  We examine the effect of laser focusing on the potential of a recently
discussed scheme [M.F. Ciappina {\em et al}, Phys. Rev. A 99, 043405 (2019);
Las. Phys. Lett. 17, 025301 (2020)] for in situ determination of ultra-high
intensities of electromagnetic radiation delivered by multi-petawatt laser
facilities. Using two model intensity distributions in the focus of a laser
beam, we show how the resulting yields of highly charged ions generated in the
process of multiple sequential tunneling of electrons from atoms, depend on the
shape of these distributions. Our findings lead to the conclusion that an
accurate extraction of the peak laser intensity can be made either in the
near-threshold regime when the production of the highest charge state happens
only in a small part of the laser focus close to the point where the intensity
is maximal, or through the determination of the points where the ion yields of
close charges become equal. We show that, for realistic parameters of the gas
target, the number of ions generated in the central part of the focus in the
threshold regime should be sufficient for a reliable measurement with highly
sensitive time-of-flight detectors. Although positions of the intersection
points generally depend on the focal shape, they can be used to localize the
peak intensity value in a certain interval. Additionally to this analysis, we
discuss the method in comparison to other recently proposed approaches for
direct measurement of extreme laser intensities.
