Influence of atmospheric scattering and turbulence on the coherence properties of a laser beam

A Note on the Deterioration of the Coherence Properties of a Laser Beam by Molecular Scattering

“…It will be necessary, however, for the communications engineer (and the radar engineer as well) to examine his particular case to ensure that the effects of molecular scattering are negligible or, if they are not negligible, that they are accounted for. Consortini et al [1963Consortini et al [ , 1964Consortini et al [ , 1965Consortini et al [ , 1966 have performed an interesting and important analysis determining the loss of coherence due to molecular scattering when propagating an ideal-monochromatic, collimated laser beam through the atmosphere. (An ideal-monochromatic laser would have zero width for its spectrum.)…”

“…These are the same assumptions made by Consortini et al [1963, 1964, 1965, 1966]; for these •assnmptions, it is possible to write the signal received as er(t) --- -Eo cos 27n, ct q-x(t) cos 27n, ct q-y(t) sin 27n,,•t ...... (1) where E0 is the received signal amplitude in the absence of molecular scattering, vc is the laser frequency, t is time, and x(t) cos 27n,,t and y(t) sin 27r/•,t are the in-phase and out-of-phase compo.nents of the field scattered by the randomly moving molecules. Also, the standard deviations of x(t) and y(t), designated as (r• and (ru, respectively, are given [Consortini et al, 1963[Consortini et al, , 1964[Consortini et al, , 1965[Consortini et al, , 1966 by E0 --E0 --2 3.1 No/ for L >> R (2) where k is signal wavenumber (=2•/X), n is index of refraction of the 'atmosphere, No is number of molecules per cm 3, and R and x are in centimeters. Under standard atmospheric temperature and pressure conditions, n -1.00029 and No -2.69 x 10 •9.…”

“…It shall be assumed throughout that one is propagating, over a horizontal path through a non-turbulent atmosphere, an idealmonochromatic, collimated laser beam of radius R. Furthermore, it is assumed that the geometric optics condition (x L)•/2 << R is satisfied, where L is the path length and x is the wavelength of the laser signal. These are the same assumptions made by Consortini et al [1963Consortini et al [ , 1964Consortini et al [ , 1965Consortini et al [ , 1966 where E0 is the received signal amplitude in the absence of molecular scattering, vc is the laser frequency, t is time, and x(t) cos 27n,,t and y(t) sin 27r/•,t are the in-phase and out-of-phase compo.nents of the field scattered by the randomly moving molecules.…”

Deterioration of the Coherence Properties of a Laser Beam by Atmospheric Turbulence and Molecular Scattering

“…However, it may be shown [Consortini, Ronchi, Scheggi, and Toraldo di Francia, 1963a] that amplitude fluctuations can be neglected. Accordingly, the amplitude will be assumed to be constant and equal to l.…”

Fluctuations of a Gaussian Light Beam Propagating Through a Random Medium

“…Until the recent appearance of other works, all of these studies were confined to the propagation of an infinite plane wave and spherical wave. Consortini et al (1964) evaluated the fluctuations of a laser beam due to the effect of molecular scattering in the atmosphere. They assumed that laser light is a plane wave within a circular cylinder.…”