The mean echo and echo cross product from a beamforming interferometric altimeter and their application to elevation measurement

This paper describes the echo from a beamforming interferometric altimeter from a uniformly scattering surface inclined at an angle to a sphere, underlain by a uniformly scattering volume. The rough "surface" impulse response and the echo and interferometric cross product are determined as functions of the beam direction and the vector surface gradient. These expressions are used to determine the multilooked echo and interferometric phase from such a system. The "effective" number of looks and the multilooked echo coherence, which determine the statistics of the echo power and the interferometric phase, are defined. The dependence of the multilooked echo power and interferometric phase are investigated as functions of the surface vector gradient, surface roughness, volume scattering, and SNR. These behaviors are illustrated using values based on a practical system. The precision of the elevation measurement is examined in the light of the effective number of looks and the coherence of the multilooked echo and cross product. Some conclusions concerning the practical recovery of the range from the echo power are discussed.