad) = 0.05 ad P t = dbm (ad) THam (ad) Tab. 1. Angula deflection limits fo the aussian beam and the Top Hat beam without any atmospheic intefeence. β a = 0.8 km -1 R (m) = ad P t = dbm (ad) THam (ad) = 0.05 ad P t = dbm (ad) THam (ad) Tab.. Angula deflection limits fo the aussian beam and the Top Hat beam with atmospheic intefeence.

7 466 J. NĚMEČEK, J. ČIŽMÁ CALCULATION OF ANULAR DEFLECTION LIMITS OF A MOBILE FSO LINK BEAM P t = 0,030 W, Θ = 0,05 ad P t = 0,030 W, Θ = 0,05 ad P t = 0,0147 W, Θ = 0,017 ad P t = 0,0147 W, Θ = 0,017 ad Fig. 7. Angula deflection limits of the aussian beam (dashed line) and the Top Hat beam (solid line) without atmospheic intefeence. The angula deflection limits of the individual beams wee calculated fo the same link vaiables and paametes as in the above mentioned cases, and fo coefficient β a = 0.8 km -1. The obtained deflections ae listed in Tab., and gaphically shown in Fig. 8. Fo the selected coefficient β a, the meteoological visibility is appoximately 3 km, within the opeating wavelengths of the FSO links. 4. Conclusion Both, the analysis of the powe budget and the eceived powe dependency on the mutual positions of the optical beam and the eceive apetue, show that the pemissible deflections of the optical beam fom the ideal pointing depend on seveal basic factos, such as beam divegence, optical intensity distibution of a specific beam type, and distance R between the link stations. The pesented analysis of eceived powe using diffeent beam types is applicable only if the following conditions ae met: The optical intensity on the beam axis, at an abitay distance R fom the tansmitte and fo all beam types is the same as the intensity of the aussian beam, in ou case I 0RTH = I 0R. The divegence of a andom beam is defined the same way as the divegence of the aussian beam. The divegence is the same fo all beam types, TH =. The eceive apetue diamete is much smalle than the beam footpint diamete, D RXA << R. Meeting these conditions assues the applicability of the above pesented conclusion when designing the link. Fig. 8. Angula deflection limits of the aussian beam (dashed line) and the Top Hat beam (solid line) with atmospheic intefeence. The condition of the identical optical intensity I 0R fo both types of beams equies two diffeent tansmitted powes. It is clea fom the optical intensity distibution pofile that the tansmitted powe fo the link using the Top Hat beam has to be geate than the powe fo the link using the aussian beam. This analysis shows that the angula deflection limits bam decease with inceasing distance R. When the angula deflection limits ae geate than the beam divegence, it is moe suitable to use the aussian beam than the Top Hat beam, as the following conditions apply: I = I TH fo the adial distances > D = w, see (9), (13), Fig. 4. Thee is a cetain distance R zv fo wich THam =. The angula deflection limits THam < and THam > fo R < R zv and R > R zv, espectively. In ou case, if atmospheic intefeence o othe factos deceasing the optical powe of the beam ae not taken into consideation, the situation when THam = occus at a distance of appoximately 1800 m. If atmospheic intefeence o any additional attenuation is included in the powe budget calculations, the situation will be diffeent. The powe budget will deteioate, the slope of the gaph fo the angula deflection limits will become steepe and the distance R zv will be shotened, see Fig. 8. That is why, when designing paametes and link featues, the pupose of the beam type should be consideed togethe with its expected distance inteval between stations. Acknowledgements The pape was witten unde the auspices of the Poject Development Depatment of the Univesity of Defense

8 RADIOENINEERIN, VOL. 3, NO. 1, APRIL Poject K06 named Complex Electonic System fo UAS, and suppoted by the association UDeMA (Univesity of Defense MATLAB oup). Refeences [1] WILFERT, O., HENNIE H. An intoduction to fee-space optical communications. Radioengineeing, June 010, vol. 19, no., p [] ČIŽMÁ J., NĚMEČEK, J. Requiements fo contol system of mobile fee space optical link. Advances in Militay Technology, 01, vol. 7, no. 1, p [3] NĚMEČEK, J. Chosen paametes of the statistical model of fee space optical link (in Czech). In Tendy ozvoja vzdusnych sil. Tatanske Zuby (Slovakia), p. [4] KOLKA, Z., WILFERT, O. Statistical model of fee-space optical data link. In Poceedings of the Intenational Symposium on Optical Science and Technology. Denve (USA), 004, p. 03. [5] NĚMEČEK, J., ČIŽMÁ J. Contol system fo positioning of a tansmitte optical beam and a eceive field of view fo a mobile fee space optical link. In Poceedings of 5th Intenational Symposium Advances in Mechatonics (AiM 010). Tencin (Slovakia), 010, p [6] YUKSEL, M., AKELLA, J., KALYANARMAN, S., DUTTA, P. Fee-space-optical mobile ad hoc netwok: Auto-configuable building blocks. Wieless Netwoks. Apil 009, vol. 15, no. 3, p [7] BARCÍK, P., HUDCOVÁ, L., WILFERT, O., ARCE-DIEO, J., FANJUL-VÉLEZ, F., SALAS-ARCÍA, I., ORTEA-QUIJANO, N. Compaison and evaluation of the lase beam - shaping techniques. In SPIE Poceedings Vol Lase Communication and Popagation though the Atmosphee and Oceans II. San Diego, p. [8] FARID, A. A., HRANILOVIC, S. Outage capacity optimization fo fee-space optical links with pointing eos. Jounal of Lightwave Technology, 007, vol. 5, no. 7, p [9] POLIAK, J., PEZZEI, P., LEITEB, E., WILFERT, O. Link budget fo high-speed shot-distance wieless optical link. In Poceedings of the 01 8th Intenational Symposium on Communication Systems, Netwoks & Digital Signal Pocessing (CSNDSP). Poznan (Poland), 01, p [10] SMITH, F.., ACCETTA, J. S., SHUMAKE D. L. The Infaed & Electo-Optical Systems Handbook. Atmospheic Popagation of Radiation. Vol.. Bellingham: SPIE Pess, [11] KHAN, M. S., RABNE M., MUHAMMAD, S. S., AWAN, M. S., LEITEB, E., KVICERA, V., NEBULONI, R. Empiical elations fo optical attenuation pediction fom liquid wate content of fog. Radioengineeing, Septembe 01, vol. 1, no. 3, p About Authos... Jiří NĚMEČEK was bon in Vyškov in In 1984 he gaduated fom the Militay Ai Univesity in Košice. In the same yea he stated to wok as a lectue at the Depatment of Special Equipment at the mentioned college. Fom 1990 to 009 he woked as a lectue at the Militay Academy and the Univesity of Defense in Bno. Nowadays he is a lectue of Special Systems and Amament at the Depatment of Aeospace Electical Systems. In 1993 he eceived the Ph.D. degee in Measuing Technology. His pedagogical wok is focused on the aea of ai sighting systems and ai missiles. His scientific and publication activities ae aimed at poblems of the fee space optical links dependability and potection of the aicaft against the missiles. Jan ČIŽMÁR was bon in Bno in He gaduated fom Antonín Zápotocký Militay Academy in In 1981 he passed though selection pocedue fo a lectue position at Antonín Zápotocký Militay Academy. He has woked at the Univesity of Defense up to this day. In 1991 he eceived the Ph.D. degee in Measuing Technology. In 008 he habilitated as associate pofesso with the thesis Modelling of Inetial Navigation Systems. His pedagogic, scientific and publication activities ae focused into the sphees of measuement of physical values, flight instuments, avionics, oxygen equipment, and ai conditioning systems of the aicaft.