Pixel area variations in sensors: a novel framework for predicting pixel fidelity and distortion in flat field response

Abstract

We describe the drift field in thick depleted silicon sensors as a superposition of a one-dimensional backdrop field and various three-dimensional perturbative contributions that are physically motivated. We compute trajectories for the conversions along the field lines toward the channel and into volumes where conversions are confined by the perturbative fields. We validate this approach by comparing predictions against measured response distributions seen in five types of fixed pattern distortion features. We derive a quantitative connection between "tree ring" flat field distortions to astrometric and shape transfer errors with connections to measurable wavelength dependence - as ancillary pixel data that may be used in pipeline analysis for catalog population. Such corrections may be tested on DECam data, where correlations between tree ring flat field distortions and astrometric errors - together with their band dependence - are already under study. Dynamic effects, including the brighter-fatter phenomenon for point sources and the flux dependence of flat field fixed pattern features are approached using perturbations similar in form to those giving rise to the fixed pattern features. These in turn provide drift coefficient predictions that can be validated in a straightforward manner. Once the three parameters of the model are constrained using available data, the model is readily used to provide predictions for arbitrary photo-distributions with internally consistent wavelength dependence provided for free.