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) is unnecessary to extract $N_e$ from the scattered signal.
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