The brighter-fatter effect and pixel correlations in CCD sensors

We present evidence that spots imaged using astronomical CCDs do not exactly scale with flux: bright spots tend to be broader than faint ones, using the same illumination pattern. We measure that the linear size of spots or stars, of typical size 3 to 4 pixels FWHM, increase linearly with their flux by up to $2\%$ over the full CCD dynamic range. This brighter-fatter effect affects both deep-depleted and thinned CCD sensors. We propose that this effect is a direct consequence of the distortions of the drift electric field sourced by charges accumulated within the CCD during the exposure and experienced by forthcoming light-induced charges in the same exposure. The pixel boundaries then become slightly dynamical: overfilled pixels become increasingly smaller than their neighbors, so that bright star sizes, measured in number of pixels, appear larger than those of faint stars. This interpretation of the brighter-fatter effect implies that pixels in flat-fields should exhibit statistical correlations, sourced by Poisson fluctuations, that we indeed directly detect. We propose to use the measured correlations in flat-fields to derive how pixel boundaries shift under the influence of a given charge pattern, which allows us to quantitatively predict how star shapes evolve with flux. This physical model of the brighter-fatter effect also explains the commonly observed phenomenon that the spatial variance of CCD flat-fields increases less rapidly than their average.