THE MUTUAL COHERENCE FUNCTION AND THE BACKSCATTER AMPLIFICATION EFFECT FOR A REFLECTED GAUSSIAN-BEAM WAVE IN ATMOSPHERIC-TURBULENCE

The influence of a modified spectrum of refractive-index fluctuations (that includes a high wavenumber rise as well as inner- and outer-scal e parameters) on the backscatter amplification effect, arising from do uble passage of an optical wave through statistically dependent inhomo geneities of a random medium, is studied here for the case of a Gaussi an-beam wave reflected by a mirror of finite size. A formal expression is first developed for the mutual coherence function, which subsequen tly leads to tractable analytic models for the mean irradiance in the strictly backward direction. When the inner scale and Fresnel zone are of comparable size, the modified spectrum predicts significantly larg er values of the enhancement factor than predicted by the Kolmogorov p ower-law spectrum. It is also shown in this analysis that by varying t he focal length of the mirror the enhancement effects can be greater o r less than those of a plane mirror, depending on focus adjustment. Al l calculations are based on weak irradiance fluctuations using complex ABCD ray-matrix representations for the propagation channel and a gen eralized spectral representation theory for the complex phase perturba tions.