The photo sensor in our digital cameras is flat. This creates a problem for the optics of the lens since the rays have to cover different distance from the lens to the sensor depending on where they have to hit the sensor, a shorter path if the ray is aimed at the center of the sensor, a longer one if it has to reach its edges. This leads to a "softness" of the image at the edges (a slight out of focus detectable on large magnification) that is compensated by the geometry of the lens (different thickness) but in turns this creates other problems (like diffraction).
Mammals, as many other animals, are smarter. They have a spherical sensors that avoid this problem.
Technology now is capable of providing flexible electronics as we have seen in the new "curved" television screens.
Researchers at the University of Wisconsin have found a way to manufacture a flexible phototransistor (a transistor that can sense light and change the modulation of the signal based on the light presence and its intensity). The technology used is different from the one adopted by television manufacturers to create curved screen, it can provide a much bigger curvature, as shown in the picture.
Its flexibility does not affect its performance. On the contrary, it is faster than today's camera photosensors.
They are using a "flip transfer" manufacturing technology where first they create the phototransistors and then they "flip" and deposit them onto a plastic substrate (that provides the desired flexibility) leaving a metal layer on the back. This layer act like a mirror and increases the sensitivity of the sensor.
The curvature of the photosensor can be designed to fit the lens (instead of having to design the lens to fit the sensor) resulting in smaller packages and higher image quality.
No indication, so far, on when we can expect this kind of sensor to hit the market.