The distance to the dome I was referring to is the subject to dome distance. The virtual image surface shape is a function of focused distance, only spherical at infinity. This is probably why small domes work for macro subjects where the dome is very close to the subject so the virtual image is flatter. Note that this thread is > 3 years old whereas FE question is new.
And for a subject at infinity the virtual images lies at a point which is 4 x the radius of the dome from the centre of the dome which is where the principal point of the lens should be positioned. This means that the centre of the mage is at 4R but because the virtual image is spherical, depending on the lens's angle of view, the edge of the image will be somewhere closer - exactly where will depend on its position and the dome's radius (radii) and thickness and refractive index - its complicated. But the camera lens is not much of a factor here because it can only image what it 'sees'. Its ability to do so will be dictated by the virtual image produced by the dome port and subject and any inconsistencies of the camera lens such as field curvature at closer focus. Its all a bit messy.
The 'less curved' dome idea is in effect the suggestion of positioning the camera lens closer towards the dome as opposed to ensuring it is aligned at the centre of the dome. You may want to try doing just this (should be easy enough). If I remember correctly, I think that you will find that it results in the trade off of reducing the field of view as opposed to doing what your diagram illustrates so is counter productive.
Sadly I suspect the 'filmdays' rule of thumb of 90 degrees being the maximum viably/easily correctable field of view still applies with dome ports though bigger does help .....
I still disagree about the unpredictability of lens performance underwater behind dome ports. Its lack of technical information which hampers prediction nothing else.
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