  We present a model for the intensity of optically thin EUV emission for a
plasma atmosphere. We apply our model to the solar corona as observed using the
six optically thin EUV channels of the SDO/AIA instrument. The emissivity of
the plasma is calculated from the density and temperature using CHIANTI tables
and the intensity is then determined by integration along the line of sight. We
consider several different profiles for the radial density and temperature
profiles, each of which are constrained by the observational data alone with no
further physical assumptions. We demonstrate the method first by applying it to
a quiet region of the corona, and then use it as the background component of a
model including coronal holes, allowing the plasma densities and temperatures
inside and outside the hole to be estimated. We compare our results with
differential emission measure (DEM) inversions. More accurate estimates for the
coronal density and temperature profiles have the potential to help constrain
plasma properties such as the magnetic field strength when used in combination
with methods such as seismology.
