Rytov approximation of the irradiance covariance and variance of a retroreflected optical beam in atmospheric turbulence

Abstract

The irradiance (intensity) covariance and variance functions associated with a reflected Gaussian-beam wave from a glint target (retroreflector) are calculated and compared with similar results based on a specular target (smooth finite mirror). Detailed results are presented for the normalized irradiance variance, or scintillation index, of the reflected wave for both types of reflector in an improved model of atmospheric turbulence that incorporates a high-wave-number rise just before the dissipation range in addition to inner–outer-scale parameters. Numerical comparisons show that values of the normalized irradiance variance based on the improved model of refractive-index fluctuations (henceforth called the modified spectrum) can be up to 32% greater than those predicted by the Kolmogorov power-law spectrum when the inner scale is comparable in size with the first Fresnel zone. All analytic expressions derived here are based on weak-fluctuation theory using generalized spectral representations of the complex phase perturbations.