Refractive Index Structure Function Research Articles

Role of the outer scale of turbulence in atmospheric degradation of optical images

The atmospheric degradation of optical images is investigated by assuming the refractive-index structure function to be independent of the distance between two correlation points when such distance is larger than the outer scale (Von Karman model). It is found that, in most practical cases, the atmospheric turbulence puts a limit to the resolution as predicted by the 2/3-power law, however, only when the turbulence is sufficiently strong. The parameter distinguishing strong from weak turbulence turns out to be the limit value of the wave structure function Dw (∞) for infinite distance. Weak turbulence, with Dw (∞) ≲ 20, does not put a limit to the resolution of an optical system.

Diurnal cycles of the refractive index structure function coefficient

The refractive index structure function coefficient Cn2 is an atmospheric parameter needed to describe scintillation and small-scale phase fluctuations of electromagnetic radiation propagated in the atmospheric surface layer. Since systematic direct measurements of Cn for many climates and seasons are not available, an indirect method is developed in which Cn is calculated from the estimates of sensible and latent heat flux components of the surface energy budgets. This indirect method is primarily for heights less than 4 meters, because low intermittency and a near-unity value of the ratio of the eddy diffusivity of heat to that of momentum are assumed. Diurnal variations of Cn at several heights above land for six combinations of climates, seasons, and surface conditions are calculated from heat fluxes measured by different investigators at many locations for moderate to high wind velocities. These predictions of Cn agree well with some direct measurements of Cn when assumptions of nearly ideal weather and sites are met. The effect of water vapor on Cn is usually an increase of about 16/β%, where β is Bowen's ratio, and thus is usually negligible above dry land but can be significant above wet surfaces.

Log-Intensity Correlations of a Laser Beam in a Turbulent Medium

The log-intensity correlation for any two points in the cross section of a collimated Gaussian laser beam is calculated in the geometrical optics approximation. The log-intensity correlation is found to.be a function of more than the separation distance between the two points. The special case of autocorrelation leads to a result that is identical to that given by Ho if diffraction effects are ignored. The autocorrelation function indicates a new method for determining the inner scale of turbulence and the refractive index structure function coefficient which does not depend upon meteorological measurements of C(N)(2).

Atmospheric Degradation of Holographic Images*†

The resolution of images formed from turbulence-degraded lensless Fourier-transform holograms is analyzed for gaussian and exponential refractive-index structure function models, first by a geometrical-optics method and then by Schmeltzer’s series-expansion method, under the assumption that the random log-amplitude and phase perturbations across the entrance pupil of the recording apparatus are locally stationary processes with gaussian statistics. Both long and short exposures are treated.The resolution of turbulence-degraded holographic images is governed primarily by a function m2(r1), for which analytical expressions are derived and results of experimental measurements are given. The analytical results obtained for m2(r1) by the geometrical-optics method are identical with those obtained by Schmeltzer’s series-expansion method. The measurements were made by an interferometric technique for horizontal atmospheric propagation paths of 86 and 542 m. In addition, holographic images of an extended object were obtained for the 86-m path.