Ronald L. Phillips

Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence

It is well know that free-space laser system performance is limited by atmospheric turbulence. Most theoretical treatments have been described for many years by Kolmogorovs power spectral density model because of its simplicity. Unfortunately, several experiments have been reported recently that show that the Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular, in portions of the troposphere and stratosphere. We present a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/3, and a generalized amplitude factor instead of constant value 0.033. Using this new spectrum in weak turbulence, we carry out, for a horizontal path, an analysis of long-term beam spread, scintillation index, probability of fade, mean signal-to-noise ratio (SNR), and mean bit error rate (BER) as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than =11/3, but not for alpha close to =3, there is a remarkable increase of scintillation and consequently a major penalty on the system performance. However, when alpha assumes a value close to =3 or for alpha values higher than =11/3, scintillation decreases, leading to an improvement on the system performance.

Speckle propagation through atmospheric turbulence: Effects of a random phase screen at the source

By using ABCD ray matrix theory and a random phase screen located near the source, analytic expressions are developed for the mutual coherence function and scintillation index of a Gaussian-beam wave propagating through weak atmospheric turbulence in both the pupil plane and image plane of a receiving. The phase screen model that we use is based on a previous double-pass analysis by the authors for analyzing speckle propagation from a rough target in a lidar system. In the present context, it serves as a model for a partially coherent Gaussian-beam wave that is currently used in laser communications. The effect of partial coherence (induced by a diffuser) on the scintillation index of the beam in the presence of weak atmospheric turbulence is investigated as a function of the correlation length of the diffuser and the propagation distance.

Fading effects due to scintillation caused by atmospheric turbulence in a wireless optical communication link

Fading due to scintillation has been measured at path lengths of up to approximately 13.3 Km. Theoretical fading and aperture averaging models based on the gamma-gamma distribution were used to generate predictions of the fade parameters. Data collected at the optical receiver was compared to the theoretical values to determine if the fade theory remains valid over greater distances then has previously been investigated in a tropical environment.

Laser radar in turbulent atmosphere: effect of target with arbitrary roughness on second- and fourth-order statistics of Gaussian beam

Analytic expressions for the mutual coherence function and the scintillation index of the lowest order Gaussian beam as a function of target roughness are developed for a bistatic configuration in weak and strong atmospheric turbulence. Results are based on Rytov theory and Kolmogorov spectrum model. The surface roughness is modeled by a thin complex phase screen with a Gaussian spectrum. The limiting cases of perfectly smooth and Lambertian targets are deduced. The particular cases of incident spherical and plane waves are also considered.

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.

Near ground measurements of beam shaping and anisotropic turbulence over concrete runway and grass range

Researchers from the University of Central Florida recently carried out a series of measurements over a concrete runway and a grass range using a 632.8 nm Gaussian beam propagated for 100 or 125 m at a height of 2 m. Mean intensity and scintillation index contours varied significantly throughout these measurements in ways that corresponded to more than simple isotropy or anisotropy of optical turbulence. A simple theory is developed to show the effect of a nonlinear index of refraction gradient in addition to the possibility of anisotropic turbulence. Theoretical contours are compared to experimental results which seem to indicate the presence of a beam shaping phenomena near the ground in addition to anisotropy.

Analysis of optical turbulence evolution over the Space Shuttle Landing Facility

Ground to air temperature gradients drive the creation and evolution of optical turbulence in the atmospheric boundary layer. Ground composition is an important factor when observing and measuring the generated optical turbulence. Surface roughness and thermal characteristics influence the formation of optical turbulence eddies. The Space Shuttle Landing Facility (SLF) at The Kennedy Space Center offers a unique opportunity to measure the generation and evolution of these turbulent eddies, while also providing a temperature gradient “Step Function” after which turbulence evolution can be analyzed. We present the analysis of data collected on the SLF during May of 2018. Mobile towers instrumented with sonic anemometers are used to examine the statistics of turbulent eddies leaving the increased heat gradient of the runway. This data is compared to an optical scintillometer and other local weather station data. Point and path average Cn2 data are calculated and attention is given to turbulence spectrum as a function of height above ground.

Propagation Through Random Phase Screens

Overview: The notion of a thin turbulent layer along a propagation path has been used for many years to model radio wave propagation through the ionosphere, scattering from a rough sea surface, or propagation of an optical wave between a satellite and the Earths surface, among other settings. Such a turbulent layer is widely known as a phase screen, although this term generally refers to only a âx80x9cvery thinâx80x9d turbulent layer. In this chapter we develop a general model for a layer of optical turbulence between a transmitter and receiver along a horizontal propagation path. If the layer is fairly thick,x80x9d it is treated much like an extended medium. However, when the ratio of the turbulent layer thickness to the propagation distance from the turbulent layer to a receiver is sufficiently small, we classify the turbulent layer as a thin phase screen. Basically, this means that only the phase of the optical wave is disrupted as it passes through the turbulent layer - x80x94not its amplitude. Consequently, it is not necessary to integrate over the thickness of the layer, thus simplifying some of the expressions for various statistical quantities concerning a laser beam propagating over a path in which only a thin phase screen exists.nnIn our analysis we neglect the presence of extended optical turbulence and concentrate on the effects generated by the phase screen itself, taking into account the placement of the screen with respect to the transmitter and receiver. It is a straightforward extension of our model to embed the phase screen directly in an extended turbulence medium, although we dont do so here. Statistical quantities, like the mutual coherence function and scintillation index developed in Chaps. 6 and 8 for optical turbulence everywhere along the propagation path, are calculated here for the case of a single phase screen. In particular, we show how proper placement of the phase screen between the input and output planes can lead to essentially the same numerical results as that obtained from an extended turbulence model. In addition, we briefly treat the case of multiple thin phase screens that can be arbitrarily located along the propagation path. All results in this chapter, however, are limited to weak irradiance fluctuations for which the Rytov approximation is valid.

Classical Theory for Propagation Through Random Media

Overview: In this chapter we introduce the stochastic Helmholtz equation as the governing partial differential equation for the scalar field of an optical wave propagating through a random medium. However, we provide only the foundational material here for the classical methods of solving the Helmholtz equation. It is interesting that all such methods are based on the same set of simplifying assumptions - x80x94backscattering and depolarization effects are negligible, the refractive index is delta correlated in the direction of propagation (Markov approximation), and the paraxial approximation can be invoked.nnThe Born and Rytov perturbation methods for solving the stochastic Helmholtz equation are introduced first. Whereas the Born approximation has limited utility in optical wave propagation, the Rytov approximation has successfully been used to predict all relevant statistical parameters associated with laser propagation throughout regimes featuring weak irradiance fluctuations. We also illustrate that the Rytov approximation can be generalized to include wave propagation through a train of optical elements that are all characterized by ABCD matrix representations. Methods applicable also under strong irradiance fluctuations are briefly discussed here but formulated in greater detail in Chap. 7. These methods are the parabolic equation method, which is based on the development of parabolic equations for each of the statistical moments of the field, and the extended Huygens-Fresnel principle.nnEarly probability density function (PDF) models developed for the irradiance of the optical wave include the modified Rician distribution, which follows from the Born approximation, and the lognormal model, which follows directly from the first Rytov approximation. Of these two PDFs, only the lognormal PDF model compares well with the lower-order irradiance moments calculated from experimental data under weak fluctuation conditions. Hence, in this regime it has been the most often-used model for calculating fade statistics associated with a fading communications channel. Nonetheless, more recent investigations of the lognormal PDF suggest that it may be optimistic in predicting fade probabilities, even in weak fluctuation regimes.nnWe end the chapter with a modification of the Rytov method called the extended Rytov theory that utilizes the two-scale behavior of the propagating wave encountered in regimes of strong irradiance fluctuations. The formalism of the method presented here permits the development of new models for beam wander and scintillation in subsequent chapters that are applicable under strong fluctuations.

Fourth-Order Statistics: Strong Fluctuation Theory

Overview: In this chapter we extend our examination begun in Chap. 8 of various fourth-order statistical quantities, like the scintillation index and the irradiance covariance function, to the strong fluctuation regime. We develop separate scintillation models for plane waves, spherical waves, and Gaussian-beam waves. These models evolve from the extended Rytov theory (Chap. 5) by taking into account the role of decreasing spatial coherence of the optical wave as it propagates further and further through the random medium. The net result is a modification of the atmospheric spectrum to an âx80x9ceffective spectrumâx80x9d arising in the form of a multiplicative spatial filter function that eliminates the effects of moderate-sized refractive-index scales (or turbulent âx80x9ceddiesâx80x9d) under strong fluctuation conditions. This is similar to the use of spatial filters in adaptive optics applications to eliminate piston and tilt effects (among others) in the received wave front.nnUnder the general irradiance fluctuation theory developed here, the covariance function acquires a two-scale behavior in the strong fluctuation regime, consistent with earlier theories. From the frozen-turbulence hypothesis, we can infer the temporal covariance function from which we calculate the temporal spectrum of irradiance fluctuations. As shown in Chap. 8, the spectral width is determined by the transverse wind velocity scaled by the first Fresnel zone under weak irradiance fluctuations, but the power becomes concentrated at higher and higher frequencies as the strength of turbulence increases. Nonetheless, under strong irradiance fluctuations the two-scale behavior in the covariance function is also evident in the power spectrum.nnIn the last two sections, we review probability distribution models proposed for the irradiance fluctuations, including the gamma-gamma distribution that is theoretically valid under all fluctuation conditions. A favorable characteristic of the gamma-gamma distribution is that it has two parameters that are completely determined by atmospheric conditions.