  A sensitive optical diffractometry method is developed and utilized for
advanced tomography of laser-induced air plasma formations. Using transverse
diffractometry and Supergaussian plasma distribution modelling we extract the
main parameters of the plasma being the plasma density, width and shape with 20
micrometer spatial resolution throughout the plasma formation. The
experimentally recorded diffraction patterns fitted by the Supergaussian plasma
model are found to capture unprecedentedly delicate traits in the evolution of
the plasma from its effective birth and on. Key features in the spatial
evolution of the plasma such as the 'escape position', the 'turning point' and
the refocusing dynamics of the beam are identified and explored in details. Our
work provides experimental and theoretical access into the highly nonlinear
dynamics of laser-induced air plasma.
