Strong Optical Turbulence Research Articles

Neural network classification of beams carrying orbital angular momentum after propagating through controlled experimentally generated optical turbulence

We generate an alphabet of spatially multiplexed Laguerre–Gaussian beams carrying orbital angular momentum, which are demultiplexed at reception by a convolutional neural network (CNN). In this investigation, a methodology for optimizing alphabet design for best classification rates is proposed, and three 256-symbol alphabets are designed for performance evaluation in optical turbulence. The beams were propagated in three environments: through underwater optical turbulence generated by Rayleigh–Bénard (RB) convection (C n 2≅10−11m−2/3), through a simulated propagation path derived from the Nikishov spectrum (C n 2≅10−13m−2/3), and through optical turbulence from a thermal point source located in a water tank (C n 2≅10−10m−2/3). We report a classification accuracy of 93.1% for the RB environment, 99.99% in simulation, and 48.5% in the point source environment. The project demonstrates that the CNN can classify the complex alphabet symbols in a practical turbulent flow that exhibits strong optical turbulence, provided sufficient training data is available and testing data is representative of the specific environment. We find the most important factor in a high classification accuracy is a diversification in the intensity profiles of the alphabet symbols.

Experimental evaluation of the impact of physical beam misalignment on the performance of an underwater wireless optical communication network utilizing machine learning

Underwater wireless optical communication systems have garnered significant interest due to advantages in speed and security over radio-frequency and acoustic underwater transmission. One example utilizes Laguerre–Gaussian beams carrying orbital angular momentum to increase bit transfer rate by spatially multiplexing information into an alphabet of symbols, sized 2N, where N is the number of bits encoded in each symbol. This system uses a convolutional neural network (CNN) to demultiplex the information, which has been shown to be capable of high levels of accuracy even in turbid environments or in the presence of significant optical turbulence. However, it has been observed that CNNs struggle when shown images affected by physical environmental effects (different levels of turbulence, optical magnification, beam misalignment) that were not present in the training set. In this paper we further investigate physical beam misalignment under two experimental conditions, quiescent and strong optical turbulence. Physical beam misalignment is defined as a translation of the beam at the receiver. Our optically turbulent environment is characterized using the scintillation of a Gaussian beam, and is estimated to have a refractive index structure constant value of ∼10−11m−2/3. We use two alphabet sizes, of 16 and 256 symbols, and demonstrate classification of received images in a combination of scenarios with adequate success (>90% accuracy) when training and testing under the same conditions, and using a pre-trained CNN, AlexNet. However, when training and testing under physically misaligned conditions, we demonstrate an issue with impractical rates of classification, at 5%–50%. Our investigation provides CNN classification at significantly higher levels of complexity than previously seen, both in terms of experimental turbulence strength and number of classifiable symbols (alphabet size), and clearly demonstrates the importance of carefully designed experiments to aid the machine learning training process for communication systems.

Experimentally evaluating beam scintillation and vortex structure as a function of topological charge in underwater optical turbulence

Optical communication links constructed using orthogonal basis beams have the potential to significantly increase data bandwidth through the use of a complex set of alphabet symbols decoded at the receiver by a machine learning-based classifier. Vortex beams theoretically have the capability to mitigate some of the deleterious effects of optical turbulence. Our research objective is to study Laguerre–Gaussian (LG) single mode basis beams under the assumption that the superimposed beams will maintain a more robust vortex structure on propagation through optical turbulence. If the vortex structure is preserved then the feature diversity of the symbols will allow effective machine learning classification. To better understand the primary drivers influencing vortex robustness, we experimentally measured the scintillation and vortex structure of zero-order LG beams through strong underwater optical turbulence as a function of topological charge ranging from one to nine. We conclude that LG beams with higher topological charges appear to distort less upon propagation, suggesting their suitability as basis beams for easier classification by machine learning techniques.

Effects of underwater optical turbulence on light carrying orbital angular momentum and its classification using machine learning

Laser-based optical links offer the possibility of secure, high data rate underwater communication. Challenges include quickly modulating the light, and rapidly and reliably decoding the received symbols, despite degradation due to optical turbulence and scattering. This paper builds upon a framework introduced in 2016 to address these challenges. We constructed two novel 5-beam Laguerre-Gaussian basis sets, creating 25 symbol alphabets via superposition. We collected 139,000 images of the symbols, transmitted 4.3 meters through water with very strong optical turbulence. We use a novel convolutional neural network to decode them. We believe this work is the first to achieve high accuracy (93.7–99.9%) in an environment with extremely high levels (2∼107-108 m-2/3) of carefully documented experimentallyinduced optical turbulence. We improve upon previous work in several ways: using a larger alphabet (47 vs. 32), faster classification rates (10,000 Hz vs. 1,000 Hz), and a larger set of test images (96,000 vs 9,600).

Performance Analysis of Wireless Adaptive Incremental Networks Under Strong FSO Link Turbulence Conditions

The aim of this paper is to show the problems of implementing the wireless adaptive networks with the free space optical (FSO) technology. Implementing adaptive networks with the wireless optical communication technology has several benefits and also some hindering problems. The thermal optical noise modeled with Gaussian distribution and link turbulence is two of the major problems of this implementation. In this paper, the theoretical analysis of the FSO link effects that are modeled with K-distribution and Negative exponential distributions are considered on the estimation performance of the adaptive incremental networks. These distributions arise when the FSO link is contaminated with strong optical turbulence. Experiments are designed to cover these conditions and the analysis is based on the steady state mean square deviation (MSD) and excess mean square error (EMSE) values for the incremental LMS (ILMS) algorithm and these are the metrics that show how well the adaptive network performs. Simulation results are presented for different parameters of $K$ -distribution and negative exponential distribution and the results show perfect match with the theoretical outcomes. Based on these results, we show that implementing the incremental adaptive networks in the strong turbulence conditions is not feasible and we must think of some countermeasures for these cases.

Phase‐sampled detection of hybrid modulation impaired by gamma‐gamma turbulence

AbstractThis article presents an alternative, though not innovative detection technique for a hybrid modulation technique based on binary pulse position modulation (PPM). Authors have numerically derived the error performance results of a hybrid modulation called pulse position modulation‐minimum shift keying using phase‐sampled detection technique and aperture averaging (AA). Furthermore, the said hybrid modulation is judged against binary phase shift keying and PPM techniques under weak to strong free space optical environment turbulence channels. For both weak and strong atmospheric turbulence, the error performance is studied using log‐normal channel model and the gamma‐gamma channel model. Furthermore, atmospheric fading probabilities in the form of outage probabilities of all modulation techniques are evaluated for log‐normal turbulence model.

Lidar Signal Amplification in a Turbulent Atmosphere under Strong Optical Scintillations

Experimental data on lidar signal amplification in a turbulent atmosphere and its dependence on the structure parameter of the turbulent fluctuations of the refractive index of air are presented. It is ascertained that the amplification coefficient first increases up to its maximum with the structure parameter of the refractive index and then decreases under the conditions of strong optical turbulence along a sounding path. The maximum of the amplification coefficient attainable at a certain distance depends on the turbulence strength during measurements. The time variations in the backscatter amplification coefficient are in a good agreement with the time variations in the structure parameter of the refractive index determined from independent measurements.

Numerical investigation of short-pulse laser radiation propagation in a turbulent atmosphere

An algorithm is presented for the numerical simulation of short-pulse optical radiation propagation in a turbulent atmosphere on the basis of the solution to the parabolic wave equation for the complex spectral amplitude of the wave field by the split-step method. We present examples of the use of this algorithm for simulating the propagation of a pulsed coherent spatially limited beam and a plane wave. It is shown that in the regime of strong optical turbulence the relative variance of fluctuations of energy density of femtosecond radiation becomes much smaller than the relative variance of the intensity of cw radiation.

Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere.

Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere have been studied based on numerical solution of the parabolic wave equation for the complex spectral amplitude of the wave field by the split-step method. It has been shown that under conditions of strong optical turbulence, the relative variance of energy density fluctuations of pulsed radiation of femtosecond duration becomes much less than the relative variance of intensity fluctuations of continuous-wave radiation. The spatial structure of fluctuations of the energy density with a decrease of the pulse duration becomes more large-scale and homogeneous. For shorter pulses the maximal value of the probability density distribution of energy density fluctuations tends to the mean value of the energy density.

Non-Gaussian statistics of multiple filamentation

We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly Gaussian random field that seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long powerlike tail that corresponds to strong non-Gaussian fluctuations, i.e., intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments.

Path-averaged C_n^2 estimation using a laser-and-corner-cube system

As a finite cross-section laser beam propagates through the atmosphere, the beam spreads due to both diffraction and atmospheric turbulence effects. Using turbulence theory valid in both weak and strong optical turbulence regimes, a relationship between atmospheric beam spread and the resulting return power for an optical system and the refractive-index structure parameter or Cn2 can be established. A technique for estimating the path-averaged Cn2 using a laser-and-corner-cube system based on this relationship is described. Experimental results using near-infrared laser wavelengths show good agreement between theoretical predictions and scintillometer-measured Cn2 values for near-ground line-of-sight propagation paths.

Effect of atmospheric spectrum models on scintillation in moderate turbulence

Experimental studies have shown that a ‘bump’ occurs in the atmospheric spectrum just prior to turbulence cell dissipation. In weak optical turbulence, this bump affects calculated scintillation. The purpose of this study was to determine if a simpler non-bump atmospheric power spectrum can be used to model scintillation for plane waves and spherical waves in moderate to strong optical turbulence regimes. Scintillation expressions were developed from an ‘effective’ von Karman spectrum using an approach similar to that used by Andrews et al. in developing expressions from an effective modified (bump) spectrum. The effective spectrum extends the Rytov approximation into all optical turbulence regimes using filter functions to eliminate mid-range turbulent cell size effects to the scintillation index. Filter cutoffs were established by matching to known weak and saturated scintillation results. The resulting new expressions track those derived from the effective bump spectrum fairly closely. In extremely strong turbulence, differences are minimal.

Observation of All-Optical Bump-on-Tail Instability

We demonstrate an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially coherent spatial beams. For weak wave coupling, we observe momentum transfer with no variation in intensity. For strong wave coupling, modulations appear in intensity and evidence appears for wave (Langmuir) collapse at large scales. Borrowing plasma language, these limits represent regimes of weak and strong spatial optical turbulence. In both limits, the internal spectral energy redistribution is observed by recording and reconstructing a hologram of the evolving dynamics. The results are universal and can appear in any wave-kinetic system with short-wave-long-wave coupling.

History, Present Status & Future of Site Testing at Dôme C

Hereafter we give a brief history of our contribution to astronomical site testing in Antarctica, at least for the high angular resolution in the visible range. The decision to undertake the first site testing at South Pole began one year after a congress organized by French Academie des Sciences, in year 1992. Indeed, in 1993 a meeting took place in Chicago with the participation of Peter Gillingham, Al Harper and Jean Vernin where each one took the respective responsibility of 1) giving a PhD student, 2) the South Pole infrastructure and 3) the relevant instruments. During winter 1995, thanks to a mast equipped with micro-thermal sensors, we demonstrated (Marks et al., 1996, A&AS, 118, 1) that the first 30 m of the surface layer was disrupted by strong optical turbulence. Then, the year after, 15 balloons equipped with micro-thermal probes were successfully launched from South Pole. Marks et al. (1999, A&AS, 134, 161) shown that most of the optical turbulence at South Pole was concentrated within a layer 200 m thick above the ice level. From this study, it becomes clear that the noticeable katabatic wind present at South Pole was generating this huge surface layer and that is why we oriented our astronomical site characterization toward Dome C. Our first summer seeing estimations began in 2000, which demonstrated (Aristidi et al., 2003, A&AS, 406, L19 & Aristidi et al., 2005, A&A, 444, 651) that, as expected, the surface wind was much less than at South Pole, and, as a matter of fact, the seeing was much better, and was even exceptional during the four hours of the afternoon where a seeing of less than 0.5 arcsec was measured. In 2005, the Concordia base was first open during the polar night, and one of us, A. Agabi was able to launch 41 balloons equipped with micro-thermal sensors. A differential image motion monitor (DIMM) was also setup with success. At mid winter, Agabi et al. (2006, PASP, 118, 344) showed that most of the optical turbulence came from the first 30 m surface layer and very little from the rest of the atmosphere (1.3 arcsec above 8.5 m and 0.37 arcsec above 30 m).

Characterizing the propagation path in moderate to strong optical turbulence

In February 2005 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation and the University of Central Florida. A Gaussian beam was propagated along a horizontal 1500 m path near the ground. Scintillation was measured simultaneously at three receivers of diameters 1, 5, and 13 mm. Scintillation theory combined with a numerical scheme was used to infer the structure constant C2n, the inner scale l0, and the outer scale L0 from the optical measurements. At the same time, C2n measurements were taken by a commercial scintillometer, set up parallel to the optical path. The C2n values from the inferred scheme and the commercial scintillometer predict the same behavior, but the inferred scheme consistently gives slightly smaller C2n values.

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.

Numerical simulation of the effect of refractive turbulence on coherent lidar return statistics in the atmosphere

We propose an algorithm and the results of a numerical study of random realizations and statistics of a pulsed coherent lidar return that allow for refractive turbulence. We show that, under conditions of refractive turbulence, the relative variance of the lidar return power can exceed unity by a factor of as much as 1.5. Clear manifestations of the turbulent effect of backscattering amplification have been revealed from simulations of space-based lidar sensing of the atmosphere with coherent lidar. Under conditions of strong optical turbulence in the atmospheric boundary layer, as a result of the backscattering amplification effect, the mean lidar return power can exceed the return power in the absence of turbulence by a factor of 3.

Effective beam parameters and the turbulent beam waist for convergent Gaussian beams

Expressions are developed for the location and the size of the beam waist for a convergent Gaussian beam in statistically homogeneous and isotropic atmospheric turbulence. Subsidiary expressions are presented that lead to the maximum distance from the transmitter at which the beam waist can be located under given optical turbulence conditions and the optimal initial radius of curvature required for placing the beam waist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship ∂W/∂z = - W/R, where z represents the path length and R is the phase-front radius of curvature at z. By enforcing this relation on the effective beam spot size in turbulence W(e), we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) leads to a pair of effective beam parameters θ(e) and Λ(e) that provide a natural extension to the complex amplitude plane. Within this context, general propagation characteristics may be described, including the coherence properties of a Gaussian beam in both weak and strong optical turbulence.

Contrast transmission predictions versus far-infrared imager measurements for low-altitude horizontal paths

The Mobile Imaging Spectroscopy Laboratory of the U.S. Army Research Laboratory was used to measure horizontal-path contrast transmission with 8- to 12-μm imagers in 1988. The values obtained were only about one-half of what was predicted by LOWTRAN7. In 1990 a large-area target board, 1.8 x 1.8 m, was used and resulted in resolvable temperatures that could be consistently measured over a 1.6-km path, even during times of strong optical turbulence, and were compared to 0.1-km reference temperatures to obtain values of contrast transmission. These new measurements compare very well with LOWTRAN7 calculations except for cases when aerosol attenuations from patches of ground fog and vehicular dust were present but not included in the calculations.

Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence

A generalized Huygens–Fresnel integral, valid for optical wave propagation through random inhomogeneities in the presence of any complex optical system characterized by an ABCD ray matrix, is used to derive a general expression for the mutual coherence function (MCF) associated with a Gaussian-beam wave in the weak-fluctuation regime. The mean irradiance obtained from this expression shows excellent agreement with all known asymptotic relations. By introducing a pair of effective beam parameters Θt and Λt that account for additional diffraction on the receiving aperture, resulting from turbulence, the normalized MCF and the related degree of coherence are formally extended into the regime of strong fluctuations. Results for the normalized MCF from this heuristic approach compare well with numerical calculations obtained directly from the formal solution of the parabolic equation. Also, the implied spatial coherence length from this analysis in moderate-to-strong-fluctuation regimes generally agrees more closely with numerical solutions of the parabolic equation than do previous approximate solutions. All calculations are based on the modified von Karman spectrum for direct comparison with established results.