Steven F. Clifford

Temporal-Frequency Spectra for a Spherical Wave Propagating through Atmospheric Turbulence

Tatarski has found the frequency spectra for the amplitude, phase, and phase-difference fluctuations of an infinite plane wave propagating through turbulence. Many practical optical beams, used in atmospheric studies, closely resemble point sources, for which the spherical-wave theory is more applicable. The same spectra, calculated for spherical waves, reveal contributions at higher frequencies for amplitude scintillations, nearly identical phase results, and a phase-difference spectrum with no nulls, in contrast with the plane-wave results. Comparison with recent data is shown.

Use of scintillations to measure average wind across a light beam.

We report the successful construction and testing of an optical wind sensor that uses the motion of the scintillation pattern to measure the transverse component of wind blowing across a laser beam. As is done for measuring ionospheric and interplanetary winds, we use a correlation method. However, in our application, the slope at zero lag of the time-lagged correlogram proves to be more useful than the more commonly used delay to the peak. The reason is that, in the atmosphere, irregularities are distributed along the entire propagation path. We use a detector spacing of 0.33 of the diameter of the first Fresnel zone to obtain a nearly uniform weighting function along the path, though the center of the path is still more effective than the ends. The sensor has been used extensively over 1-km and 15-km paths, and field tests of various applications are planned.

Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium

The correlation function of the fluctuations of the depolarized component of a plane wave as a function of the distance between two parallel line-of-sight paths is derived in terms of the index of refraction variations. A first-order solution to the wave equation is found using spectral analysis techniques. The mean square polarization fluctuation is predicted to have a \lambda^{2} dependence, in contrast to the work of another author which showed no wavelength dependence. Some numerical values are calculated and the restrictions on the solutions are discussed. At optical wavelengths the depolarized component is extremely small. From the point of view of minimizing the noise introduced by a turbulent atmosphere, polarization modulation seems attractive compared to amplitude or angle modulation. The problem of determining the angle-of-arrival fluctuations when using a wave optics formulation is discussed. If one accepts the statement that the angle-of-arrival is the normal to the wave front at any point, then the correlation function of the angle-of-arrival is simply related to the correlation function of the phase fluctuations and agrees with the ray optics results.

Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations

Stellar scintillations, when appropriately analyzed, yield information about the turbulence throughout the atmosphere. We describe an instrument involving a 36-cm telescope and an on-line minicomputer that provides, after 20 min of observation, the refractive-turbulence profile of the atmosphere. The height resolution is sufficient to divide the atmosphere into about four independent regions. The principal limitation to greater accuracy and resolution is the nonstationary behavior of the atmosphere during the 20-min observing period.

Phase Variations in Atmospheric Optical Propagation

Temperature structure in the atmosphere, transported by the wind across a laser beam, produces time variations in the optical path length. Using a He-Ne laser (0.6328 μm) on a 70-m propagation path, we measured the optical phase variations at four different spacings, ρ≤30 cm. Simultaneously, a midpath measurement of wind velocity and temperature structure parameter, CT2, provided the necessary meteorological measurements to compare the observed phase structure function with Tatarski’s theoretical curve. We obtained excellent agreement between theory and experiment. Direct measurements of the outer scale of turbulence, taken continuously over a 24-h period at a height of 1.6 m, indicated an average outer scale of 1.3 m with diurnal variations of ±20%. The frequency spectrum of the received phase difference at each of the four spacings is plotted and its implications for the data-sampling rate are examined. The curves obtained exhibit excellent agreement with the predicted spherical-wave phase-difference frequency spectrum.

Optical wind sensing by observing the scintillations of a random scene

We demonstrate the feasibility of using a naturally illuminated scene, such as a hillside or forest, as a passive optical source to measure the path-averaged crosswind between the scene and the observer. The resultant path weighting function for the crosswind cannot be varied arbitrarily, but we can obtain a useful range of weighting functions by adjusting the geometry of the receiver.

Space-time acoustic scintillation analysis: A new technique for probing ocean flows

We present a new approach to the measurement of ocean flows. The technique exploits the coherence of the fine structure in the ocean under the influence of advection. Sound passing through this fine structure is modulated in space and time, so that the evolution and motion of the resulting pattern at a distant receiving plane contains information about the intervening flow field. The details of the fine-scale structure itself may also be recovered, to an extent determined by the complexity of the transmitter and receiver array. Two special cases of oceanographic interest are considered. First, a fully developed turbulent flow, such as that encountered in tidal channels, for which the scale of fine structure contributing to the scintillation field lies within the inertial subrange, and second, the internal wave field more generally applicable to the open ocean. We describe an experimental test of the concept. Sound traveling across a 0.66-km path in Cordova Channel, British Columbia, Canada, is detected by two closely spaced receivers. The flow speed is derived using three separate estimators and the results compared with current measurements obtained from a moored current meter. Agreement between the two types of measurement is excellent.

Ocean flow measurements using acoustic scintillation

A wave propagating in a medium having random fluctuations in refractive index will suffer phase and amplitude perturbations. In the receiving plane, a random interference pattern will appear and this so‐called scintillation pattern will vary in time for two reasons: (1) the decay of the refractive‐index fluctuations producing the amplitude perturbation (eddy decay) and (2) advection of the eddies by the flow. In the case where eddy lifetimes are long compared with the scintillation period, we can derive estimates of flow from a statistical analysis of the scintillation pattern. In this paper, we discuss the propagation theory and report measurements of oceanic flows by analysis of the acoustic scintillation pattern produced by the density fluctuations in the ocean. By mounting a 214‐kHz source and two receivers on opposite sides of a barge such that the axis of propagation is perpendicular to the direction of travel, we induce a known flow rate equal to the barge velocity. We compute the slope of the time...

The range limitation on radar-acoustic sounding systems (RASS) due to atmospheric refractive turbulence

The effects of acoustic refractivity fluctuations on the operation of a radar-acoustic sounding system (RASS) have been calculated. Using the Born approximation, the electromagnetic field scattered from a spherical acoustic pulse whose sphericity is perturbed by transmission through the turbulent medium between the source and scattering volume was determined. The resultant system gain reduction factor changes the dependence on range R of the total received power from an R^{-2} dependence for a homogeneous atmosphere to R^{-18/5} in strong turbulence. This new range dependence can occur at distances of the order of a few hundred meters for sufficiently strong turbulence.

Equivalence of two theories of strong optical scintillation

We demonstrate that the theories of strong irradiance fluctuations of Yura and Clifford et al., although they start from slightly different physical models, produce the same predictions for the behavior of an optical wave propagating through strong turbulence. Both theories predict a saturation of the irradiance variance and that in the saturation regime the amplitude correlation length is equal to the lateral coherence length of the optical wave. The detailed structure of the amplitude correlation functions is also similar, showing a more-rapid decay at the origin and an enhanced tail at large separations in comparison to the results of the weak scattering theory.