This paper derives the far-field back-scatter radar cross section of a spherical shell segment for nose-on (propagation vector along axis of symmetry) and near nose-on aspects. The method used involves computing the specular contribution by geometrical optics, and adding to it the edge-diffracted term. This edge term is determined from the Sommerfeld half-plane solution. The result obtained is valid when

(where

is the edge radius), for segments smaller than a hemisphere. For nose-on incidence, it is shown that the edge contribution has the same value as the well-known specular contribution. An important consequence of this is strong interference between these two contributors. Comparison of this result with experiment shows that it is in good agreement. It is found to be much more accurate than the ordinary Physical Optics result.