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The variance and spectrum of amplitude scintillations due to scattering in both turbulent clear air and rain, are investigated. Included are the important aspect of antenna aperture smoothing with special emphasis on earth-space paths and the equations derived are applicable to system design and remote sensing. A detailed comparison with published experimental results is carried out and the agreement found is good. Two approaches are described in detail: 1) the point receiver classical wave scattering results are modified to include aperture effects, 2) a scalar scattering cross-section approach is combined with the radar equation and the results derived are similar to those of 1). In addition, approach 2) includes the case of rain. Among the results found it is shown that because the scintillation intensity depends on the ratio between the antenna diameter and the diameter of the Fresnel zone in the turbulent region, low elevation paths counteract the tendency to smoothing by large earth station antennas and the scintillations observed remain large. Also pure scattering induced rain scintillations, even in the millimeter region, are in general reduced to an almost negligible level due to aperture smoothing even though for a theoretical point receiver they would be very intense. The time variability of rain attenuation and its polarization dependence as a source of apparent scintillations are also discussed.