S. F. Clifford

Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation

Recent experiments reveal the high-wave-number form of the power spectrum of temperature fluctuations in turbulent flow. It is precisely this high-wave-number portion of the temperature spectrum that strongly affects optical propagation in the atmosphere. An accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation. An outstanding feature of the model and the observed temperature spectrum is a “bump” at high wave numbers. The accurate model of the temperature spectrum is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length. These results are compared with the predictions of Tatarskii’s spectrum. The bump in the temperature spectrum produces a corresponding bump in the temperature structure function, the variance of log intensity, and the structure function of phase. The accurate model is also used to determine the shape of the structure function of aerosol concentration fluctuations; it is found that this structure function varies as the logarithm of the separation distance for small separations.

Saturation of optical scintillation by strong turbulence

The diffraction theory of optical scintillations has so far failed to describe the propagation of light over paths where the integrated amount of refractive-index turbulence is sufficient to cause saturation of the scintillations. We present a simple, physically based elaboration of the first-order perturbation theory and compare it with observations. Our theory reproduces in detail the observed saturation curve and the observed spatial covariance of the scintillations. In particular, we show why the fine-scale structure of scintillations persists deep into the saturation regime.

Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity, and pressure fluctuations

The dependence of fluctuations in atmospheric absorption and refraction upon fluctuations in temperature, humidity, and pressure is found for infrared frequencies. This dependence has contributions from line and continuum absorption and from anomalous refraction by water vapor. The functions that relate these fluctuations are necessary for evaluating degradation of electromagnetic radiation by turbulence. They are computed for a given choice of mean atmospheric conditions and graphed as functions of frequency in the wavelength range 5.7 μm to radio waves. It is found that turbulent fluctuations in total pressure give a negligible contribution to absorption and refraction fluctuations. Humidity fluctuations dominate absorption fluctuations, but contributions by temperature and humidity affect refraction fluctuations. Sufficiently strong humidity fluctuations can dominate the refraction fluctuations for some infrared frequencies but not for visible frequencies. We examine the variance of log amplitude for scintillation of infrared light to determine whether absorption or refraction fluctuations dominate under several conditions.

Measurements of Atmospheric Turbulence Relevant to Optical Propagation

The aspect of atmospheric turbulence of interest to optical-propagation studies is the variation of refractive index. We demonstrate the application of high-speed temperature sensors to the direct measurement of this variation at optically important scale sizes, as small as a few millimeters. The thermometers, used in pairs with spacings ranging from 3 mm to 1 m, disclose that the turbulence near the ground frequently differs substantially from the Kolmogoroff model, and that the temperature difference does not follow the gaussian probability-distribution function. A model of the turbulent atmosphere containing sharply bounded regions with stronger than average turbulence agrees well with our observations. We also demonstrate the use of a single sensor mounted on an airplane to observe refractive-index variations at heights up to 3 km.

Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra

There is strong evidence that the amplitude of a light wave propagating through turbulence becomes Rayleigh distributed (i.e., the irradiance becomes exponentially distributed) in the limit of strong turbulence, which implies that the log-amplitude variance tends to π2/24. We find that the theory by Clifford et al. [ J. Opt. Soc. Am.64, 148– 154 ( 1974)] for saturation of scintillation by strong refractive turbulence can be made to obey this limit for power-law refractive-index spectra. However, for a nonzero inner scale of turbulence (no matter how small), the theory predicts that log-amplitude variance tends to zero in the limit of strong turbulence. A generalization of the theory is derived that obeys the π2/24 limit for arbitrary refractive-index spectra, a nonzero inner scale being a particular case. The new theory has no arbitrary parameters. Both old and new modulation transfer functions have different behavior for nonzero inner scale at both very large and very small spatial wave numbers when compared with the case of zero inner scale. This differing behavior affects the log-amplitude variance even if the Fresnel-zone size is much greater than the inner scale, provided that the lateral coherence length of phase is less than the inner scale. This differing behavior also applies at all spatial wave numbers if the Rytov variance is strongly affected by the inner scale. For strong (but finite) turbulence strength, the predicted log-amplitude variance is larger for a smaller ratio of Fresnel-zone size to inner scale, which is in quantitative agreement with observations.

Second-order Rytov approximation

Abstract : An explicit and useful formulation of the solution for the second- order Rytov approximation is given. From this solution a condition of validity for the Rytov solution is obtained. It is concluded that, in general, both the Born and Rytov approximations have the same domain of validity.

Relation between irradiance and log-amplitude variance for optical scintillation described by the K distribution

We derive the relationship between log-amplitude (or log-irradiance) variance and irradiance variance for optical scintillation described by a K probability distribution. The results indicate that all observations of maximum variance values, whether log-irradiance or irradiance data are used, are consistent. The K distribution appears to be a reasonable assumption for scintillation in the region of maximum variance. The K distribution is also consistent with data and theory in the very strong refractive turbulence region where exponential irradiance statistics are observed.

Millimeter Wave Atmospheric Turbulence Measurements: Preliminary Results And Instrumentation For Future Measurements

Increasing emphasis is being placed on the study of the effects of atmospheric turbulence on the propagation of millimeter and submillimeter waves because of the potential usefulness of these frequency bands in both military and civilian applications. The characterization of millimeter wave turbulence effects is more complicated than that of the optical propagation case because of a strong dependence on the humidity structure parameter CO2, as well as on the temperature structure parameter Gr2. In addition, there is a dependence on the cross-correlation of these two parameters, denoted by CI-0. Measured results on the effects of atmospheric turbulence on millimeter wave propagation, which include both amplitude and phase fluctuations, are very limited and have generally been obtained incidental to other propagation measurements. However, comparison of these limited experimental results with theory has shown good agreement. This paper compares scattered results measured at 35, 94,140, and 220 GHz to theory, and shows that agreement in most cases is plausible. A future experiment specifically designed to characterize millimeter wave turbulence, with special emphasis on measurement of the pertinent atmospheric parameters, is also described.

The Effects Of Turbulence In Clear And Turbid Atmospheres On Millimeter Wave Propagation

Atmospheric turbulence, which is a readily observed phenomenon at visible wavelengths, also causes fluctuations in intensity and phase at millimeter wavelengths. This paper describes a series of experiments conducted at a site near Flatville, IL which measured these effects at a broad range of MMW frequencies in clear air, rain, fog, and snow. It was found that the maximum rms intensity fluctuations observed were 14% of the mean, while the largest rms angle-of-arrival fluctuations were 36 microradians. Discussions of the experimental arrangement, as well as results obtained in measuring the probability distribution functions of fluctuations, the mutual coherence function, spectral densities, and pertinent atmospheric parameters will be presented.

Millimeter wave propagation turough the turbulent atmosphere

An extensive set of millimeter wave propagation measurements was made during 1983 to 1985 by a team of scientists from NOAAs Wave Propagation Laboratory and Georgia Institute of Technology. Millimeter wave fre quencies from 116 to 230 GHz were propagated over a 1.4 km horizontal path in Flatville, Illinois. Simultaneous, extensive measurements of the meteorology allowed a detailed comparison of the propagation characteristics with the current state of the atmosphere. We report on the observations of millimeter wave propagation characteristics in clear air. Amplitude and phase spectra for propagation in clear air are compared with theory derived using the weak refractive turbulence approximation. Excellent agreement is found when refraction fluctuations dominate over absorption fluctuations. Further, probability density functions appear to be, respectively, lognormal (amplitude) and Gaussian (phase difference).