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DEM analysis is a major diagnostic tool for stellar atmospheres. But both itsderivation and its interpretation are notably difficult because of random andsystematic errors, and the inverse nature of the problem. We use simulationswith simple thermal distributions to investigate the inversion properties ofSDO/AIA observations of the solar corona. This allows a systematic explorationof the parameter space and using a statistical approach, the respectiveprobabilities of all the DEMs compatible with the uncertainties can becomputed. Following this methodology, several important properties of the DEMinversion, including new limitations, can be derived and presented in a verysynthetic fashion.  In this first paper, we describe the formalism and we focus on isothermalplasmas, as building blocks to understand the more complex DEMs studied in thesecond paper. The behavior of the inversion of AIA data being thus quantified,and we provide new tools to properly interpret the DEM. We quantify theimprovement of the isothermal inversion with 6 AIA bands compared to previousEUV imagers. The maximum temperature resolution of AIA is found to be 0.03 logTe, and we derive a rigorous test to quantify the compatibility of observationswith the isothermal hypothesis. However we demonstrate limitations in theability of AIA alone to distinguish different physical conditions.

On the Accuracy of the Differential Emission Measure Diagnostics of Solar Plasmas. Application to AIA/SDO. Part I: Isothermal plasmas