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

Abstract

Turbulence and scattering can be considered as chiefly responsible for the deterioration of coherence properties of laser radiation when propagating through the atmosphere.The effect of atmospheric turbulence as well as the effect of molecular scattering (in a quiet atmosphere) on the space and time coherence, respectively, have been theoretically investigated within the limits of ray theory.As a result we found that there is a limiting diameter for the beam cross section beyond which the advantages of the space coherence are largely offset by the intervention of turbulence. On the other hand, the thermal movements of molecules may affect the time coherence (that is, the monochromaticity) of a highly monochromatic 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.)…”

“…designated as (r• and (ru, respectively, are given [Consortini et al, 1963[Consortini et al, , 1964[Consortini et al, , 1965[Consortini et al, , 1966 modulation. The receiver output signal-to-noise ratib (snr) per bit required for such a system is about 11 db for a bit error probability of 10 -6 [Viterbi, 1966].…”

“…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.…”

Propagation of Visible and Infrared Waves in the Atmosphere (Rasprostranenie Vidimykh i Infrakrasnykh Voln v Atmosfere)

“…The authors of article [749] estimated the limiting dimensions of the diameter of the cross section of the light beam beyond which the turbulent movements in the atmosphere sharply decrease the spatial coherence of the beam.…”