Evaluation of turbulent parameters based on angle-of-arrival fluctuation Yang LI 1,Chao GAO 2, Yi-Ming LI 2, Gang YANG 2 & Xiao-Feng LI 2

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1 Iteratioal Coferece o Iformatio Techology ad Maagemet Iovatio (ICITMI 15) Evaluatio of turbulet parameters based o agle-of-arrival fluctuatio Yag LI 1,Chao GAO, Yi-Mig LI, Gag YANG & Xiao-Feg LI 1 Accoutig School, Southwester Uiversity of Fiace ad Ecoomics, Chegdu, Chia School of Astroautics ad Aeroautic, Uiversity of Electroic Sciece ad Techology of Chia, Chegdu, Chia KEYWORD: laser propagatio i the atmosphere, agle-of-arrival fluctuatio, correlatio model for evaluatio, comprehesive performace of trasmissio characteristics ABSTRACT: This paper ivestigates the feasibility of adoptig sigle quatified parameter of atmospheric turbulece effect to evaluate others. To erich ad expad the test method o the trasmissio characteristics of atmospheric turbulece, this method could greatly reduce both the workload ad costs of sythetic tests o the laser trasmissio characteristics, which has very positive ad importat sigificaces for applicatios of space optical commuicatio. The correlatio models amog the quatified parameters of atmospheric turbulece effects is deduced. The experimetal results idicates that the agle-of-arrival fluctuatio is related to other atmospheric turbulece effects based o the theory of Kolmogorov turbulece. Thus, other quatified parameters of atmospheric turbulece effects could be evaluated via acquired data of agle-of-arrival fluctuatio. INTRODUCTION The characteristics of laser propagatio through the turbulet atmosphere has bee attractig icreasig attetios i the field of quatitative aalyses for suspeded particles. Based o the large amout of statistical data collected from actual eviromet i log term, the mathematical models could be built to direct the developmet of istrumetatios for atmospheric pollutio testig (Adrews 5, Rao 5). The tests for the characteristics of laser propagatio usually last for 4 hours a day, ad 7 days a week without itermissio. For accuracy, the sample data for further aalyses should be collected i similar coditios, ad the umber of samples should be greater tha or equal to te. Curretly, the Chia govermet has bee buildig may localized testig sites for atmospheric pollutio i large-scale. The test work i some testig sites has accumulated a large umber of data. The followig work should be coducted for estimatig the characteristics of laser propagatio based o collected data ad thus estimatig the degree of atmospheric pollutio. 1) Accomplish the correlatio aalyses for the testig data i the same area. Build the estimatio models for the characteristics of laser propagatio. The models should be validated ad optimized. ) Accomplish the correlatio aalyses for the testig data i differet areas. Build the estimatio models for the characteristics of laser propagatio, which have more applicability. Both the work are still i the iitial stage. The comprehesive characteristics of laser propagatio iclude atmospheric atteuatio, atmospheric turbulece, ad meteorology. There are at least twelve importat parameters i total. To test these parameters simultaeously will lead to huge workload ad also make the aalyses may ad miscellaeous with trifles. To reduce the workload of tests for the characteristics of laser propagatio, a alterative approach is to use the statistics ad the ecoometrics. Based o the relatioships amog the parameters for the characteristics of laser propagatio, some certai parameters could be estimated by a few other parameters. Udoubtedly, this method could largely cut the costs for testig, ad promote the developmet of istrumetatios for atmospheric pollutio testig. CORRELATION MODELSFOR CHARACTERISTICS OF LASER PROPAGATION The stochastic fluctuatio of the atmospheric refractivity would lead to the variatio of optical phase of laser propagatio through the turbulet atmosphere. The commo turbulece effects iclude agle-of-arrival fluctuatio, irradiace scitillatio, beam wader, ad beam spreadig (Toselli 9, Gudimetla 14). 15. The authors - Published by Atlatis Press 85

2 Agle-of-arrival fluctuatios of a optical wave i the plae of the receive aperture are associated with image jitter i the focal plae of a imagig system. Fluctuatios i received irradiace resultig from propagatio through atmospheric turbulece is commoly described as scitillatio, which icludes the temporal variatio i received irradiace ad spatial variatio withi a receiver aperture. I the presece of optical turbulece, a fiite optical beam will experiece radom deflectios as it propagates, causig further spreadig of the beam by large-scale ihomogeeity of the atmosphere, ad the istataeous ceter of the beam is therefore radomly displaced i the receiver plae, producig what is commoly called beam wader. Beam spreadig at the receiver plae ca be modeled as if it arises from a radom tilt agle at the trasmitter plae, similar to agle-of-arrival fluctuatios of a reciprocal propagatig wave with the receiver diameter replaced by the trasmitter beam diameter (Cui 15). Accordig to the Kolmogorov spectrum, the theoretical models of the four turbulece effects for the plae wave are give below (Kolmogorov 1991). 1) Agle-of-arrival fluctuatio: 13 α =.9CD L (1) ) Irradiace scitillatio: I = 1.3Ck L () 3) Beam wader: 13 3 r =.97CD L (3) 4) Beam spreadig: ( ) W =.13D C k L (4) where C is the atmospheric structure costat of refractive idex, D is the optical atea aperture, L is the propagatio optical path legth, k = π λ is the agular wave-umber, λ is the wavelegth. Accordig to these theoretical models, agle-of-arrival fluctuatio, irradiace scitillatio, beam wader, ad beam spreadig are associated with each other turbulece effects by the atmospheric structure costat of refractive idex. O the coditio of fixed de-siged parameters for certai optical commuicatio system, it is possible to estimate oe turbulece effect by other turbulece effect. Based o Equatio 1-4, the correlatio models betwee agle-of-arrival fluctuatio ad other turbulece effects are deduced below. 1) Irradiace scitillatio: I =.4D k L α (5) ) Beam wader: r =.33L α (6) 3) Beam spreadig: ( ) W =.13D D k L α (7) COLLECTED DATA OF THE CHARACTERISTICS OF LASER PROPAGATION The laboratory of space optical commuicatio techology i Uiversity of Electroic Sciece ad Techology of Chia (UESTC) has bee coductig the testig of the characteristics of laser propagatio sice 11. The testig chael locates ear the Qigshuihe Campus of UESTC, which is i the suburb of Chegdu. The legth of testig chael is.7km, ad the wavelegth is 83m. The tests last for 4 hours a day, ad 7 days a week without itermissio. The collectio ad storage of geerated data are full automatic. This paper use the data collected from 6 a.m. to 8 a.m. o March, April, ad May (9 days i total) of 13 year. There are approximate 18 samples for each turbulece effect, which satisfies the requiremets for statistical aalyses. The weather of Chegdu betwee March ad May is relative stability, ad the chael betwee 6: ad 8: is relatively good. O this ote, those samples used i this paper have litter sigular 86

3 values, ad the aalytical results could be beeficial to the estimatio of the characteristics of laser propagatio i other areas. Figure 1-4 depicts the collected data of agle-of-arrival fluctuatio, irradiace scitillatio, beam wader, ad beam spreadig from 6 a.m. to 8 a.m. o March, April, ad May of 13 year i Chegdu. 5 x α 1 Figure 1.Collected data of agle-of-arrival fluctuatio I.5 Figure. Collected data of irradiace scitillatio. 87

4 1.5 x r.5 Figure 3. Collected data of beam wader. COMPARISON OF ESTIMATED VALUES AND COLLECTED DATA Based o the correlatio models betwee the agle-of-arrival fluctuatio ad other turbulece effects deduced i Equatio 5-7, the curves of irradiace scitillatio, beam wader, ad beam spreadig are computed, followed by the compariso of estimated values ad collected data as show i Figure 5-7. We use the actual optical parameters of testig equipmet for the calculatios of the correlatio models. The legth of testig chael L is.7km, the wavelegth λ is 83m, ad the optical atea aperture D is.6m..3. W.1 Figure 4. Collected data of beam spreadig. 88

5 .15 Collected Data Estimated Values.1 I.5 Figure 5. Compariso of estimated values ad collected data of irradiace scitillatio. Table 1. Estimatig Errors of Correlatio Models based o Agle-of-Arrival Fluctuatio absolute errors relative errors I 8.546e % r 9.719e-7 16.% W.85e % The results idicate that the estimated values match collected data. Further ivestigatios ivolve the errors about the correlatio models, as show i Table 1. The absolute ad relative errors of irradiace scitillatio are 8.546e-3 ad 19.13%, respectively. The absolute ad relative errors of beam wader are 9.719e-7 ad16.%, respectively. The absolute ad relative errors of beam spreadig are.85e-3 ad17.6%, respectively. 1.5 x 1-5 Collected Data Estimated Values 1 r.5 Figure 6. Compariso of estimated values ad collected data of irradiace scitillatio. 89

6 .3 Collected Data Estimated Values. W.1 Figure 7. Compariso of estimated values ad collected data of irradiace scitillatio. The stochastic fluctuatio of atmospheric refractivity will lead to the stochastic fluctuatio of wave frot phase whe propagatio. Based o the Kolmogorov spectrum, there are certai relevacies betwee the agle-of-arrival fluctuatio ad other turbulece effects. It is available to estimate other turbulece effects for further aalyses by collectig the data of agle-of-arrival fluctuatio. CONCLUSION This paper adopts the collected data of agle-of-arrival fluctuatio to evaluate other turbulece effects such as irradiace scitillatio, beam wader, ad beam spreadig. This method could erich ad expad the testig method o the trasmissio characteristics of atmospheric turbulece. Based o the correlatio models ad the actual optical parameters of testig equipmet, the relative errors of estimated values for irradiace scitillatio, beam wader, ad beam spreadig are smaller tha %. It must be poited that the collected data of agle-of-arrival fluctuatio is relevat to the actual parameters of testig equipmet, o which the quatitative aalyses are based. Nevertheless, the method proposed i the paper is ot limited to the actual parameters of testig equipmet. REFERENCES [1] Adrews, L.C. 5. Laser Beam Propagatio through Radom Media, d. Belligham: SPIE Press Moograph. [] Cui, L. 15. Aalysis of marie atmospheric turbulece effects o ifrared imagig system by agle of arrival fluctuatios. Ifrared Physics ad Techology 68(1): [3] Gudimetla, V.S.R, Holmes, R.B., &Riker, J.F. 14. Aalytical expressios for the logamplitude correlatio fuctio for spherical wave propagatio through aisotropic o- Kolmogorov atmosphere. Joural of the Optical Society of America A: Optics, Image Sciece, ad Visio 31(1): [4] Kolmogorov, A.N The local structure of turbulece i icompressible viscous fluid for very large Reyolds umbers. Proceedigs of the Royal Society A 434(189): [5] Rao, R. 5. Light Propagatio i the Turbulet Atmosphere. Hefei: Ahui Sciece ad Techology Press. [6] Toselli. I., Adrews, L.C., Phillips, R.L., &Ferrero, V. 9. Free space optical system performace for a Gaussia beam propagatig through o-kolmogorov weak turbulece. IEEE Trasactios o Ateas ad Propagatio 57(6):

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