optics - What is the shape of the focal plane?

This is something I just realised I don't entirely know the answer to, so I'm going to ask it here as I think it's interesting.

In most non-scientific writing on depth of field, diagrams generally show camera and subjects as being perfectly parallel, e.g.

However, is this a more accurate representation of the focal plane?

Are there ways to optically alter the shape of the focal plane?

Note: Obviously these diagrams are two dimensional, but I'm assuming in the second diagram the shape would be spherical with the sensor at the center.

Answer

The effect is called field curvature. A good discussion comes from Nikon. It is a lens aberration that can reduce the resolution of the lens when coupled with a flat sensor. In the old days, the film could be bent a little to try to follow the image plane and reduce the effect, but our sensors today are rigid. It can be reduced with lens design.