J. Richard Kerr

Statistics of speckle propagation through the turbulent atmosphere

We have utilized the extended Huygens-Fresnel principle to make an analysis of the first- and second-order statistics of the received intensity for speckle propagation through the turbulent atmosphere. The treatment includes the effects of the turbulent atmosphere on the laser beam as it propagates to the target and on the speckle as it propagates back to the receiver. Formulations have been developed for both the focused and collimated cases. It is assumed in the analysis that phase perturbation of the waves is the dominant effect due to the atmosphere. Utilizing this assumption it can be shown that the fields at the receiver are marginally Gaussian and that the space-averaged, spatial power spectral density at the receiver is “white.” Because of these results, we have assumed that the field statistics at the receiver are jointly Gaussian. This appears to be a reasonable assumption and allows a closed form solution for the variance and covariance to be derived. For a point detector it is found that the normalized variance is unity and independent of the turbulence strength, and that the transverse correlation length becomes proportional to ρ0 as the turbulence strength increases.

Scintillation measurements for large integrated-path turbulence*

Scintillation measurements are described for a very-large integrated-path turbulence. Measurements were made with simultaneous, coincident beams at 10.6 μm and 4880 A over a 6-km uniform path. The experimental results include (i) the (log amplitude) variance at 10.6 μm showed saturation at a level comparable to that for shorter wavelengths; (ii) the variance beyond saturation at 4880 A decreased for increasing turbulence (Cn2), with an exponent of (−0.48) and no apparent asymptote; (iii) the covariance functions, Cl(r), exhibited the emergence of two scale sizes, as manifested by a rapid initial drop vs (r), and a residual correlation out to large separations; (iv) a corresponding effect was revealed by the spectra of scintillations; (v) receiver-aperture smoothing at 4880 A was very poor, owing to the large residual correlation sizes; and (vi) the amplitude statistics at both wavelengths approximated log-normal distributions.

Experiments on Turbulence Characteristics and Multiwavelength Scintillation Phenomena

Measurements of atmospheric turbulence structure and multiwavelength scintillation statistics are described. The scintillation measurements use coincident virtual point sources, and include log-amplitude variances and covariances, spectra, and receiver-aperture smoothing. These are related to turbulence strength, spectral slope, and inner scale. The saturation of scintillations is found to be wavelength independent. The Kolmogorov atmospheric model breaks down under weak turbulence conditions, and hence the commonly used atmospheric and propagation theories tend to apply under mutually contradictory conditions. The transverse amplitude-correlation length and resultant receiver-aperture smoothing depart from theoretical predictions under strong scintillations. Scintillation spectra show much data spread but averages support the Taylor hypothesis. Short-path optical determinations of turbulence strength are seriously affected by nonzero inner scales of turbulence. Correlations of multiwavelength scintillations vs time indicate nonuniformity of both turbulence spectra and strength over the path.

Effect of the log-amplitude covariance function on the statistics of speckle propagation through the turbulent atmosphere

The extended Huygens-Fresnel principle has been used to make an analysis of the first- and second-order statistics of the received intensity for speckle propagation through the turbulent atmosphere. These formulations include the effects of the log-amplitude covariance as well as the wave structure function and represent a significant extension of previous work. It was found that, with the inclusion of the log-amplitude covariance, the normalized variance is dependent on the turbulence strength and rises above unity.

Experimental effects of finite transmitter apertures on scintillations

The use of large transmitter apertures has been theoretically predicted to result in a substantial reduction of laser-beam scintillations under certain conditions. Experiments have been conducted on transmitter-aperture effects through turbulence, including photographic studies for qualitative interpretation, and measurements of log-amplitude variance, covariance, probability distributions, and the spectra of scintillations. It was found that the predicted reduction imposes strict requirements on transmitter optical adjustments, and will not be realized in the presence of significant beam wander. In the case of either transmitter misadjustment or strong turbulence, the beam at the receiver plane consists of a proliferation of transmitter-diffraction-scale patches, with large attendant scintillations. The theory suggests a novel means of reducing scintillations arising from a thin layer of turbulence at the tropopause in earth-to-space systems. Comparisons of the beam-wave analyses with results from a recent theory of reciprocity suggest a limited range of validity for the analytical predictions.

Turbulence effects on target illumination by laser sources: phenomenological analysis and experimental results

A phenomenological and analytical description is given of atmospheric turbulence effects oh laser beam waves, including the improved target irradiance characteristics resulting from cancellation of turbulenceinduced beam wander through reciprocity tracking. The mechanisms related to the mean irradiance include diffraction, wander, and wavefront distortion (beamspread), while irradiance-fading is caused by wander, first-order scintillation, and coherent fading. The phenomenological description unifies the often fragmentary and inconsistent treatment of beam wave phenomena found in the literature and is sufficiently accurate for engineering purposes. It will be shown that wander-cancellation and control of the transmitter beam diameter can result in substantial improvements in target illumination. The analyses are compared with experimental data for the detailed statistical and spectral characteristics of on-axis target irradiance.

Transmitter-Size and Focus Effects on Scintillations*

We present generalized numerical predictions of the effects of transmitter-aperture size and divergence on the on-axis scintillations of a laser beam propagating through a turbulent stmosphere, utilizing analytical results obtained from the literature. The sharp reduction of scintillation that has been predicted for a large, focused beam is shown to depend very critically upon the focus adjustment; small misadjustments result in increases by orders of magnitude. This also implies that diffraction-limited optics may be required. This requirement, together with the implications of turbulent beam-wander and spreading effects, suggest that the predicted reduction is of little practical significance. We also present the conditions necessary for obtaining point-source results in scintillation experiments.

Optical propagation in laboratory-generated turbulence

A versatile and useful facility for simulating the effects of atmospheric turbulence on optical propagation is described, and the relevant system parameters are characterized. The scattering medium is a turbulent liquid (ethanol) with the turbulence created by unstable convection generated by a strong vertical thermal gradient. Measurements of the structure function and the spatial spectrum of the resulting refractive index fluctuations are presented and compared with the theoretically predicted forms. The effects of this scattering medium on laser beam propagation are determined and compared to the first-order Rytov theory. In particular, probability density functions, moments, and spatial covariance functions of the irradiance resulting from propagation through the system with a variety of turbulence levels and path lengths are presented.

Generalized Analysis of the Dispersion of Modulated or Time-Varying Light

The dispersion of modulated or time-varying light is analyzed for an arbitrary disperser, general modulation, gaussian and incoherent illumination, and nonideal optical systems. The conditions for quasi-static response are examined in detail, and a stricter condition than that previously published is derived. The practical implications of this condition are discussed. The moments of the intensity distribution are derived for the general case. The analysis is related to specific dispersing elements.

Research Progress On Speckle Propagation Through The Turbulent Atmosphere

The effect of speckle after propagation through the turbulent atmosphere is an important consideration in remote sensing, coherent imaging through the atmosphere, optical coherent radar, speckle interferometry and COAT systems. In order to assess the effects of speckle, first and second order statistics and the temporal power spectral density for the received intensity are needed. A review of the current state of knowledge and new work in progress will be presented.