Some space-time statistics of the turbulent point-spread function (original) (raw)
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Studies of the Effects of Atmospheric Turbulence on Free Space Optical Communications
2005
Even after several decades of study, inconsistencies remain in the application of atmospheric turbulence theories to experimental systems, and the demonstration of acceptable correlations with experimental results. This dissertation shows a flexible empirical approach for improving link performance through image analysis of intensity scintillation patterns coupled with frame aperture averaging on a free space optical (FSO) communication link. Aperture averaging is the effect of the receiver size on the power variance seen at the receiver. A receiver must be large enough to collect sufficient power and reduce scintillation effects at a given range, but must also be of practical size. An imaging system for measuring the effects of atmospheric turbulence and obscuration on FSO links will be presented. Weak and intermediate turbulence results will be shown for an 863 meter link at the University of Maryland. Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and FSO communications systems. A new geometrical model to assess the effects of turbulence on laser beam propagation in such applications will be presented. The atmosphere along the laser beam propagation path is modeled as a spatial distribution of spherical bubbles with refractive index discontinuity statistically distributed according to various models. For each statistical representation of the atmosphere, the path of rays is analyzed using geometrical optics. These Monte Carlo techniques can assess beam wander, phase shifts and aperture averaging effects at the receiver. An effective C n 2 can be determined by correlating beam wander behavior with the path length. In addition, efficient computational techniques have been developed for various correlation functions that are important in assessing the effects of turbulence. The Monte Carlo simulations are compared with the predictions of wave theory. This is the first report to present weak and intermediate turbulence results using an efficient imaging technique. It is also the first report to geometrically simulate aperture averaging.
Imaging and communications through non-Kolmogorov turbulence
Atmospheric Optics: Models, Measurements, and Target-in-the-Loop Propagation III, 2009
At present, system design usually assumes the Kolmogorov model of refractive index fluctuation spectra in the atmosphere. However, experimental data indicates that in the atmospheric boundary layer and at higher altitudes the turbulence can be different from Kolmogorov's type. In optical communications, analytical models of mean irradiance and scintillation index have been developed for a traditional Kolmogorov spectrum and must be revised for non-Kolmogorov turbulence. The image quality (resolution, MTF, etc.) is essentially dependent on the properties of turbulent media. Turbulence MTF must be generalized to include non-Kolmogorov statistics. The change in fluctuation correlations of the refractive index can lead to a considerable change in both the MTF form and the resolution value. In this work, on the basis of measurements and model calculations, the influence of non-Kolmogorov turbulence on imaging and communications through the atmosphere is estimated for different scenarios of vertical and slant-path propagation. The atmospheric model of an arbitrary (non-Kolmogorov) spectrum is applied to estimate the statistical quantities associated with optical communication links (e.g., scintillation and fading statistics) and imaging system. Implications can be significant for optical communication, imaging through the atmosphere, and remote sensing.
Free-Space Laser Communications VIII, 2008
The performance of free space optical (FSO) links in a clear atmosphere is affected by the non-ideal characteristics of the communication channel. Atmospheric turbulence causes fluctuations in the received signal level, which increase the bit errors in a digital communication link. In order to quantify performance limitations, a better understanding of the effect of the intensity fluctuations on the received signal at all turbulence levels is needed. Theory reliably describes the behavior in the weak turbulence regime, but theoretical descriptions in the intermediate and strong turbulence regimes are less well developed. We have developed a flexible empirical approach for characterizing link performance in strong turbulence conditions through image analysis of intensity scintillation patterns coupled with frame aperture averaging on an FSO communication link. These measurements are complemented with direct measurements of temporal and spatial correlation functions. A He-Ne laser beam propagates 106 meters in free-space over flat terrain about a meter above the ground to provide strong atmospheric turbulence conditions. A high performance digital camera with a frame-grabbing computer interface is used to capture received laser intensity distributions at rates up to 30 frames per second and various short shutter speeds, down to 1/16,000s per frame. A scintillometer is used for accurate measurements of the turbulence parameter C n 2. Laboratory measurements use a local strong turbulence generator, which mimics a strong phase screen. Spatial correlation functions are measured using laterally separated point detectors placed in the receiver plane. Correlations and captured image frames are analyzed in Labview to evaluate correlation functions, C n 2 , and the aperture averaging factor. Our correlation measurement technique represents a probe into the length scales of different flows and make for a "fingerprint" of the air conditions at the time. The aperture averaging results demonstrate the expected reduction in intensity fluctuations with increasing aperture diameter, and show quantitatively the differences in behavior between various strengths of turbulence. This paper will present accurate empirical data in the strong turbulence regime. Such results can help build upon existing empirical data and lead to the development of new theories.
Light propagation through multilayer atmospheric turbulence
Optics Communications, 1997
A new treatment is presented for light propagation through multilayer turbulence. Equations for the intensity and phase of an observed wavefront are derived together with their validity conditions for both single and multiple layer systems. A method for finding the statistics of observed scintillations is presented together with a detailed calculation for a single layer system. 0 1997 Elsevier Science B.V.
Long-range propagation through inhomogeneous turbulent atmosphere: analysis beyond phase screens
Physica Scripta, 2018
Many applications rely on the propagation of electromagnetic waves through extended regions of the atmosphere over which the refractive index can vary in a complex manner. Gradients and curvature of the mean refractive index profile result in ray bending and the associated phenomena of mirages, atmospheric lensing, and wave trapping in parabolic cavities. Stochastic refractive index fluctuations due to turbulence cause a random displacement of the trajectory and give rise to the wander, or spot dancing, of a propagating optical beam. In this paper we model these features of the refractive index profile locally and describe propagation through the corresponding regions. We derive formulas for the mean ray path that capture the effects of both atmospheric turbulence and variations in the mean refractive index profile, including the non-paraxial effects associated with the bending of the guiding ray path. We also give formulas for the mean-squared transverse displacement of a ray from the mean trajectory, which can provide for example an estimate of the magnitude of the beam wander due to turbulence.
Non-Kolmogorov atmospheric turbulence and optical signal propagation
Nonlinear Processes in Geophysics, 2006
In the present review, we make an attempt to attract attention to the effect of non-Kolmogorov behavior of turbulence in various scales on the characteristics of electromagnetic waves propagation through a turbulent atmosphere on the example of certain atmospheric experiments. We discuss the interpretation of experimental data based on the model of spectral behavior of a passive scalar field within a broad range of scales, which has been developed recently.
Effects of light propagation in middle intensity atmospheric turbulence
Frontiers of Optoelectronics in China, 2009
The purpose of this report is to present an experimental study of the effects of light propagation through atmospheric turbulence. Free space optical communication is a line-of-sight technology that transmits a modulated beam of visible light through the atmosphere for broadband communication. The fundamental limitations of free space optical communications arise from the environment through which it propagates. However these systems are vulnerable to atmospheric turbulence, such as attenuation and scintillation. Scintillation is due to the air index variation under the temperature effects. These factors cause an attenuated receiver signal and lead to higher bit error rate (BER). An experiment of laser propagation was carried out to characterize the light intensity through turbulent air in the laboratory environment. The experimental results agree with the calculation based on Rytov for the case of weak to intermediate turbulence. Also, we show the characteristics of irradiance scintillation, intensity distribution and atmospheric turbulence strength. By means of laboratory simulated turbulence, the turbulence box is constructed with the following measurements: 0.5 m wide, 2 m long and 0.5 m high. The simulation box consists of three electric heaters and is well described for understanding the experimental set up. The fans and heaters are used to increase the homogeneity of turbulence and to create different scintillation indices. The received intensity scintillation and atmosphere turbulence strength were obtained and the variation of refractive index, with its corresponding structure parameter, is calculated from the experimental results.
Light propagation through anisotropic turbulence
Journal of the Optical Society of America A, 2011
A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς 2−α .
Imaging and communications through non-Kolmogorov turbulence
2009
At present, system design usually assumes the Kolmogorov model of refractive index fluctuation spectra in the atmosphere. However, experimental data indicates that in the atmospheric boundary layer and at higher altitudes the turbulence can be different from Kolmogorov's type. In optical communications, analytical models of mean irradiance and scintillation index have been developed for a traditional Kolmogorov spectrum and must be revised for non-Kolmogorov turbulence. The image quality (resolution, MTF, etc.) is essentially dependent on the properties of turbulent media. Turbulence MTF must be generalized to include non-Kolmogorov statistics. The change in fluctuation correlations of the refractive index can lead to a considerable change in both the MTF form and the resolution value. In this work, on the basis of measurements and model calculations, the influence of non-Kolmogorov turbulence on imaging and communications through the atmosphere is estimated for different scenarios of vertical and slant-path propagation. The atmospheric model of an arbitrary (non-Kolmogorov) spectrum is applied to estimate the statistical quantities associated with optical communication links (e.g., scintillation and fading statistics) and imaging system. Implications can be significant for optical communication, imaging through the atmosphere, and remote sensing.
Non-Classic Atmospheric Optical Turbulence: Review
Applied Sciences
Theoretical models and results of experimental campaigns relating to non-classic regimes occurring in atmospheric optical turbulence are overviewed. Non-classic turbulence may manifest itself through such phenomena as a varying power law of the refractive-index power spectrum, anisotropy, the presence of constant-temperature gradients and coherent structures. A brief historical introduction to the theories of optical turbulence, both classic and non-classic, is first presented. The effects of non-classic atmospheric turbulence on propagating light beams are then discussed, followed by the summary of results on measuring the non-classic turbulence, on its computer and in-lab simulations and its controlled synthesis. The general theory based on the extended Huygens–Fresnel method, capable of quantifying various effects of non-classic turbulence on propagating optical fields, including the increased light diffraction, beam profile deformations, etc., is then outlined. The review conclu...