On the Accuracy of the Differential Emission Measure Diagnostics of   Solar Plasmas. Application to AIA/SDO. Part I: Isothermal plasmas
  DEM analysis is a major diagnostic tool for stellar atmospheres. But both its derivation and its interpretation are notably difficult because of random and systematic errors, and the inverse nature of the problem. We use simulations with simple thermal distributions to investigate the inversion properties of SDO/AIA observations of the solar corona. This allows a systematic exploration of the parameter space and using a statistical approach, the respective probabilities of all the DEMs compatible with the uncertainties can be computed. Following this methodology, several important properties of the DEM inversion, including new limitations, can be derived and presented in a very synthetic fashion.   In this first paper, we describe the formalism and we focus on isothermal plasmas, as building blocks to understand the more complex DEMs studied in the second paper. The behavior of the inversion of AIA data being thus quantified, and we provide new tools to properly interpret the DEM. We quantify the improvement of the isothermal inversion with 6 AIA bands compared to previous EUV imagers. The maximum temperature resolution of AIA is found to be 0.03 log Te, and we derive a rigorous test to quantify the compatibility of observations with the isothermal hypothesis. However we demonstrate limitations in the ability of AIA alone to distinguish different physical conditions. 
Chlo\'e Guennou, Fr\'ed\'eric Auch\`ere, Elie Soubri\'e, Karine   Bocchialini, Susanna Parenti
astro-ph.SR