  An ultrarelativistic electron beam passing through an intense laser pulse
emits radiation around its direction of propagation into a characteristic
angular profile. Here we show that measurement of the variances of this profile
in the planes parallel and perpendicular to the laser polarization, and the
mean initial and final energies of the electron beam, allows the intensity of
the laser pulse to be inferred in way that is independent of the model of the
electron dynamics. The method presented applies whether radiation reaction is
important or not, and whether it is classical or quantum in nature, with
accuracy of a few per cent across three orders of magnitude in intensity. It is
tolerant of electron beams with broad energy spread and finite divergence. In
laser-electron beam collision experiments, where spatiotemporal fluctuations
cause alignment of the beams to vary from shot to shot, this permits inference
of the laser intensity at the collision point, thereby facilitating comparisons
between theoretical calculations and experimental data.
