A useful approximation for the flat surface impulse response

The flat surface impulse response (FSIR) is a very useful quantity in computing the mean return power for near-nadir-orientated short-pulse radar altimeters. However, for very small antenna beamwidths and relatively large pointing angles, previous analytical descriptions become very difficult to compute accurately. An asymptotic approximation is developed to overcome these computational problems. Since accuracy is of key importance, a condition is developed under which this solution is within 2% of the exact answer. The asymptotic solution is shown to be in functional agreement with a conventional clutter power result and gives a 1.25-dB correction to this formula to account properly for the antenna-pattern variation over the illuminated area