  We consider the absorption of probe photons by electrons in the presence of
an intense, pulsed, background field. Our analysis reveals an interplay between
regularisation and gauge invariance which distinguishes absorption from its
crossing-symmetric processes, as well as a physical interpretation of
absorption in terms of degenerate processes in the weak field limit. In the
strong field limit we develop a locally constant field approximation (LCFA) for
absorption which also exhibits new features. We benchmark the LCFA against
exact analytical calculations and explore its regime of validity. Pulse shape
effects are also investigated, as well as infra-red and collinear limits of the
absorption process.
