Question: Explain how it is possible for the horizontal resolution of a radar altimeter to exceed the limit set by diffraction at the antenna, provided that

Explain how it is possible for the horizontal resolution of a radar altimeter to exceed the limit set by diffraction at the antenna, provided that the pulse duration t_pis short enough, and derive the result that the resolution is given by 2(cHt_p)^1/2, where c is the speed of light and H is the range to the surface. (Ignore any effects arising from the Earth€™s curvature.)
Hence show that the vertical resolution of a pulse-limited radar altimeter is given by

1/4 64Hp²

where v is the speed of the platform relative to the Earth€™s surface and pis the pulse repetition frequency. Estimate the best vertical resolution achievable from a space-borne radar altimeter if t_p > 3 ns and p < 2 kHz.

1/4 64Hp

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