  The total number of electrons in a classical microplasma can be
non-intrusively measured through elastic in-phase coherent microwave scattering
(CMS). Here, we establish a theoretical basis for the CMS diagnostic technique
with an emphasis on Thomson and collisional scattering in short, thin
unmagnetized plasma media. Experimental validation of the diagnostic is
subsequently performed via linearly polarized, variable frequency microwave
scattering off laser induced air-based microplasmas with diverse ionization and
collisional features. Namely, conducted studies include a verification of
short-dipole-like radiation behavior, plasma volume imaging via intensified
charge-coupled device (ICCD) photography, and measurements of relative phases,
total scattering cross sections, and total number of electrons $N_e$ in the
generated plasma filaments following absolute calibration using a dielectric
scattering sample. Findings of the paper suggest an ideality of the diagnostic
in the Thomson "free-electron" regime - where a detailed knowledge of plasma
and collisional properties (which are often difficult to accurately
characterize due to the potential influence of inhomogeneities, local
temperatures and densities, present species, and so on) is unnecessary to
extract $N_e$ from the scattered signal.
