Current mathematical models describing laser propagation through the atmosphere were developed for terrestrial
environments. An atmospheric index of refraction power spectrum specifically tailored to the marine environment has
been created and applied to scintillation theory. Optical measurements of a diverge laser beam propagating in a marine
environment, in combination with scintillation theory and a numerical scheme, were used to infer the refractive index
structure parameter, Cn2, along the propagation paths. The analysis was repeated for both marine and terrestrial
theoretical scintillation expressions, each resulting in one set of inferred Cn2-values. In the moderate-to-strong
fluctuation regime, the inferred Cn2-values based on marine theory were about 20% smaller than those based on
terrestrial theory, but a minimal difference was observed in the weak fluctuation regime.
The performance of lasercom systems operating in the atmosphere is reduced by optical turbulence, which causes irradiance fluctuations in the received signal. The result is a randomly fading signal. In this work, fade statistics obtained from experimental data were compared to theoretical predictions based on the lognormal and gamma-gamma distributions. The probability of fade and expected number of fades per second were calculated from the irradiance fluctuations of a Gaussian beam wave propagating through the atmosphere on a horizontal path, near ground, in the moderate-to-strong turbulence regime. Irradiance data was collected simultaneously at three receiving apertures of different size. Atmospheric parameters were inferred from the measurements and used to calculate the parameters for the theoretical distributions. A new integral expression for the expected number of fades based on the gamma-gamma distribution was developed and shown to make a significant difference compared to the existing approximation.
April 2005, a laser propagation experiment was conducted over a 470m horizontal maritime path. Scintillation
measurements of a divergent Gaussian beam wave were taken simultaneously for different receiver aperture sizes.
Terrestrial scintillation theory combined with a numerical algorithm was used to infer the atmospheric parameters Cn2
and lo from the optical maritime scintillation measurements. This paper presents the initial results.
In an attempt to mitigate the effects of the atmosphere on the coherence of a laser beam, interest has recently been shown in changing the beam shape to determine if a different power distribution at the transmitter will reduce the effects of the random fluctuations in the refractive index. We develop a model for the scintillation index of a flattened Gaussian beam and compare this with that of the standard TEM00 Gaussian beam. We verify our results by comparison with a computer simulated model for the flattened beam.
The lognormal and gamma-gamma distributions are compared to simulated and experimental data of the irradiance
fluctuations of a Gaussian beam wave propagating through the atmosphere on a horizontal path, near ground, in the
moderate-to-strong turbulence regime. Irradiance data was collected simultaneously at three receiving apertures of
different size. Atmospheric parameters were inferred from the measurements and used to reproduce the experimental
data with numerical simulations and calculate the parameters for the theoretical probability density functions (PDFs).
The simulation values agree well with the experimental data for all three aperture sizes, while the support for the
theoretical PDFs depends on the size of the receiving aperture.
Scintillation is one of the most common statistics in the literature of mathematical modeling of laser propagation through random media. One approach to estimating scintillation is through the Rytov approximation, which is limited to weak atmospheric turbulence with the standard Kolmogorov spectrum. Recently, a modification to the Rytov approximation was developed. Through a filter function approach, the new results for scintillation are valid for moderate to strong fluctuations along a horizontal path. To date, expressions governing scintillation for plane, spherical, and Gaussian beam waves has been developed for horizontal propagation paths. For the special cases of plane and spherical waves, expressions have been developed for slant paths. In this paper, an expression governing scintillation of a Gaussian beam along an uplink slant path valid in all regimes of turbulence is presented.
In May 2004 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation, the Office of Naval Research and the University of Central Florida. A 45 mm divergent Gaussian beam was propagated along a horizontal 1500 meter path approximately 2 meters above the ground. At the receiver were 3 apertures of diameter 1mm, 5mm, and 13mm. The scintillation was measured at each aperture and compared to scintillation theory, recently developed for all regimes of optical turbulence. Three atmospheric parameters, Cn2, lo and Lo, were inferred from these optical measurements. Simultaneously, a commercial scintillometer, which recorded values for Cn2, was set up parallel to the optical path. In this paper, a numerical scheme is used to infer the three atmospheric parameters and comparisons are made with the Cn2 readings from the scintillometer.
Mean irradiance data from a field experiment conducted jointly by the Australian Defence Science and Technology Organisation, the Office of Naval Research, and the University of Central Florida is presented. The experiment was conducted in May 2004 in Adelaide, Australia. The propagation path was characterized by conditions of moderate to strong irradiance fluctuations. The data is compared to existing theoretical results and a new theoretical result developed in this paper. The new theoretical result is based on a modified Rytov method that extends the validity of the Rytov method into moderate to strong irradiance fluctuation conditions.
While the wave structure function has been analytically calculated for a variety of beam types, recent work has begun the exploration of higher-order beams and partially coherent beams. For these waves, no analytic wave structure function has been developed. By extending the well known split step phase screen simulations, we have developed a method of numerically simulating the wave structure function. We present the methods and results of this simulation technique, and describe its applicability to general beams.
It is well known that the transmission of an optical signal through the turbulent atmosphere results in random phase fluctuations. In turn, these random phase fluctuations impart a random frequency fluctuation onto the optical signal. As laser radar (lidar) systems rely on the evaluation of micro-Doppler frequency shifts of the reflected optical wave to determine certain target characteristics, it is critical to understand the impact of the atmospheric induced frequency fluctuations. Additionally, lidar systems used for defense applications would typically operate in moderate to strong atmospheric turbulence conditions. Hence, for such applications, it is necessary to develop models describing atmospheric induced frequency fluctuations of an optical wave that are valid in all regimes of optical turbulence. In this paper, we present preliminary results for a model of atmospheric induced frequency fluctuations for the double pass propagation problem in weak optical turbulence conditions and a possible method for extension of these results into moderate to strong turbulence conditions.
The authors have recently developed analytical expressions governing atmospheric induced frequency fluctuations of an optical signal along a horizontal path. Expressions valid in conditions of weak irradiance fluctuations were derived using the Rytov approximation and extended to conditions of moderate to strong irradiance fluctuations via an effective atmospheric spectral model. However, many optical systems, such as coherent ground to satellite communication, imaging, and
astronomical systems, operate in a slant path setting. In this paper, the horizontal path frequency variance results have been extended to slant path scenarios. Integral expressions for one-way slant path, both uplink and downlink, are presented. Additionally graphical results for various operational settings are also provided.
Recently, new theory governing laser beam scintillation was developed for all regimes of optical turbulence. This theory is based on the Rytov approximation but modified with a filter function that eliminates intermediate scale sizes that do not contribute to the refractive and diffractive effects of propagation. This modification extends the validity of the Rytov approximation into moderate to strong regimes as is evident by the agreement with experimental data. In this paper this scintillation theory is summarized and new expressions governing phase fluctuations are presented. The phase structure function is then compared with previous experimental data.
Recently, a heuristic model for scintillation in moderate to strong turbulence was developed. It is based on the idea of filter functions that eliminate scale sizes that lose their ability to affect a laser beam as it propagates. This approach allows the validity of the Rytov approximation to be extended into moderate to strong turbulence. In this paper, we investigate applying this theory to second order statistics.
Recently, new theory governing laser beam scintillation was developed for all regimes of optical turbulence. This theory is based on the Rytov approximation but modified with a filter function that eliminates intermediate scale sizes that do not contribute to the refractive and diffractive effects of propagation. This modification extends the validity of the Rytov approximation into moderate to strong regimes as evidenced by the agreement with simulations and experimental data. In this paper we apply this theory to the phase covariance and new expressions governing phase fluctuations are presented. The phase structure function is then compared with previous experimental data.
In this paper an analytic expression governing the two-frequency mutual coherence function (MCF) for a Gaussian beam wave is developed for moderate to strong fluctuations. Using a temporal moments approach combined with this new expression for the MCF, expressions governing pulse statistics (delay and broadening) are developed. These general analytic results are compared with previous results in special cases.
It is well known that laser beams spread as they propagate through free space due to natural diffraction, and that there is additional spreading when optical waves propagate through atmospheric turbulence. Previous studies on Gaussian beams have mainly involved the lowest order mode (zero- order). The study of higher order mode Gaussian beams has involved Hermite-Gaussian and Laguerre-Gaussian beams for rectangular and cylindrical geometry respectively. These studies have developed expressions for the field and intensity in free space in addition to developing new definitions of beam size in the receiver plane for the higher order modes. In this paper we calculate the mean intensity of higher order mode Gaussian beams propagating through atmospheric turbulence, and, based on previously developed definitions for beam radius, we calculate the additional beam spreading due to random media. It is shown that higher order mode Gaussian beams experience less percentage of additional broadening due to atmospheric fluctuations than the zero order mode beams.
Renewed interest in laser communication systems has sparked development of useful new analytic models. This book discusses optical scintillation and its impact on system performance in free-space optical communication and laser radar applications, with a detailed look at propagation phenomena and the role of scintillation on system behavior. Intended for practicing engineers, scientists, and students.
By using a recently developed theory of scintillation that is valid under fluctuation conditions that include the focusing and saturation regimes, we develop a general model for predicting power fluctuations (or aperture averaging) over a finite-size collecting aperture. In addition, we calculate the covariance function and implied temporal spectrum of such power fluctuations. Increasing the size of the collecting aperture decreases the high frequency content of the irradiance spectrum.
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 model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed here under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The resulting scintillation index from this theory has the form (sigma) 12 equals (sigma) x2 + (sigma) y2 + (sigma) x2 (sigma) y2 where (sigma) x2 denotes large-scale scintillation and (sigma) y2 denotes small-scale scintillation. By applying a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, tractable expression are developed for the scintillation index of a Gaussian beam wave that are valid under moderate- to-strong irradiance fluctuations. The expected scintillation of Gaussian beams predicted by these analytic models is compared to the experimental data previously published.
In this paper, analytic expressions for the temporal broadening of narrowband space-time Gaussian pulses propagating in weak optical turbulence are derived for both near and far fields. General results are presented for nominal parameter values characterizing laser communication through the atmosphere. Specific examples are calculated for both upper atmosphere UAV-UAV cross-links and uplink/downlink satellite communication paths. It is shown that for both the near and far fields, pulses on the order of 10 - 20 femtoseconds can broaden by more than 100% whereas pulses greater than 500 femtoseconds have negligible broadening.
A general expression is developed for the wave structure function (WSF) of a Gaussian beam wave using a modified spectrum of refractive-index fluctuations that features a high wave number bump. Effective beam parameters that characterize the turbulent spot size and phase front radius of curvature are used to formally extend this expression into the strong turbulence regime. The implied spatial coherence length from this expression for the WSF is less than that predicted by conventional spectral models whenever the Fresnel zone size is much larger than the initial beam radius. In the case of a focused beam, the predicted coherence length is slightly greater than that predicted by conventional spectral models when the Fresnel zone size is much smaller than the initial beam radius. The presence of the spectral bump appears to have little effect on coherence when the Fresnel zone size and initial beam radius are of comparable size.
Expressions are derived for the mutual coherence function (MCF) for a Gaussian beam wave using a bump spectral model for refractive-index fluctuations with inner scale parameter but assuming infinite outer scale. The analysis is based on both weak and strong fluctuation theories, and comparisons are made between theories where possible. The presence of a bump in the spectrum is shown to slightly increase the beam spread and reduce implied spatial coherence length.