When a rolling shutter activates it exposes the sensor through a slit (vertical/horizontal) - I can see why every bit of the sensor is exposed for the same amount of time. The "exposure slit" starts from the top and ends at the bottom.
A leaf shutter on the other hand starts exposing the image from the center which would expose the center of the sensor first; it then opens up all the way which still includes the center of the image; and while it's closing down the center of the sensor will still be exposed. It seems that the center of the sensor receives the most amount of light and that is reduced in a radial gradient way across the sensor, correct? (well, it's not even a perfect circle due to the geometry of the leaves)
Do digital cameras have to compensate for this? How did they compensate in the film era?