Turning a flat sensor into a semi-spherical one

Ahh apologies, I think i’m abusing the term distortion.

I need a precise measure of optical flow around an agent, so I need to make sure that all angles of light that enter the camera are treated uniformly by the sensor. Quite rightly, this is not distortion but instead an unfavourable projection that means objects on the sensor would appear to ‘move faster’ towards the edges. So my goal is to map perfectly the light that enters the camera at all angles, like the eye of an insect does.

Currently, i’m actually dealing with a virual camera so there is no lens distortion, only the issues from projecting onto a plane.