Robert Crabbs

Propagation of a Gaussian-beam wave in general anisotropic turbulence

Mathematical models for a Gaussian-beam wave propagating through anisotropic non-Kolmogorov turbulence have been developed in the past by several researchers. In previous publications, the anisotropic spatial power spectrum model was based on the assumption that propagation was in the z direction with circular symmetry maintained in the orthogonal xy-plane throughout the path. In the present analysis, however, the anisotropic spectrum model is no longer based on a single anisotropy parameter—instead, two such parameters are introduced in the orthogonal xyplane so that circular symmetry in this plane is no longer required. In addition, deviations from the 11/3 power-law behavior in the spectrum model are allowed by assuming power-law index variations 3 < α < 4 . In the current study we develop theoretical models for beam spot size, spatial coherence, and scintillation index that are valid in weak irradiance fluctuation regimes as well as in deep turbulence, or strong irradiance fluctuation regimes. These new results are compared with those derived from the more specialized anisotropic spectrum used in previous analyses.

Deep turbulence propagation of a Gaussian-beam wave in anisotropic non-Kolmogorov turbulence

In the conventional Kolmogorov model of turbulence the turbulent fluctuations of the index of refraction are assumed to be statistically homogeneous and isotropic, and there is a specific mathematical form for the power spectral density of the index of refraction fluctuations. Development of the turbulent theory of passive scalar transfer has shown that although the conventional Kolmogorov spectrum model with a 11/3 power-law index is generally correct near the ground (within the inertial subrange), it constitutes only one part of the more general behavior of passive scalar transfer in a turbulent flow. Hence, deviations from the conventional Kolmogorov model are possible. In this study we develop theoretical models for beam spot size, spatial coherence, and scintillation index that are valid in weak irradiance fluctuation regimes as well as in deep turbulence, or strong irradiance fluctuation regimes. These theoretical models are based on power-law index variations 3

Near-ground vertical profile of refractive-index fluctuations

The most commonly used altitude-dependent model for refractive index fluctuations, over long high-altitude slant paths or ground/space links, is the Hufnagel-Valley model. For the near-ground turbulence portion of the path, this model uses an exponential decay term suggested by Valley to connect ground level turbulence with the original Hufnagel model which was constructed for turbulence above 3 km. However, it has long been observed that refractive-index fluctuations in the first few hundred meters near the ground decrease with altitude raised to the -4/3 power rather than exponentially. Recent and some earlier measurements of refractive-index fluctuations are presented in this paper along with a theoretical modification of the Hufnagel model to account for low-altitude turbulence exhibiting this power-law behavior.

Prediction of the ground-level refractive index structure parameter from the measurement of atmospheric conditions

Evaluation of the methods developed by Bendersky, Kopeika, and Blaunstein1 to predict the refractive index structure parameter from the direct measurement of macroscopic atmospheric conditions were investigated. Measurements of ground-level temperature, relative humidity, wind speed, solar flux, and aerosol loading taken by the University of Central Florida weather station were compared against concurrent measurements of the refractive index structure parameter made by Scintec SLS-20 scintillometers positioned near the weather station. Wind measurements were obtained by three, three-axis sonic anemometers (capable of resolving a three-dimensional wind vector) positioned at heights of 1, 1.5, and 2.5 meters above the ground. Temperature measurements were taken at ground level, and at heights of 1 and 1.5 meters. Data were collected for two days atop Antelope Peak, NV. Collection times covered both daytime and nighttime measurements.

Creating a C n 2 profile as a function of altitude using scintillation measurements along a slant path

Using a three-aperture scintillometer system (TASS) to measure irradiance fluctuations along a slant path, it is possible to create a Cn2 profile model as a function of altitude up to (and possibly beyond) the maximum altitude of a laser beam along the propagation slant path. This technique was demonstrated recently in June 2011 on a beacon beam transmitted between Hollister Airport in California and Fremont Peak at a slant range of 17 km. Although the primary experiment was to test a hybrid optical RF communication system (FOENEX), the beacon signal at the transmitter was intercepted by the TASS from which weighted path-average values of Cn2, inner scale l0, and outer scale L0 were determined. Path-average values were then entered into an algorithm that determines the parameters of the HAP Cn2 profile model (a variation of the HV profile model). In this paper we report on these recent measurements and how this method of constructing the HAP model can be used over other propagation paths.

Atmospheric channel characterization for ORCA testing at NTTR

The DARPA Optical RF Communications Adjunct (ORCA) program was created to bring high data rate networking to the warfighter via airborne platforms. Recent testing of the ORCA system was conducted by the Northrop Grumman Corporation (NGC) at the Nevada Test and Training Range (NTTR) at the Nellis Air Force Range near Tonopah, NV. The University of Central Florida (UCF) conducted a parallel test to measure path-averaged values of the refractiveindex structure parameter, the inner scale of turbulence, and the outer scale of turbulence along the ORCA propagation path from an airborne platform to the ground at Antelope Peak. In addition, weather instrumentation was set up at ground level on Antelope Peak to measure local conditions on the mountain top. This paper presents background information on expected atmospheric conditions for the channel, models that were used by UCF for the measurements, path-averaged values of the three atmospheric parameters, and a Cn2 profile model as a function of altitude.

Using turbulence scintillation to assist object ranging from a single camera viewpoint

Image distortions caused by atmospheric turbulence are often treated as unwanted noise or errors in many image processing studies. Our study, however, shows that in certain scenarios the turbulence distortion can be very helpful in enhancing image processing results. This paper describes a novel approach that uses the scintillation traits recorded on a video clip to perform object ranging with reasonable accuracy from a single camera viewpoint. Conventionally, a single camera would be confused by the perspective viewing problem, where a large object far away looks the same as a small object close by. When the atmospheric turbulence phenomenon is considered, the edge or texture pixels of an object tend to scintillate and vary more with increased distance. This turbulence induced signature can be quantitatively analyzed to achieve object ranging with reasonable accuracy. Despite the inevitable fact that turbulence will cause random blurring and deformation of imaging results, it also offers convenient solutions to some remote sensing and machine vision problems, which would otherwise be difficult.

Near ground surface turbulence measurements and validation: a comparison between different systems

Recently, the number of optical systems that operate along near horizontal paths within a few meters of the ground has increased rapidly. Examples are LIDAR or optical sensors imbedded in a vehicle, long range surveillance or optical communication systems, a LIFI network, new weather monitoring stations, as well as directed energy systems for defense purposes. Near ground turbulence distortion for optical waves used in those systems cannot be well described by conventional turbulence and beam propagation theory. Phenomena such as anisotropy, micro mirage effects, a temporal negative relation between diurnal dips and altitude, and condensation induced measurement errors are frequently involved. As a result, there is a high risk of defective designs or even failures in those optical systems if the near ground turbulence effects are not well considered. To illustrate such risk, we make Cn2 measurements by different approaches and cross compare them with associated working principles. By demonstrating the reasons for mismatched Cn2 results, we point out a few guidelines regarding how to use the general anisotropy theorem and the risk of ignoring it. Our conclusions can be further supported by an advanced plenoptic sensor that provides continuous wavefront data.

Buffer requirements of an optical communication system in atmospheric turbulence

Expressions related to the buffer requirements of an optical communication system in atmospheric turbulence are developed from the channel signal fade time statistics. Laser irradiance data were recorded over the course of one day by a receiving aperture of variable diameter at the Townes Institute Science and Technology Experimentation Facility (TISTEF) 1km laser range located within the Kennedy Space Center at Cape Canaveral, FL. Fade statistics of collected data and scintillometer measurements were compared to the derived model gamma-gamma fade model. Parallel to the laser instrumentation was a commercial scintillometer unit which reported the refractive index structure coefficient, Cn2 and the inner-scale of atmospheric turbulence, l0. The atmospheric parameters inferred from the collected laser data and the commercial instruments were compared. Mean and variance of the fade times were found to agree well with theory for smaller apertures where effects of aperture averaging are not present and in cases where scintillation is weak to moderate. It is suggested that a more appropriate PDF, with a heavier focus on aperture averaging, may be applied in future studies of free space optical communication system fade statistics.

A multi-aperture laser transmissometer for detailed characterization of laser propagation over long paths through the turbulent atmosphere

We present an experimental evaluation of a multi-aperture laser transmissometer system which profiles long-term laser beam statistics over long paths. While the system was originally designed to measure the aerosol extinction rate, the beam profiling capabilities of the transmissometer system also allows experimental observations of Gaussian beam statistics in weak and strong turbulence. Additionally, measurement of long-term beam spread at the receiver allows the system to estimate a path-averaged Cn2, including in strong turbulence regimes where scintillometers experience saturation effects. Additionally, a phase-frequency correlation technique for synchronizing with transmitter ON/OFF modulation in the presence of background ambient light is presented. In application, our ruggedized and weather resistant laser transmissometer system has significant advantages for the measurement and study of aerosol concentration, absorption, scattering, and turbulence properties over multi-kilometer paths, which are crucial for directed energy systems, ground-level free-space optical communication systems, environmental monitoring, and weather forecasting.