Antenna aperture effects on measurements of propagation through turbulence

The first Born approximation is applied to propagation of a spherical wave through a layer of random irregularities to an aperture antenna. The effect of the receiving aperture on measurements of the variance of in-phase and quadrature components of the received signal, and the variances of their spatial derivatives is determined. In the weak scattering limit, these quantities are related to the scintillation index, mean-square phase fluctuations, mean-square angle-of-arrival fluctuations, and fading rates. Physical situations corresponding to the generic problem considered here include satellite communication through ionospheric fluctuations, solar wind observations, observations through irregularities caused by instabilities in barium release clouds, etc. Numerical results are presented which show the aperture effect for irregularities with power law spectra of the form
S(K) \propto (1 + K^{2}L_{0}^{2})^{-N/2}
for values of the spectral index
N
ranging from 3 to 5 and for many ratios of the three lengths, turbulent outer scale
L_{0}
, aperture radius, and Fresnel length. These results are presented in convenient form for estimating the aperture effect in many cases of interest. Aperture effects (aperture smoothing) generally dominate the behavior of the spatial derivatives, while a nearfield effect is shown which causes enhancement of the variance of the in-phase fluctuations over the value predicted ignoring the receiving aperture. It is suggested that this effect may be useful to explain some aspects of observed gigahertz scintillation.