2. COMBAT EXPERIMENTAL SETTINGS

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1 Coparison of turbulence-induced scintillations for ulti-wavelength laser beacons over tactical (7 k) and long (149 k) atospheric propagation paths M. Vorontsov 1, V. S. Rao Gudietla, G. Carhart 3, T. Weyrauch 1, S. Lachinova 4, E. Polnau 1,. Reierson 1, L. Beresnev 3,. Liu 3, and. F. Riker 5 1. University of Dayton, School of Engineering, 300 College Park College Park Center, LOCI, Dayton, OH, U. S. Air Force Research Laboratory, Directed Energy Directorate, Det. 15, 535 Lipoa Parkway, Kehie, Hi U. S. Ary Research Laboratory, 600 Powder Mill Road, Adelphi. MD, Optonicus LLC, 711 E. Monuent Ave. Suite 101, Dayton, OH U. S. Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Ave SE, Kirtland AFB, NM ABSTRACT We report results of the experiental analysis of atospheric effects on laser bea propagation over two distinctive propagation paths: a long-range (149 k) propagation path between Mauna Loa (Island of Hawaii) and Haleakala (Island of Maui) ountains, and a tactical-range (7 k) propagation path between the roof of the Dayton Veterans Adinistration Medical Center (VAMC) and the Intelligent Optics Laboratory (IOL/UD) located on the 5th floor of the University of Dayton College Park Center building. Both testbeds include three laser beacons operating at wavelengths 53 n, 1064 n, and 1550 n and a set of identical optical receiver systes with fast-fraing IR caeras for siultaneous easureents of pupil and focal plane intensity distributions. The results reported here are focused on analysis of intensity scintillations that were siultaneously easured at three wavelengths. Coparison of experiental results shows significant differences in the physics of atospheric turbulence ipact on laser bea propagation over the long- and tactical-range distances. 1. INTRODUCTION In this paper we continue analysis (see ref. [1]) of the experiental data obtained during the Coherent Multi-Bea Atospheric Transceiver (COMBAT) experients perfored in February 010 using a 149 k long nearhorizontal atospheric path between a laser beacon platfor located on Mauna Loa peak and the 3.67 AMOS receiver telescope at the suit of Haleakala in the Hawaii Islands. For coparison of atospheric turbulence ipact on laser bea propagation over considerably different distances, we also included results of ore recent laser bea propagation experients using a 7 k long near-horizontal path. The COMBAT experiental capaign provided a large aount of intensity scintillation data that were obtained by utilizing ulti-wavelength laser beacons. In these experients intensity scintillations were siultaneously easured using three closely (6 c apart) located identical laser beacons that generated truncated (<8% of total energy) Gaussian beas at the following wavelengths: λ 1 = 0.53 μ, λ = 1.06 μ, and λ 3 = 1.55 μ. The COMBAT experiental setting and easureent techniques are described in [1]. After copletion of the longrange experients the COMBAT syste was relocated to the IOL at the University of Dayton and re-assebled using a 7 k propagation path with the beacon platfor located on the roof of the Dayton VA Medical Center (VAMC) and the sensing odules positioned on the 5th floor of the UD College Park Center building. In this paper we copare results of intensity scintillation easureents perfored over the 149 k and the 7 k atospheric propagation paths using identical experiental settings. These two experients are referred to here as long- and tactical-range COMBAT settings or COMBAT/LR and COMBAT/TR.

2 Fig. 1. Elevation profile along the propagation path fro the Mauna Loa NOAA observatory to the AFRL AEOS telescope on Haleakala in the long-range COMBAT experiental setting (left) and snapshot of the 3.67 AEOS receiver telescope (right) taken during the COMBAT/LR experient. The telescope is illuinated by the green (λ 1 = 0.53 μ) laser beacon. The photo provides a rough estiation of the bea footprint of approxiately 10 in diaeter.. COMBAT EXPERIMENTAL SETTINGS The propagation geoetries of both long- and tactical-range COMBAT settings are shown in Figs. 1 and. In the COMBAT/LR setting in Fig. 1 the laser beacon platfor was located on Mauna Loa ountain at elevation h ML = 3397 (11,140 ft), and the receilver telescope at the suit of Haleakala at elevation h H = In the COMBAT/TR setting in Fig. the beacon platfor was located on an optical table inside a shed that was anchored to concrete slabs on the roof of VA edical center building. In both experiental settings, the laser beacon assebly was coprised of three single-ode fiber colliators (each with a clear aperture of 6 ) and the corresponding fiber-coupled laser diodes at wavelengths of λ 1 = 0.53 µ λ = µ and λ 3 = 1.55 µ. For technical reasons only two laser beacons with wavelengths λ 1 = 0.53 µ and λ = µ were used in the COMBAT/TR experients described here. The fiber colliators were ounted together with an aiing telescope in a gibal syste (see Fig. 3) with a sallest angular step size of 1.75 µrad that was used for alignent. After propagation to the receiver site (3.67 AEOS telescope at Haleakala in the COMBAT/LR setting, or 0.35 Schidt-Cassegrain telescope just beyond the IOL window in the COMBAT/TR syste), optical waves fro the Fig.. Graphical representation of the 7 k long atospheric propagation path in the tactical-range COMBAT experiental setting (left) and snapshot of green laser beacon iage taken fro the receiver site at IOL/UD (window on the 5 th floor of the College Park Center building). The beacon platfor was located at elevation 40, while COMBAT/TR optical receiver syste at elevation 15. beacons were received by the telescopes and deagnified by corresponding optical relay systes. The resulting colliated bea of diaeter 10 c (in both COMBAT settings) was subdivided into separate subapertures, each having a usable diaeter of 5, and sent to the receiver odules as shown in Fig. 3 and Fig. 4. Each subaperture corresponds to an area with a diaeter of 91.7 c at the telescope pupil for the long-range and 8.5 c for the tactical-range COMBAT settings. The angular diension of the corresponding receiver subapertures are 6.1 µrad for the COMBAT/LR and 1.1 µrad for the COMBAT/TR settings. Three separate subapertures in the longrange sensing syste and a single sub-aperture in the tactical-range setting were used to record pupil-plane and focal-plane irradiance distributions of the received beas as shown in Fig. 3. Narrow bandpass filters were used to dedicate each receiver odule to a specific wave fro a single beacon. In this paper we discuss only easureents of the pupil-plane intensity distributions, which were recorded using three Sensors Unliited (SU640SDWHvis) 14-

3 Fig. 3. Conceptual scheatics of the long-range (left) and tactical range (right) COMBAT experiental settings. The identical beacon assebly (shown at left upper corner) and the pupil and focal plane sensing odules (shown at right) were used in both COMBAT systes. The adaptive optics and 1550 n sensing odules in the COMBAT/TR syste were not included in the experients described. bit caeras. The caeras were operating in a windowed ode with a 5656 pixel window with pixel size of 55 μ, providing an actual sensor area of and a 100% fill factor. A four-to-one bea reducer was installed in the optical train of each subaperture to atch the bea (pupil) size with the active window size. 3. MEASUREMENTS AND RESULTS 3.1 Short-exposure Intensity Scintillation Patterns. Characteristic snapshots of the received light pupil-plane intensity distributions for beacons with different wavelengths easured in both COMBAT experients are illustrated in Fig. Error! Reference source not found.. The iages show that the spatial scale of intensity scintillations is strongly dependent on the wavelength, i.e., the longer the wavelength the larger the atospheric effects induced intensity speckles. This observation is consistent with the theoretical findings and was also confired by our nuerical siulations. At the sae tie intensity scintillation patterns for the long-range (first Fig. 4. Characteristic exaples of the short-exposure intensity scintillation patterns recorded during the long-range (three photos fro left to right) and tactical-range (two photos at right) COMBAT experients. The bean wavelength is identified by color of sall circles at left upper corner of each photograph: green circle corresponds to λ 1 = 0.53 µ, red to λ = µ and blue to λ 3 = 1.55 µ. three iages at right) and the tactical-range propagation distances are profoundly different despite the fact that in both cases the ratios of the bea footprint (for λ 1 = 0.53 μ) to receiver aperture diaeter were nearly equal in both experiental settings. These ratios are 10.9 for COMBAT/LR and 10.6 for COMBAT/TR. The characteristic speckle size in the intensity iages for λ 1 = 0.53 μ in Fig. 4 are 5-10 for 149 k and 17-0 for 7 k propagation distances. 3. Received Power Fluctuations and Giant Spikes. Consider characteristic exaples of teporal dynaics of the received light power easured inside the 91.7 c aperture for the long-range and 8.5 c aperture for the tactical-range COMBAT settings. The power fluctuations data were siultaneously recorded for three beacons in the long-range and for two (for λ 1 = 0.53 μ and for λ = 1.06 μ) beacons in tactical-range experients. The

4 dependencies of the noralized power Pn ˆ( ) on the consequent short-exposure pupil-plane frae nuber n are shown in Fig. 5 for the long-range and in Fig. 6 for the tactical-range experients. In both cases the received power was noralized by the axiu value corresponding to each experient. As can be seen fro these figures, dynaics of receiver power fluctuations are quite different for 149 k and 7 k propagation paths. The long-range propagation results in appearance of large spikes in the received power that were absent in the experients perfored over the tactical-range distance. These giant spikes, each lasting for only a few illiseconds, result in up to ten-fold increase in received power. Note that in the experients in Fig. 5 the aplitude of spikes appeared to be significantly higher for λ 1 = 0.53 μ. At the sae tie in a different set of experients the largest aplitude of the spikes were observed at different wavelengths. For exaple Fig. 7 shows results of a different set of experients with the largest aplitude spikes observed at λ 3 = 1.55 μ. The giant spikes appeared quite randoly with a characteristic delay tie of the order of a few seconds. This tie scale can be associated with changes occurring in coherent atospheric structures and/or with the dynaics of stable (refractive) and unstable (turbulent) layers aligned with the Earth curvature that the beacon beas propagate through. On the other hand, the extreely Fig. 5. Characteristic teporal dynaics of received optical power fluctuations P ˆ Pn ax n Pn for laser beacons with wavelengths λ 1 = 0.53 μ (top), λ = 1.06 μ (iddle), and λ 3 = 1.55 μ (botto) obtained in the long-range experients. All three sequences of short-exposure fraes with s integration tie and frae rate 00 f/sec were captured siultaneously. short duration (on the order of 5-0 s) of spikes cannot be directly associated with atospheric processes that occur over a significantly longer tie scale. As a possible physical explanation for the foration of these giant spikes, we consider the trapping of the beacon bea inside a relatively narrow stratified layer of air with sharp changes of refractive index at its boundaries. Such a layer can act as a wave-guide siilar to the way an optical fiber acts with respect to an optical bea with wavelength atched to the fiber core size. This waveguiding effect is extreely sensitive to the wavelength of the propagating bea and the coupling angle and can be destroyed with sall variation of the stratified layer geoetry or of the angle of optical wave incidence. These sall variations can indeed occur at a tie scale of the duration of the observed spikes. Fig. 6. Characteristic teporal dynaics of received optical power fluctuations P ˆ Pn ax n Pn for laser beacons with wavelengths λ 1 = 0.53 μ (top) and λ = 1.06 μ (botto) obtained in the tactical-range experients. Sequences of 6000 short-exposure fraes with s integration tie and frae rate 00 fr/sec were captured siultaneously.

5 Fig. 7. Exaple of the received power fluctuation dynaics over 149 k propagation path (siilar to as shown in Fig. 5) with strongest received power spikes at λ 3 = 1.55 μ (left), and the corresponding evolution of the aperture-average scintillation indices ( n) (solid lines) and ( n) for n W = 000 (dashed lines). ns Scintillation Index Dynaics. For analysis of teporal dynaics of the pupil-plane intensity scintillations consider coputation of the noralized variance of intensity fluctuations at each pixel of the photo-array within the receiver aperture area, 1 I ( r ) I ( r ) I ( r ) ( r ), (1) n1 n where r is the transverse coordinate vector defining the th pixel in the plane of the photo-array, { I n ( r ) } (n=1,,n) is the set of N short-exposure pupil-plane intensity distributions that are recorded with frae rate 00 fr/sec, and 1 n n1 WS I ( r ) I ( r ) is an intensity distribution obtained by averaging of subsequent fraes (tieaverage iage). Note that averaging over the set of =N fraes in Eq. (1) is equivalent to tie averaging over nearly 50 seconds. The noralized variance (1) is referred to as the scintillation index. By averaging ( r ) over all pixels inside the receiver aperture area we obtain the aperture-average scintillation index ( r, S ) S where < > S defines averaging over receiver aperture or space averaging. In order to evaluate whether the observed intensity scintillations can be considered as a stationary rando process, consider teporal dynaics of the scintillation index by using either increasing nuber =n of subsequent fraes ns ( n ) or oving (window) averaging of =n sequential fraes WS ( nn, W ), where n W is a nuber of fraes in the selected averaging window. Both ns ( n ) and WS ( n ) dependencies are shown in Fig. 7; the values NS are given inside the corresponding plots.

6 Fig. 8. Characteristic exaples of teporal power spectra for pupil-plane intensity scintillations easured in the long-range COMBAT experients for four different experiental trials. In each plot the spectra correspond to intensity scintillations siultaneously easured at three different wavelengths (λ 1 = 0.53 μ, λ = 1.06 μ, and λ 3 = 1.55 μ). The data were taken on 0/13/10 at 7:30p (top left), and at 10:30p (top right), and on 0/16/10 at 9:51p (botto left), and on 0/17/10 at 9:05p local tie. For convenience of coparison with the teporal power spectru of intensity fluctuations derived fro the Kologorov theory the characteristic -8/3 slope of this spectru as well as -5/3 slope observed in ref [] are shown by the corresponding straight lines. The frequency is noralized by 1.0 Hz. The dependences ns ( n ) and WS ( n ) characterize teporal changes of the aperture-average scintillation index occurring during the tie of easureents trial. The scintillation index plots clearly indicate the statistical nonstationary character of the intensity scintillation process and strong ipact of spikes in the received power. The appearance of the giant spikes results in rapid increases in the scintillation index WS ( nn, W ) that akes the scintillation process highly non-stationary. In Fig. 7 this effect is ore pronounced for the set of data obtained at λ 3 = 1.55 μ. The giant spikes also contribute to non-ergodicity of intensity scintillations. The assuption of ergodicity of the intensity scintillation statistical process can be challenged by coparing values of the scintillation indexes NS and SN that are obtained by changing the order of spatial and teporal averaging in the sae experiental trial. Coparison of the corresponding values NS and SN shows that these values are quite different which akes questionable the applicability of the ergodic hypothesis [3,4]. 3.4 Teporal Spectru of Intensity Scintillations. Consider exaples of a teporal power spectru of the pupil-plane intensity fluctuations which are obtained using coputer processing of the COMBAT experiental data. The aperture-average spectral density of intensity fluctuations S() was defined as M S si (, r ) / si ( 0, ) 1 S( ) r M S 1, () where si (, r ) is a rando realization of a teporal power spectru corresponding to the th pixel of the photoarray, and M S the nuber of pixels used for the power spectru coputations. For each th pixel, teporal spectra si (, r ) were calculated by taking digital Fourier transfors of the set of N=10000 intensity values I n ( r ), where n=1,, N. Note that the photo-array pixel corresponded to a area of the receiver aperture in the longrange and 0.3x0.3 in the tactical-range COMBAT settings. To reduce coputational tie in each of N

7 149 k, λ = 0.53 µ 149 k, λ = 1.06 µ -5/3-5/3-8/3-8/3 λ 7 k = 0.53 λ = 0.53 µ µ -5/3-8/3 Fig. 9. Suary of pupil-plane intensity scintillations teporal power spectra analysis for long-range (top) and tactical-range (botto) experients. The calculated fro the experiental data exponents in the approxiating spectru power-low for different experiental trials and the exaple of the power spectra for 7 k propagation path (botto left) corresponding to the experiental trial indicated by arrow. processed fraes only M S = 1000 intensity values were used. The pixels r, =1,, M S, selected for coputation of si (, r ) were those foring a grid with 10 pixel spacing that was centered on and covers the receiver aperture. Four exaples of the teporal power spectra obtained using COMBAT long-range data are show in Fig. 8. As can be seen fro these exaples the spectral functions S () were changing considerably fro one to another experiental data collection trial. Also note that these experiental spectra are quite different fro the corresponding teporal power spectru functions that are derived fro the Kologorov turbulence theory and Taylor s frozen turbulence hypothesis [3,5]. These theory-based teporal power spectru functions are essentially 1/ 8 / 3 unchanged within the low-frequency band for 0 0.5V /( L) and decay as for higher frequencies [5]. Here V is a transversal coponent of wind velocity. The teporal power spectru curves in Fig. 8 (except the plots at botto right) decay with a nearly constant, and significantly different than -8/3, exponent in the approxiating spectru power-law within the entire frequency band. The exponents in the power-law approxiations of the experiental teporal power spectra obtained for several COMBAT/LR experiental trials are suarized in Fig. 9 for λ 1 = 0.53 μ and λ = 1.06 μ wavelengths. As can be seen fro the data presented 1 in Fig. 9 in ost experiental trials the teporal power spectra can be approxiated as for both wavelengths. These results present significant deviation fro the existing predictive odels. Exaples of intensity fluctuation power spectru obtained for the tactical-range distance and the values of exponent for eight different set of easureents are correspondingly shown in botto left and right plots in Fig. 9. Note that in this case within the low-frequency band ( 0 30 Hz) the power spectru is nearly constant and decays with exponent = -. at higher frequencies as theory predicts. This shape of the power spectru is consistent with the theoretical prediction although the decay exponent is slightly larger than -8/3. In all tactical range experiental trails we observed shapes of spectra siilar to Fig. 9 (botto left) having decay paraeters ranging between -.5 and -1 as shown in Fig. 9 (botto right). This deviation fro theoretical (plane wave) 8 / 3

8 approxiation is ost likely related with violation of Taylor s frozen turbulence hypothesis that assues constant wind velocity along the entire propagation path. 4. SUMMARY To optially design, build, and understand the perforance of the new generation of long-range optical systes requires analysis of optical wave propagation along various atospheric paths that ay cross several extended (deep) regions of atosphere with quite distinctive spatial structures and teporal dynaics, and quite likely, developent of techniques to itigate these effects. This analysis is currently perfored using a fraework of the classical fully developed Kologorov-Obukhov optical turbulence theory [6,7]. In this theory the atosphere is described by three diensional boundless, statistically hoogeneous and isotropic rando fields of refractive index fluctuations (atospheric eddies). In this idealization, the ipact of boundary conditions iposed by terrain, and hydro-therodynaic processes in the atosphere is assued to be forgotten due to a cascade of energy transfer fro larger to saller scale eddies the process that rationalizes the Kologorov s assuption of statistical isotropy of fully developed turbulence. In reality, these ideal hoogeneity and isotropy conditions do not exist at large scales, as they are destroyed by gravity and solar radiation induced buoyancy and friction forces that lead to foration of distinct nearly horizontally aligned atospheric layers [8,9]. These atospheric effects can severely ipact optical wave propagation over long distances. The results of the atospheric characterization experients over long- (149-k) and relatively short (7-k) paths presented allow direct coparison of atospheric effects induced scintillations of laser bea intensity for different wavelengths. They also clearly show difficulties in interpretations of the observed long-range phenoena based solely on the classical Kologorov optical turbulence theory. As a path forward we can point out several future research and developent directions towards better understanding physics of laser bea propagation along longdistances, including: 1. Research focused on erging statistical (Kologorov turbulence based) and deterinistic coputational fluid dynaics approaches, cobined with wave optics odeling of optical wave propagation over atospheric paths.. Developent of atheatical and coputational techniques for predictive odeling of optical wave propagation in highly anisotropic turbulence layers. 3. Developent of theoretical fraework nuerical siulation tools that erge refractive and diffractive optics approaches. 4. Engineering of unconventional optical fields (laser beas) and optical syste architectures which are less sensitive to atospheric distortions over long propagation paths. 5. Developent of unconventional adaptive bea control techniques. We also believe that ore long-range atospheric optical propagation experients are needed to directly associate the observed anoalies in laser bea and iage characteristics with eteorological data and the results of highperforance coputing of atospheric dynaics. 5. ACKNOWLEDGEMENTS This project was supported through the Cooperative Agreeents between the US Ary Research Laboratory and both the University of Dayton and Optonicus LLC. 6. REFERENCES [1] M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudietla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev,. Liu, K. Rehder, and. F. Riker, Characterization of atospheric turbulence effects over 149 k propagation path using ulti-wavelength laser beacons, in Proceedings of the 010 AMOS Conference, S. Ryan, ed., p. E18 (010). [] V.V. Nosov, V.P. Lukin, E.V. Nosov, A.V. Torgaev, V.M. Grigoriev, P.G. Kovadlo, Coherent structures in the turbulent atosphere, Matheatical Models of Non-linear Phenoena, Processes and Systes: Fro Molecular Scale to Planetary Atosphere. By ed. A. Nadykto et al. - N.Y.: Nova Science Publishers, Chapter 0, (010).

9 [3] V. I. Tatarskii, Wave Propagation in a Turbulent Mediu, ser. McGraw-Hill Series in Electrical Engineering. New York: McGraw-Hill, (1961). [4] A. Ishiaru, Wave Propagation and Scattering in Rando Media. New York: Acadeic Press, (1978). [5] L. C. Andrews and R. L. Phillips, Laser Bea Propagation through Rando Media, SPIE, (1998). [6] A. N. Kologorov, The local structure of turbulence in incopressible viscous fluid for very large Reynolds nubers, Dokl. Akad. Nauk SSSR, vol. 30, no. 4, pp , 1941, [English translation in Turbulence: Classic Papers on Statistical Theory (ed. S. K. Friedlander and L. Topper), p. 151, Interscience, NY, (1961). [7] A. M. Obukhov, On the distribution of energy in the spectru of turbulent flow, Dokl. Akad. Nauk SSSR, vol. 3, no. 1, p., (1941). [8] S. Lovejoy, A. F. Tuck, S.. Hovde, and D. Schertzer, Do stable atospheric layers exist? Geophysical Research Letters, vol. 35, L0180, (008). [9] S. Lovejoy, A. F. Tuck, S.. Hovde, and D. Schertzer, Is isotropic turbulence relevant in the atosphere? Geophysical Research Letters, Vol.. 34, L1580, ( 007).