Resolution of a Radar Antenna for Distributed Targets

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Abstract
The measured reflectivity of a distributed target is given by the integration of reflectivity over the radar antenna radiation pattern. Assuming a Gaussian form for the main antenna lobe and fairly simple exponential and Gaussian distributions of true reflectivity, the measured reflectivity is computed as a function of sharpness of reflectivity relative to antenna beam size. The resolving power of the radar antenna for measurement of a single reflectivity feature to a specified accuracy, or for discrimination between two identical features, is also a function of relative sharpness of the target reflectivity field. Relative sharpness is defined by the product of reflectivity gradient, range, and half-power beam radius (exponential case) or of derivative of reflectivity gradient, range squared, and half-power beam radius squared (Gaussian case). Relative sharpness is also a determining factor of the size of the area in which side-lobe errors may be considered negligible. A method is developed for recovery of the gross structure of true reflectivity from measurements. The intersection of the true reflectivity distribution, so derived, with a standard equivalent reflectivity factor of 0.1 mm6 m−3 is suggested as an objective estimate of cloud tops measured by radar.

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