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)
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