What is causing the camera to have pincushion distortion in air and then barrel distortion in water?

Question

I have been working on a research project this summer looking at penguin body cameras and how we can measure the size of prey they catch from the video footage. This involved me taking some measurements and creating a correction factor to convert pixel measurements of prey items into mm measurements in the lab at known distances.

The tests were done in air and in water which produced differing results. In water we saw barrel distortion whereas in air we saw pincushion distortion. I am wondering what could be causing the distortion to change between the two mediums.

The camera we used is a modified Mobius action cam (https://pengu.cam/) that has a wide angle lens (135 deg).

Currently I am thinking that a change in the medium and thus a change in refractive index interacts with the wide angle lens and flat pane in front of the lens to change the distortion.

I would love to hear any thoughts on this and/or would appreciate getting pointed in the right direction of some research that may have looked into this already. Thanks!

Answer 1

What is causing the camera to have pincushion distortion in air and then barrel distortion in water?

In your own question, your speculation is exactly correct: "Currently I am thinking that a change in the medium and thus a change in refractive index interacts with the wide angle lens and flat pane in front of the lens to change the distortion."

It's simply that the refractive index of water is different of that from air. The wide-angle lens doesn't "interact" with the flat plane in front of the lens, so much as a wide-angle lens will magnify or make barrel or pincushion distortions more apparent. Essentially, the water in front of the lens acts as another lens element, with its own refractive index. And adding lens elements to a lens changes its overall optical formula.

I would love to hear any thoughts on this and/or would appreciate getting pointed in the right direction of some research that may have looked into this already.

As far as "research that may have looked into this already", well, that's pretty much the entire history of optical physics. This is very simply a result of immersing the subject in a different optical medium than what the camera lens + imaging system exists in. That is, the water surrounding and in between the subject and the front lens (or lens protector / waterproof case or element) results in a different angular magnification in the scene than you get when everything is in air.

Answer 2

Purely guesswork on my part. That being said, the position of the iris diaphragm (aperture) is important. Place wrong and you get either pincushion or barrel. I am guessing that the shift from air to the higher density media of water changes the refractive power of the array and this induces this change.