Propagation Channel Characterization: Impact on Optical Systems Performance Marie-Thérèse Velluet, Clélia Robert, Nicolas Védrenne ONERA, The French Aerospatial Lab, 92322 Chatillon Cedex FRANCE marie-therese.velluet@onera.fr, clelia.robert@onera.fr, nicolas.vedrenne@onera.fr ABSTRACT High performance optical systems suffer from atmospheric turbulence effects near the ground, limiting their range and resolution. Analytical and numerical models have been developed to evaluate the degradation induced by atmospheric turbulence on such optical systems, as a loss of resolution for a specific range or the impairment of high rate optical link because of intensity fluctuations. These models require a sufficient knowledge of the turbulence (including wind speed when temporal study is necessary) along the line of sight. Physically, turbulence near the ground depends strongly on many variables, such as sunlight, wind, soil nature, humidity of the air, air and soil temperatures This leads to a large spatial as well as temporal variability of turbulence conditions and lead to a varying impact and degradation level on the system performance. We present here instrumental approaches to evaluate the turbulence strength in relation with the performance requirements. Finally, a better knowledge of turbulence impact can help to optimize turbulence mitigation techniques including optimization of the optical design. We will give an overview of the main mitigation techniques and their limitations in the context of tactical applications. 1.0 INTRODUCTION Through turbulence, electro-optics (EO) and laser systems are no more diffraction limited but turbulence limited. That is particularly noticeable for near-ground applications (horizontal or slant paths) where turbulence strength is high and propagation distances are often larger than a few kilometers. For example, the impacts of atmospheric turbulence are: image blurring and dancing under hot desert conditions in high resolution visible/infrared (IR) imaging (Figure 1, experimental images), angle of arrival and intensity fluctuations of a laser beam after propagation through atmospheric turbulence (Figure 2, numerical data). Figure 1: Instantaneous visible images of a checkboard for two different turbulence conditions, range 7 km. Left C n 2 10-16 m -2/3, integration time 8 ms, right C n 2 10-15 m -2/3, integration time 10 ms. STO-MP-SET-241 11B-1-1
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Propagation Channel Characterization: C n 2, expressed in m -2/3. Atmospheric turbulence is a dynamic phenomenon with temporal evolution of a few ms. The strength of turbulence depends on many parameters like the time (sunset or sunshine, day or night), the season, the location, the nature of the soil... (see Figure 6, variation of C n 2 between some 10-16 m -2/3 to some 10-12 m -2/3 during the day, with a maximum around noon). Besides, in case of long propagation distances, the turbulence profile is not necessarily homogenous along the path and the impact on the image quality or laser beam delivery could be completely different than theoretically expected for a constant C n 2 along the path. C n 2 strength decreases with the altitude. The well-known Hufnagel-Valley profile is most commonly used as vertical C n 2 profile, with a power law of -4/3 or -2/3 in the atmospheric boundary layer for daytime and night-time respectively. Figure 6: Evolution of the turbulence strength, C n 2 expressed in m -1/3, left measurement done over several days of July at 1.5 m above the ground level at Observatoire de la Côte d Azur (OCA); right standard vertical profiles. The spatial statistics of refractive index fluctuations were first derived by Kolmogorov [5]. In the weak turbulence regime, formalism based on the Kolmogorov turbulence and the Rytov approximation can be applied to describe most of the optical phenomena related to the turbulence effect on propagation of optical waves in the atmosphere [6]. For stronger turbulence (for example propagation near the ground over horizontal and slant propagation paths) characterized by strong scintillations, the classical atmospheric turbulence models may not be sufficient to describe and correctly predict optical turbulence effects [7]. To overcome these difficulties, heuristic and statistical models [8] [9] were developed in the framework of laser beam propagation but their application is also limited as well as the numerical (Monte Carlo based) computer simulations that utilize a phase screen (split operator) approach [3] called also wave optics simulation. All the models described above depend on the C n 2 and wind profiles. To evaluate system performance or develop method to compensate for turbulence effect, the knowledge of these profiles is crucial. At Onera, we have developed an instrument working in infrared (IR) (3-5 µm). It is composed of a Shack- Hartmann wavefront sensor (WFS), with 5*5 microlens array and which acquires images of two point-like sources at a frame rate of 400 Hz (see [10] for the description of the WFS, [11]for the measurement principle and [12] for measurement illustrations). The slope and intensity auto and intercorrelation are used to provide by inverse problem an estimation of the profile. A trial was conducted in Lannemezan (France), we can see in Figure 7 the evolution of C n 2 during the day and also the non-homogeneity of its value along the path. Moreover, the relative amplitude of the evolution of each layer is different with its position. It reveals the inhomogeneity of the soil nature below the line of sight. 11B-1-6 STO-MP-SET-241
Propagation Channel Characterization: Figure 7: Mean C n 2 profiles averaged over 10 minutes (red) and their standard deviations (blue). Variation during the afternoon, evening (upper graphs), night, morning (lower graphs) on consecutive and sunny dates. In the context of optical links study between space and ground, Onera has implemented an Adaptive Optics (OA) bench at the foyer-coudé of the telescope Meo at OCA. The data recorded by the Shack-Hartmann WFS (8*8 sub-apertures, working in the visible spectral bandwidth) at a frame rate higher than 1 khz were analysed to characterize the propagation channel. Both phase perturbations and intensity fluctuations were considered. The works are presented in [13] and an illustration of the characterization of turbulence profile is shown in Figure 9. The C n 2 profile estimated from WFS data analysis is plotted and compared with a typical Hufnagel-Valley (H-V) model. The C n 2 at ground level of the H-V model is adapted so that the two profiles present the same Fried parameter (here, 10 cm along the line of sight at λ = 976 nm). The spectrum of the intensity fluctuation derived from the shack-hartman WFS data is compared with the analytical expression considering the estimated C n 2 profile and wind speed profile induced by the satellite velocity. The agreement is excellent. STO-MP-SET-241 11B-1-7
Propagation Channel Characterization: Figure 8: left: C n 2 profiles estimated from the Shack-Hartman WFS data and right: comparison of temporal spectra of data with its analytical expression taken into account this C n 2 profile. 3.0 MITIGATION TECHNIQUES Various techniques can be implemented to mitigate the turbulence effects, such as AO systems (hardware) or image processing techniques (software). In the context of tactical applications (line of sight close to the ground), anisoplanatism and strong scintillation are the most important issues. Because of a reduced isoplanatism domain (of the order of the pixel size or even smaller), AO technique is not well adapted to compensate for image distortion and blur, image processing techniques are more appropriate. Their complexity increases with the turbulence strength but they are for the moment limited to weak and moderate turbulence regimes. However, for a slant path, in the context of ground-to-air observation application, adaptive optics system have been implemented and tested by Onera (INCA experiment). These experiments took place between Canjuers military camp (1000 m height) and Mont Lachens (1700 m height) in summer and autumn 2008 (France). The distance between both locations is 11 km. Enhancement of the image quality can be observed; better contrast and observation of thinner details (see Figure 9). But it is limited because of the anisoplanatism. For this experiment we have developed algorithm to use shack-hartman WFS on extended scene [14]. The measure was done on a part of the scene, the upper antenna. Figure 9: Upgrade in resolution brought by AO on an extended source (telecom tower) located on the top of the Mount Lachens. Left the AO system is off, right it is on. 11B-1-8 STO-MP-SET-241
Propagation Channel Characterization: Adaptive optics techniques can be used to improve laser beam delivery, focusing. Moreover, in strong turbulence regime, phase and amplitude must be pre-compensated (see [15] as an example in the context of free space optical telecommunication applications). In weak scintillation scenarios, conventional adaptive optics systems used in astronomy and consisting of a deformable mirror and a wavefront sensor (e.g. Shack- Hartmann sensor, curvature sensor, shearing interferometer sensor) can be transferred to laser system applications. As the turbulence increases, phase branch points and scintillation make phase measurements difficult or impossible with conventional WFS. New WFS, robust to scintillation must be developed. Holographic sensors are studied for this specific case [16]. Sensorless adaptive optics are also proposed to overcome this issue, they are based on the optimization of a metric as maximum power or contrast in an image. Experimental demonstration of this concept was performed and compare to conventional one. They can operate in stronger turbulence regime [17]. 4.0 CONCLUSIONS Atmospheric turbulence and their impact on EO and laser systems performance had been presented through some illustrations: reduction of the range, distortion and blur of the image, intensity fluctuations (scintillations) for laser beam delivery. It limits their resolution and range. Simplified models are developed to provide system parameters for performance assessment and system optimization. One major issue is the knowledge of the turbulence volume between the source and the receiver. An instrument has been developed and used to measure turbulence profile. Mitigation techniques can be proposed but their capabilities depend on the turbulence strength and its distribution along the line of sight. Further works on these two last subjects are ongoing. 5.0 REFERENCES [1] Conan J.-M., Rousset G., and Madec P.-Y., "Wave-front temporal spectra in high-resolution imaging through turbulence," J. Opt. Soc. Am. A 12, 1559-1570 (1995). 1 [2] Robert C., Conan J.-M., Michau V., Renard J., Robert C., and Dalaudier F., "Retrieving parameters of the anisotropic refractive index fluctuations spectrum in the stratosphere from balloon-borne observations of stellar scintillation," J. Opt. Soc. Am. A 25, 379-393 (2008). 2 [3] Martin J., and Flatté S., "Intensity images and statistics from numerical simulation of wave propagation in 3-D random media," Appl. Opt. 27, 2111-2126. 3 [4] Fried, D. L. (1966). Optical resolution through a randomly inhomogeneous medium for very long and very short exposures. JOSA, 56(10), 1372-1379. 4 [5] A.N. Kolmogorov, C.R. Acad. Sci. URSS 30, 301 305 (1941) -5 [6] Tatarski V. I., Wave propagation in a Turbulent Medium, McGraw-Hill Book Company, New York, (1961). -6 [7] Brown, JR W. P.., "Validity of the Rytov Approximation," J. Opt. Soc. Am. 57, 1539-1542 (1967). -7 [8] Fante, R. L., "Electromagnetic beam propagation in turbulent media," Proceedings of the IEEE, vol.63, no.12, pp. 1669-1692, (1975). _8 [9] Andrews L. C., and Philipps R. L., Laser Beam Propagation through Random Media, 2nd ed. SPIE Optical Engineering Press, Bellingham, (2005).-9 STO-MP-SET-241 11B-1-9
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