  We revisit a recently proposed scheme [M.F. Ciappina et al 2019 Phys. Rev. A
99 043405] for accurate measurement of electromagnetic radiation intensities in
a focus of high-power laser beams. The method is based on the observation of
multiple sequential tunneling ionization of atoms and suggests the
determination of the peak intensity value from the appearance in the focal area
ions with a certain charge number. Here we study the sensitivity of the
approach to two essential factors: the focal volume effect and the tunneling
ionization model chosen to calculate ionization rates. We show, on the one
hand, that the results appear almost model-independent for ionization of
helium- and hydrogen-like ions and, on the other hand, that the focal averaging
leaves the intensity-dependent features visible. Our findings are in favor to a
practical implementation of the atomic diagnostics of extreme laser
intensities.
