This paper describes STECMAP (STEllar Content via Maximum A Posteriori), a flexible, non-parametric inversion method for the interpretation of the integrated light spectra of galaxies, based on synthetic spectra of single stellar populations (SSPs). We focus on the recovery of a galaxys star formation history and stellar age-metallicity relation. We use the high resolution SSPs produced by PEGASE-HR to quantify the informational content of the wavelength range 4000 - 6800 Angstroms. A detailed investigation of the properties of the corresponding simplified linear problem is performed using singular value decomposition. It turns out to be a powerful tool for explaining and predicting the behaviour of the inversion. We provide means of quantifying the fundamental limitations of the problem considering the intrinsic properties of the SSPs in the spectral range of interest, as well as the noise in these models and in the data. We performed a systematic simulation campaign and found that, when the time elapsed between two bursts of star formation is larger than 0.8 dex, the properties of each episode can be constrained with a precision of 0.04 dex in age and 0.02 dex in metallicity from high quality data (R=10 000, signal-to-noise ratio SNR=100 per pixel), not taking model errors into account. The described methods and error estimates will be useful in the design and in the analysis of extragalactic spectroscopic surveys.
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