Fog and low clouds are the two atmospheric elements with the greatest impact on the performance of a free space optical (FSO) network. Predicting the effects of low clouds and ground based fog on FSO equipment performance is a challenging exercise. Usually, surface visibility records from airports in proximity to the deployment area are used to calculate the link availability. However, very little data are available on visibility within clouds, which have a larger impact on elevated links. To estimate the visibility in low clouds we have deployed visibility sensors at three different heights (33, 119, 188 meters above mean sea level) and a ceilometer in San Francisco from June to October of 2001. The data collected show substantial difference between the visibility reported at San Francisco International Airport (SFO) and the visibility recorded by our sensors in downtown San Francisco. More importantly, the data indicate a greater prevalence of low clouds downtown than at the airport.
Under favorable visibility conditions, scintillation becomes the limiting factor in estimating free space optical (FSO) link availability. In the summer of 2001, Terabeam performed several experiments to characterize the impact of scintillation on FSO products under development. In the experiment, a transmitter and a receiver were placed 1000 and 2600 meters apart and operated with the receiver at several different sized apertures and under diverse atmospheric conditions. The experimental probability of fade is then calculated and compared with two theoretical models, namely the lognormal and the gamma-gamma.
KEYWORDS: Clouds, Visibility through fog, Visibility, Fiber optic gyroscopes, Free space optics, Data modeling, Data archive systems, Signal attenuation, Meteorology, Data analysis
Meteorological visibility data are the most commonly used data to estimate terrestrial Free Space Optics (FSO) availability in a given city. Visibility data can be used to estimate transmission efficiency at desired IR wavelengths using a semi-empirical equation, and are often archived over many years allowing the calculation of long-term averages of availability. However, these data are taken at near-surface levels (historically within a few meters of the surface) and are therefore only appropriate for estimating FSO availability near the surface. Examination of long term cloud observations, including percent frequency of cloud ceilings occurring at various heights above the ground, show the importance of including low clouds into the consideration of FSO availability for any situation above about 30-m above ground level (AGL). In most locations, low clouds occurring very near the surface are relatively common -- more so than surface-based fog (which is measured in terms of visibility). Thus, FSO availability will decrease with height, sometimes dramatically, in most cities. Cloud data is also archived over long periods of record and can thus be used to calculate long-term averages of availability.
Under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations, we developed a heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium. This model takes into account the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between two scale size, hereafter called the upper bound and the lower bound. These mid-range scale size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cutoff frequencies as the optical wave propagates. By applying a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, tractable expressions are developed for the scintillation index of a Gaussian beam wave that are valid under moderate- to-strong irradiance fluctuations. Inner scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. We also include the effect of a finite outer scale in addition to inner scale.
For a Gaussian-beam wave incident on a point target, we use a recently developed scintillation theory and the gamma- gamma probability density function to calculate the fade statistics of the echo wave as a function of threshold below the mean irradiance. We also compare the results with experimental data collected by a coherent receiver array over a 1-km propagation path to the target using from one to eight apertures of the array. The propagation channel was determined to be a bistatic configuration for the lidar system. Values of inner scale and refractive index structure constant were simultaneously measured during the experiment by use of a scintillometer instrument. The scintillation theory employed in this work utilizes a spatial filter function that results from adapting a modulation scheme in which it is assumed that the intensity of the propagating laser beam is a product of two quantities: one related to the large scale turbulent eddies of the atmosphere and the other related to the small scale eddies. The theoretical curves arising from this analysis provide a good fit with experimental data up to four active apertures of the array, but deviate somewhat from the data for a greater number of apertures.
Free space optical beam propagation is largely limited by the visibility of the channel at a particular location and at a particular time. In the absence of highly scattering particles, such as rain drops and snow flakes, the scintillation is the most severe limitation to system performance in an optical channel. An area of application mathematically similar to optical communications is laser radar. In a laser radar, a beam is transmitted through a channel, the atmosphere in our case, reflected by a target and received either at the same location it was transmitted from (monostatic channel) or another location (bistatic channel). Knowledge of the scintillation of the reflected beam could not only help design an appropriate receiving system, but could also give information about the reflecting object that could be utilized in forming its optical signature. Using our recently developed theory, we calculate the scintillation of a Gaussian beam propagating through atmospheric turbulence and reflected by a point target. The double pass scintillation is investigated for monostatic and bistatic channels and results are compared with our experimental data collected by an eight aperture heterodyne detection system.
Interest in the use of optical communications over terrestrial links has greatly increased during the last several years. In many applications, the path is horizontal so the index of refraction structure parameter can be taken as constant. In addition, optical communication channels offer a number of advantages over conventional RF channels. However, due to the short wavelength, the reliability of an optical link can be seriously degraded over that of an RF system by atmospheric scintillation. In particular, scintillation can cause severe fading of the channel. In our analysis here we assume that the refractive index structure parameter Cn2 is constant and use our recently developed gamma-gamma model and the well known lognormal model to consider the fading statistic associated with a spherical wave model for simplicity. The results are similar to a Gaussian-beam wave with perfect pointing. Our analysis show that compared to the gamma-gamma model, the lognormal model predicts optimistic values of probability of fade, underestimate the number of fades per second and consequently does not measure the mean fade time correctly.
Interest in the use of optical communications over terrestrial links has greatly increased during the last several years. In many applications, the path is horizontal so the index of refraction structure parameter can be taken as constant. In addition, optical communication channels offer a number of advantages over conventional RF channels. However, due to the short wavelength, the reliability of an optical link can be seriously degraded over that of an RF system by atmospheric scintillation. In particular, scintillation can cause severe fading of the channel. In our analysis here we assume that the refractive index structure parameter C2n is constant and use our recently developed gamma-gamma model and the well known lognormal model to consider the fading statistics associated with a spherical wave model for simplicity. The results are similar to a Gaussian-beam wave with perfect pointing. Our analysis show that compared to the gamma-gamma model, the lognormal model predicts optimistic values of probability of fade, underestimate the number of fades per second and consequently does not measure the mean fade time correctly.
Laser satellite communication systems are subject to signal fading below a prescribed threshold value owing primarily to optical scintillations associated with the received signal. At large zenith angles between the transmitter and receiver the intensity fluctuations can be much stronger than at small zenith angles, easily exceeding the limitations imposed by weak fluctuation theory. Under such strong conditions the intensity fluctuations cannot be properly modeled by the longitudinal distribution. In this paper we use recently developed expressions for the scintillation index associated with an uplink or downlink path at large zenith angles and calculate the probability of signal fade as a function of threshold below the mean signal level. The analysis presented here is based on both the conventional lognormal model and the gamma-gamma distribution that has recently been proposed for the intensity fluctuations over all conditions of atmospheric turbulence. The gamma-gamma distribution, based on a model that treat intensity fluctuations as a modulation of small-scale scintillations by large-scale scintillations, has two parameters that are naturally linked to the large-scale and small-scale scintillations of the new scintillation model.
A new doubly stochastic probability distribution function (PDF), namely the two parameter gamma-gamma distribution, is developed to describe the intensity fluctuations of a laser beam propagating through turbulent media. The lognormal distribution is the traditional governing distribution in the weak region; however in strong turbulence the intensity of a laser beam is better described by Beckman's PDF and lognormal modified PDF. It is shown in this analysis that the gamma-gamma PDFs in the strong region. The gamma-gamma PDF is compared here with recently published simulation data over a range of atmospheric conditions. Although the parameters of the gamma-gamma PDF are determined based on best fitted curves, the purpose of this analysis is to explore the existence of such a universal PDF. Unlike all other models, the gamma-gamma has a closed form CDF, making it of extreme importance for real time calculations.
Using a recent theory of scintillation, including the development of a probability density function (PDF) for the irradiance, a theoretical analysis is carried out on the system performance of a coherent array receiver in terms of the scintillation index, the implied carrier-to-noise (CNR), and signal fade statistics. We also describe a field experiment in which measured data from a wave reflected from a rough (Lambertian) target located 1000 m from the transceiver was used to calculate the scintillation index, CNR, and probability of fade. The results of this study support the theoretical models.
There is an upper bound on the effective size of receiving aperture for both the improvement in carrier-to-noise ratio and the reduction in signal fading of a conventional coherent detection system due to the atmospheric turbulence-induced finite transverse coherence length of the received laser field for laser radar and communications. But a coherent array detection system, which uses multiple independent apertures/receivers whose IF's are electro-optically co-phased in real time and then added, can overcome the effective aperture limitation and mitigate the signal fading. This paper presents experimental comparison of the performance of an eight-aperture coherent array detection system and the conventional coherent detection system. The field tests were conducted over two-km range (round-trip). The carrier-to-noise ratio and the fade statistics of the IF signals were investigated for both systems. The results show a gain factor of up to six on the mean carrier-to-noise ratio of the IF signal from the eight-aperture coherent array detection system compared to the conventional coherent detection system even though the two systems collected the same power of laser signal. Also shown is a factor of 100,000 reduction in probability of fade of the IF signal.
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