The Rough Surface Impulse Response of a Pulse-Limited Altimeter With an Elliptical Antenna Pattern

This letter describes the impulse response of a pulse-limited altimeter with an elliptical antenna pattern from a uniformly rough surface inclined at an angle to a sphere or, equivalently, from spherical surface and mispointed antenna. An integral for the impulse response is given, and analytic forms for the special cases of a mispointed circular antenna and a nadir-pointed elliptical antenna are derived. An analytic approximation for the case of small ellipticity and small surface gradient (or mispointing) are also given. The letter is illustrated with numerical examples that show the general effect of ellipticity on the impulse response. It also shows that in the practical case of the elliptical CryoSat-2 satellite SIRAL antenna, the analytic approximation is sufficiently accurate to provide a correction for the ellipticity for CryoSat-2 echoes from the ocean surface.