  The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed
in terms of the Hermite polynomials squared. It is shown that measurements of
optical-field intensities may be used to determine the tomograms of
electromagnetic-radiation modes. Furthermore, entropic uncertainty relations
associated with these tomograms are found and applied to establish the
compatibility conditions of the the field profile properties with
Hermite--Gauss beam description. Numerical evaluations for some Hermite--Gauss
modes illustrating the corresponding entropic uncertainty relations are finally
given.
