  We present a novel technique to assess the focal volume of petawatt-class
lasers at full power. Our approach exploits quantitative measurement of the
angular distribution of electrons born in the focus via ionization of rarefied
gas, which are accelerated forward and ejected ponderomotively by the field. We
show that a bivariate ($\theta, \phi$) angular distribution, which was obtained
with image plates, not only enables the peak intensity to be extracted, but
also reflects nonideality of the focal-spot intensity distribution. In our
prototype demonstration at intensities of a few $\times 10^{19}$ to a few
$\times 10^{20}$ $\mathrm{W/cm^2}$, an f/10 optic produced a focal spot in the
paraxial regime. This allows a plane-wave parameterization of the peak
intensity given by $\tan{\theta_c} = 2/a_0$ ($a_0$ being the normalized vector
potential and $\theta_c$ the minimum ejection angle) to be compared with our
measurements. Qualitative agreement was found using an $a_0$ inferred from the
pulse energy, pulse duration and the focal spot distribution with a modified
parameterization, $\tan{\theta_c} = 2\eta/a_0$ ($\eta = 2.02^{+0.26}_{-0.22}$).
This highlights the need for (i) better understanding of intensity degradation
due to focal-spot distortions and (ii) more robust modeling of the ejection
dynamics. Using single-shot detection of electrons, we showed that while there
is significant shot-to-shot variation in the number of electrons ejected at a
given angular position, the average distribution scales with the pulse energy
in a way that is consistent with that seen with the image plates. Finally, we
note that the asymptotic behavior as $\theta \to 0^{\circ}$ limits the
usability of angular measurement. For 800 nm, this limit is at an intensity
$\sim 10^{21}\ \mathrm{W/cm^2}$.
