Flash turns up the optical volume so that whatever lies behind the lens - be it film or a digital sensor - is a little more receptive.
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If you think about all the light that enters - that enters the lens of a camera, that's much more than a photo. The light field is all the higher-dimensional information that's lost in a regular photo. When we record all this information, that provides us the opportunity in software after the fact.
Unlike regular digital or film cameras, which can only record a scene in two dimensions, light field cameras capture all of the light rays traveling in every direction through a scene. This means that some aspects of a picture can be manipulated after the fact.