Abstract
This is a review of Glauber’s asymptotic diffraction theory, in which
diffractive scattering is described in terms of interference between
semiclassical amplitudes, resulting from a stationary-phase
approximation. Typically two such amplitudes are sufficient to
accurately describe elastic scattering, but the stationary points are
located at complex values of the impact parameter. Their separation
controls the interference pattern, and their offsets from the real axis
determine the overall fall-off with momentum transfer. Asymptotically,
at large momentum transfers, the stationary points move towards
singularities of the profile function. I also include some reminiscences
from our collaboration.