Angle Of Arrival Fluctuations Research Articles

High-bandwidth fine tracking system for optical communication with double closed-loop control method

A fine tracking system is crucial for maintaining the accuracy of the optical communication terminals that aim at each other. To ensure the reliability of the communication link, the fine tracking system requires high bandwidth to mitigate the effect of arrival angle fluctuation caused by atmospheric turbulence. Traditionally, the fine tracking system includes only a single feedback loop; a high bandwidth is obtained by increasing the high gain of the fine tracking system, which usually suffers considerably from the time delay engendered by sampling and data processing, the hysteresis nonlinearity of a fast steering mirror (FSM), and the limitations of dynamic response of FSM. To track the beacon in real time and with high precision, a pioneering control method is presented in our paper, namely, double closed-loop control (DCC), which performs better in a tracking system compared with a traditional single-feedback loop. In the inner feedback loop, the response of FSM is measured by a strain gauge sensor (SGS) and used as the inner feedback signal. Thus, by co-operating with the outer CCD-based feedback loop, a DCC scheme is proposed for the fine tracking system. With the SGS signal, the inner loop controller is designed to obtain a rapid response without overshooting; meanwhile, the hysteresis nonlinearity is diminished. Experimental results indicate that the static hysteresis nonlinearity of FSM is reduced from 15.6% to 1.4% by an inner feedback loop, and the dynamic response and stability of FSM is greatly improved, thereby simplifying the outer loop controller design. Then, with the SGS signal, the time delay of the outer loop can be compensated accurately with a predicted signal compensation method. The experimental results show that the −3 dB error rejection bandwidth is increased from 76 to 85 Hz, and the coupling efficiency in our optical communication system is improved by 16.87% after using the DCC fine tracking method. These results indicate that the DCC method can effectively achieve the goal of fast and accurate tracking for optical communications systems.

Optical wave angle of arrival fluctuations in deep anisotropic turbulence

Previous investigations of optical wave angle of arrival (AOA) fluctuations focused on either isotropic turbulence or weak anisotropic turbulence. In this investigation, new analytic models of optical wave AOA fluctuations will be developed for deep (moderate-to-strong or strong) anisotropic turbulence. Compared with the published models, the new derived models consider both the asymmetric turbulence cells and a wide range of turbulence strength at the same time. Results indicate that the anisotropy in turbulence is advantageous to reduce the optical wave AOA fluctuations in contrast to the isotropic turbulence. In weak anisotropic turbulence region, it is found that the new derived models can be simplified as the known ones acquired with classic Rytov theory. Increasing in the anisotropic degree of turbulence can decrease the difference between the new models and the known ones acquired with classic Rytov theory.

Free-Space Optical Communication Impaired by Angular Fluctuations

In this paper, the impairments of free-space optical (FSO) communication systems caused by angular fluctuations including beam misalignment and angle-of-arrival (AOA) fluctuations are modeled in the presence of both atmospheric turbulence and transceiver vibrations. In particular, assuming FSO receivers with a limited field-of-view (FOV), the fading caused by AOA fluctuations is studied. The outage probability expressions for both coherent and direct detections are derived in both shot-noise-limited and thermal-noise-limited regimes. For direct detection, the optimal receiver FOV that achieves the minimum outage probability is considered. Furthermore, the issue of imperfect phasefront tracking in practical coherent receivers is investigated.

Laboratory simulation of non-Kolmogorov turbulence based on a liquid crystal spatial light modulator

An experimental platform was built for the atmospheric turbulence simulation upon a liquid crystal spatial light modulator. The phase-only spatial light modulator is driven by a series of dynamic phase screens that have non-Kolmogorov turbulence characteristics. After passing through the simulated non-Kolmogorov turbulence, the angle-of-arrival (AoA) and light intensity of the laser beam were analyzed statistically. The variation trends of the AoA fluctuation and the scintillation index exhibited by the experimental results are in accordance with the theoretical predictions. Although there was some divergence between the experiments and theory that needs to be improved further, the experimental data demonstrate the feasibility of using the platform to simulate the turbulence influence on laser communication in the lab.

Investigation of inhomogeneity and anisotropy in near ground layers of atmospheric air turbulence using image motion monitoring method

In this work the anisotropy and inhomogeneity of real atmospheric turbulence have been investigated using image motion monitoring and differential image motion monitoring methods. For this purpose the light beam of a point source is propagated through the atmospheric turbulence layers in horizontal path and then impinged to a telescope aperture. The telescope and point source were 350m apart. In front of the telescope's aperture a mask consisting of four subapertures was installed. Image of the point source was formed on a sensitive CCD camera located at the focal plane of the telescope. By displacing CCD camera along the axis of telescope, four distinct images were recorded. Angle of arrival (AA) of each spot was calculated by image processing. Air turbulence causes AA to fluctuate. By comparing AA fluctuation variances of different spots in two directions isotropy and homogeneity of turbulence were studied. Results have shown that atmospheric turbulence in near ground layers is treated as an anisotropic and inhomogeneous medium. In addition, the inhomogeneity and anisotropy of turbulence decreases with the distance from earth surface.

Intensity and angle-of-arrival spectra of laser light propagating through axially homogeneous buoyancy-driven turbulence.

Frequency spectra obtained from the measurements of light intensity and angle of arrival (AOA) of parallel laser light propagating through the axially homogeneous, axisymmetric buoyancy-driven turbulent flow at high Rayleigh numbers in a long (length-to-diameter ratio of about 10) vertical tube are reported. The flow is driven by an unstable density difference created across the tube ends using brine and fresh water. The highest Rayleigh number is about 8×109. The aim of the present work is to find whether the conventional Obukhov-Corrsin scaling or Bolgiano-Obukhov (BO) scaling is obtained for the intensity and AOA spectra in the case of light propagation in a buoyancy-driven turbulent medium. Theoretical relations for the frequency spectra of log amplitude and AOA fluctuations developed for homogeneous isotropic turbulent media are modified for the buoyancy-driven flow in the present case to obtain the asymptotic scalings for the high and low frequency ranges. For low frequencies, the spectra of intensity and vertical AOA fluctuations obtained from measurements follow BO scaling, while scaling for the spectra of horizontal AOA fluctuations shows a small departure from BO scaling.

Effect of non-Kolmogorov turbulence on BER performance in uplink ground-to-satellite laser communication

Based on the non-Kolmogorov turbulence model of the stratosphere, a theoretical model for the influence of the angle of arrival (AOA) fluctuations on the performance of the bit error rate (BER) is established. A closed form expression of BER is then derived based on this model. Then, considering the combined effect of scintillation, beam wander and AOA fluctuations, the probability density function of the received intensity and the closed form expressions of BER for uplink are derived. Coherent detection of Circle Polarization Shift Keying modulation which is suitable for ground-to-satellite laser communication is employed. For an uplink, the BER performance is emulation analyzed and compared to the condition without taking AOA fluctuations into account. And the variation of BER as a function of AOA fluctuations has also been researched. The influence of intensity scintillation, beam wander and AOA fluctuations on BER has been analyzed based on laser transmit power restrictions.

Angle of Arrival Fluctuations for Optical Waves Propagating Through Joint Moderate to Strong Atmospheric Turbulence

Satellite laser communication has gained wide attention both at home and abroad. The pointing, acquisition, and tracking (PAT) technology is the kernel of satellite laser communication systems, and the atmospheric layer is a part of the communication channel for satellite-to-ground links. Thus, angle of arrival (AOA) fluctuations caused by atmospheric turbulence inevitably influence long-distance satellite laser communication. Therefore, it is very important to analyze the impact of AOA fluctuations in satellite laser communication systems. According to the actual situation of satellite-to-ground links, a joint atmospheric turbulence power spectrum model is defined that includes Kolmogorov turbulence from the ground to 6 km in portions of the troposphere and non-Kolmogorov turbulence above 6 km in the stratosphere. Based on the extended Rytov theory, we derive the large-scale and small-scale variances of AOA fluctuations propagating in the uplink and downlink channels for a satellite laser communication system and analyze the influence of large zenith angle variations on the AOA fluctuations. It has long been a focus of concern that the expressions for the AOA variance obtained must be concise and of closed form.

部分相干光在大气湍流中的到达角起伏

部分相干光在大气湍流中的到达角起伏

Generalized anisotropic turbulence spectra and applications in the optical waves' propagation through anisotropic turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this work, two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence. They consider simultaneously the finite turbulence inner and outer scales and the asymmetric property of turbulence eddies in the orthogonal xy-plane throughout the path. Two anisotropy factors which parameterize the asymmetry of turbulence eddies in both horizontal and vertical directions are introduced in the orthogonal xy-plane, so that the circular symmetry assumption of turbulence eddies in the xy-plane is no longer required. Deviations from the classic 11/3 power law behavior in the spectrum model are also allowed by assuming power law value variations between 3 and 4. Based on the derived anisotropic spectral model and the Rytov approximation theory, expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence. Calculations are performed to analyze the derived spectral models and the variance of AOA fluctuations.

Mean-square angle-of-arrival difference between two counter-propagating spherical waves in the presence of atmospheric turbulence.

The mean-square angle-of-arrival (AOA) difference between two counter-propagating spherical waves in atmospheric turbulence is theoretically formulated. Closed-form expressions for the path weighting functions are obtained. It is found that the diffraction and refraction effects of turbulent cells make negative and positive contributions to the mean-square AOA difference, respectively, and the turbulent cells located at the midpoint of the propagation path have no contributions to the mean-square AOA difference. If the mean-square AOA difference is separated into the refraction and diffraction parts, the refraction part always dominates the diffraction one, and the ratio of the diffraction part to the refraction one is never larger than 0.5 for any turbulence spectrum. Based on the expressions for the mean-square AOA difference, formulae for the correlation coefficient between the angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are derived. Numerical calculations are carried out by considering that the turbulence spectrum has no path dependence. It is shown that the mean-square AOA difference always approximates to the variance of AOA fluctuations. It is found that the correlation coefficient between the angles of arrival in the x or y direction of two counter-propagating spherical waves ranges from 0.46 to 0.5, implying that the instantaneous angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are far from being perfectly correlated even when the turbulence spectrum does not vary along the path.

Investigation of the inhomogeneity of atmospheric turbulence at day and night times

In this work, we introduce for the first time the use of a pair of telescopes facing each other in conjunction with the use of a pair of moiré deflectometers for the investigation of the inhomogeneity of atmospheric turbulence. In the experiment, a laser beam enters a telescope from its back focal point by virtue of a focusing lens and is expanded and re-collimated by it before passing through the turbulent ground level atmosphere. It then enters the aperture of a second telescope, where it is again re-collimated behind the focal point, finally entering a pair of moiré deflectometers. We use the instrument for measuring the fluctuations of two components of the angle of arrival (AA) across the second telescope's aperture. Calculation of the structure functions of the vertical and horizontal components of the AA fluctuations on the second telescope's aperture (over typical vertical and horizontal moiré fringes) at different altitudes and at different latitudes allows a quantitative measure of the inhomogeneity at the day and night times in the atmospheric surface layer. Experimental results show that on sunny days the difference between the structure functions of the horizontal component of the AA fluctuations calculated at two different altitudes over two horizontal moiré fringes is changed as a function of the time and its value meaningfully correlated to the mean value of the temperature of the Earth's surface. We did not find any interpretative correlation for the difference between the structure functions of the vertical component of the AA fluctuations calculated at two different latitudes. In addition, for the data recorded on windy days the observed correlation between the inhomogeneity of the atmospheric turbulence and the Earth's temperature almost disappeared.

Temporal power spectra of angle of arrival fluctuations for optical waves propagating through moderate-to-strong non-Kolmogorov refractive turbulence

The temporal statistical property of angle of arrival (AOA) fluctuations is investigated in detail both analytically and numerically. New analytic expressions for the temporal power spectra of AOA fluctuations are derived with the extended Rytov theory for both plane and spherical waves propagating through moderate-to-strong (or strong) non-Kolmogorov atmospheric turbulence. They cover a more wide range of turbulence strength, and can reduce correctly to previously published analytic expressions for the weak non-Kolmogorov turbulence case. The final results indicate that, as turbulence strength increases up to moderate-to-strong (or strong) turbulence regime, the expressions derived in this work deviates from those obtained via the Rytov theory and the discrepancy increases with the increased turbulence strength. These results are useful for the understanding the potential impact of derivations from the standard non-Kolmogorov spectrum.

Influence of asymmetry turbulence cells on the angle of arrival fluctuations of optical waves in anisotropic non-Kolmogorov turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. Very recent analyses of angle of arrival (AOA) fluctuations of an optical wave in anisotropic non-Kolmogorov turbulence have adopted the assumption that the propagation path was in the z-direction with circular symmetry of turbulence cells maintained in the orthogonal xy-plane throughout the path, and one single anisotropy factor was adopted in the orthogonal xy-plane to parameterize the asymmetry of turbulence cells or eddies in both horizontal and vertical directions. In this work, the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane is no longer required, and two anisotropy parameters are introduced in the orthogonal xy-plane to investigate the AOA fluctuations. In addition, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. With the Rytov approximation theory, new theoretical models for the variance of AOA fluctuations are developed for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. When the two anisotropic parameters are equal to each other, they reduce correctly to the recently published results (the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane was adopted). Furthermore, when these two anisotropic parameters equal one, they reduce correctly to the previously published analytic expressions for the cases of optical wave propagation through weak isotropic non-Kolmogorov turbulence.

Phase structure function and AOA fluctuations of plane and spherical waves propagating through oceanic turbulence

Based on the characteristics of a hypergeometric function, the analytical expressions for the phase structure function and angle-of-arrival (AOA) fluctuations of plane and spherical waves propagating through oceanic turbulence are derived. The results are verified by comparing them with the numerical calculations of the definitions using four important parameters (i.e., the rate of dissipation of mean-squared temperature the rate of dissipation of kinetic energy per unit mass of fluid the ratio of temperature to salinity contribution to the refractive index spectrum and the Kolmogorov microscale The relation between AOA fluctuations and the spatial coherence radius is also investigated.

到达角起伏与闪烁效应测量折射率结构常数的比较

到达角起伏与闪烁效应测量折射率结构常数的比较

Analysis of marine atmospheric turbulence effects on infrared imaging system by angle of arrival fluctuations

For the long-range infrared imaging system, the marine atmospheric turbulence degrades seriously the probability of object recognition and tracking. In this study, the angle of arrival fluctuations of an optical wave, which describes the distortion effects of marine atmospheric turbulence on an infrared optical imaging system, is investigated in detail both analytically and numerically. Analytic expressions of the angle of arrival fluctuations are derived for optical plane and spherical waves propagating through weak marine atmospheric turbulence with horizontal path, and they consider simultaneously finite turbulence inner scale, turbulence outer scale, wavelength, and aperture diameters. Numerical calculations are conducted to analyze the influence of marine weak turbulence on the infrared imaging. The results are useful for understanding the potential impact of deviations from the terrestrial turbulence.

Effects of wind-driven telescope vibrations on measurements of turbulent angle-of-arrival fluctuations.

Turbulence in the atmospheric refractive-index field causes optical angle-of-arrival (AOA) fluctuations that can be used for atmospheric remote sensing of various parameters, including wind velocities and the optical refractive-index turbulence structure parameter, C(n)2. If AOA measurements are contaminated by wind-induced telescope vibrations, the underlying retrieval algorithms may fail. In order to study the effects of wind-driven telescope vibrations on optical-turbulence measurements, we conducted a field experiment in which we exposed two small telescopes deliberately to the wind. We measured AOA fluctuations of visible light propagating along a horizontal, 174 m long path 1.7 m above flat terrain, and we used fast-response ultrasonic anemometers to measure the wind velocity at multiple locations along the path. We found (1) that the AOA turbulence spectra were contaminated by multiple resonance peaks, (2) that the resonance frequencies were independent of the wind speed, and (3) that the AOA variance associated with the dominating vibration mode was proportional to the fourth power of the wind speed.

Angle of arrival fluctuations considering turbulence outer scale for optical waves’ propagation through moderate-to-strong non-Kolmogorov turbulence

Based on the generalized von Kármán spectrum and the extended Rytov theory, new analytic expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through moderate-to-strong non-Kolmogorov turbulence with horizontal path. They consider finite turbulence outer scale and general spectral power law value, and cover a wide range of non-Kolmogorov turbulence strength. When the turbulence outer scale is set to infinite, the new expressions can reduce correctly to previously published analytic expressions [J. Opt. Soc. Am. A, 302188 (2013]. The final results show that the increased turbulence outer scale value enlarges the variance of AOA fluctuations greatly under moderate-to-strong (or strong) non-Kolmogorov turbulence.

Measuring significant inhomogeneity and anisotropy in indoor convective air turbulence in the presence of 2D temperature gradient

Using a novel set up, experimental study of the statistical properties of a light beam propagating horizontally through indoor convective air turbulence in the presence of a 2D temperature gradient (TG) is presented. A laser beam enters a telescope from its back focal point by virtue of an optical fiber and is expanded and recollimated by it and then passes through the turbulent area. Then the beam enters another telescope’s aperture. A mask consisting of four similar widely separated small subapertures was installed in front of the second telescope’s aperture. The subapertures were equidistant from the optical axis of the telescope and located at the corners of a square. A flat plane heater is used to produce a vertical TG in the medium. Due to the limited width of the heater, a horizontal component for the TG appeared. Near the focal plane of the second telescope, four distinct images of the source are formed and recorded by a CCD camera. Due to the turbulence all the images (spots) in the successive frames fluctuate. Using the four spot displacements we have calculated the fluctuations of the angle of arrival (AA) over the subapertures. The statistical properties of the optical turbulence are investigated using variance analysis of the AA component fluctuations at horizontal and vertical directions over the subapertures for different temperatures of the heater at different heights of the beam path from the heater. Experimental results show that when the heater is turned off, the variances of horizontal and vertical components of the AA fluctuations are approximately equal to zero over all the subapertures. When it is turned on, the variance of the horizontal component of the AA fluctuations over all of the subapertures are larger than those from the vertical one. In addition, in this case, we find a significant dependence of the variance of the AA components on the height from the heater.