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Vision in scattering media is important but challenging. Images suffer from poor visibility due to backscattering and attenuation. Most prior methods for scene recovery use active illumination scanners (structured and gated), which can be slow and cumbersome, while natural illumination is inapplicable to dark environments. The current paper addresses the need for a non-scanning recovery method, that uses active scene irradiance. We study the formation of images under widefield artificial illumination. Based on the formation model, the paper presents an approach for recovering the object signal. It also yields rough information about the 3D scene structure. The approach can work with compact, simple hardware, having active widefield, polychromatic polarized illumination. The camera is fitted with a polarization analyzer. Two frames of the scene are taken, with different states of the analyzer or polarizer. A recovery algorithm follows the acquisition. It allows both the backscatter and the object reflection to be partially polarized. It thus unifies and generalizes prior polarization-based methods, which had assumed exclusive polarization of either of these components. The approach is limited to an effective range, due to image noise and illumination falloff. Thus, the limits and noise sensitivity are analyzed. We demonstrate the approach in underwater field experiments.