Instrumental response model and detrending for the Dark Energy Camera

We describe the model for the mapping from sky brightness to the digital output of the Dark Energy Camera, and the algorithms adopted by the Dark Energy Survey (DES) for inverting this model to obtain photometric measures of celestial objects from the raw camera output. The calibration aims for fluxes that are uniform across the camera field of view and across the full angular and temporal span of the DES observations, approaching the accuracy limits set by shot noise for the full dynamic range of DES observations. The DES pipeline incorporates several substantive advances over standard detrending techniques, including: principal-components-based sky and fringe subtraction; correction of the "brighter-fatter" nonlinearity; use of internal consistency in on-sky observations to disentangle the influences of quantum efficiency, pixel-size variations, and scattered light in the dome flats; and pixel-by-pixel characterization of instrument spectral response, through combination of internal-consistency constraints with auxiliary calibration data. This article provides conceptual derivations of the detrending/calibration steps, and the procedures for obtaining the necessary calibration data. Other publications will describe the implementation of these concepts for the DES operational pipeline, the detailed methods, and the validation that the techniques can bring DECam photometry and astrometry within ~2 mmag and ~3 mas, respectively, of fundamental atmospheric and statistical limits. The DES techniques should be broadly applicable to wide-field imagers.