  Laser induced plasmas have found numerous applications including
plasma-assisted combustion, combustion diagnostics, laser induced breakdown
spectroscopy, light detection and ranging techniques (LIDAR), microwave
guiding, reconfigurable plasma antennae etc. Multiphoton ionization (MPI) is a
fundamental first step in high-energy laser-matter interaction and is important
for understanding of the mechanism of plasma formation. With the discovery of
MPI more than 50 years ago, there were numerous attempts to determine basic
physical constants of this process in the direct experiments, namely
photoionization rates and cross-sections of the MPI, however, no reliable data
is available until today and spread in the literature values often reaches 2-3
orders of magnitude. This is due to inability to conduct absolute measurements
of plasma electron numbers generated by MPI which leads to uncertainties and,
sometimes, contradictions between the MPI cross-section values utilized by
different researchers across the field. Here we report first direct measurement
of absolute plasma electron numbers generated at MPI of air and subsequently we
precisely determine ionization rate and cross-section of eight-photon
ionization of oxygen molecule by 800 nm photons
${\sigma}_8=(3.32{\pm}0.3)*10^{-130} W^{-8}m^{16}s^{-1}$. Method is based on
the absolute measurement of electron number created by MPI using elastic
scattering of microwaves off the plasma volume in Rayleigh regime and
establishes a general approach to directly measure and tabulate basic constants
of the MPI process for various gases and photon energies.
