  A semi-classical approach is used to calculate radiation emission in the
collision of an electron with an intense focused laser pulse. The results are
compared to predictions from the locally constant field and locally
monochromatic approximations. It is found that simulations employing the
semi-classical approach capture features in the energy spectra, such as
subharmonics and bandwidth structure, which are beyond local approaches. The
formation length is introduced as a diagnostic to select between approaches as
the electron is propagated through the pulse.
