  Spatial distributions of electrons ionized and scattered from ultra-low
pressure gases are proposed and experimentally demonstrated as a method to
directly measure the intensity of an ultra-high intensity laser pulse. Analytic
models relating the peak scattered electron energy to the peak laser intensity
are derived and compared to paraxial Runge-Kutta simulations highlighting two
models suitable for describing electrons scattered from weakly paraxial beams
($f_{\#}>5$) for intensities in the range of $10^{18}-10^{21}$Wcm$^{-2}$.
Scattering energies are shown to be dependant on gas species emphasizing the
need for specific gases for given intensity ranges. Direct measurements of the
laser intensity at full power of two laser systems is demonstrated both showing
a good agreement between indirect methods of intensity measurement and the
proposed method. One experiment exhibited the role of spatial aberrations in
the scattered electron distribution motivating a qualitative study on the
effect. We propose the use of convolutional neural networks as a method for
extracting quantitative information of the spatial structure of the laser at
full power. We believe the presented technique to be a powerful tool that can
be immediately implemented in many high-power laser facilities worldwide.
