Great effort Adam! I see that you were a bit "location challenged" - From, my own testing I have concluded that public indoor swimming pools are not the greatest location due to dim light and need for high ISO.
I was a bit confused by this: "Given that most domes are spherical, the amount of curvature is hence more as it approached the edges of the dome than it is in the center."
Domes with spherical surfaces (i.e., most of them) have constant curvature by definition. BTW I think radius of curvature is the more straightforward way of comparing dome curvatures and we should encourage the manufacturers to provide this datum (the inner radius preferred over the outer radius; the difference being the glass or other material thickness) along with the physical outer dimension that they seem to prefer to use probably because it is the bigger number.
I think what you meant to express is that the focused plane of the camera lens increases in its deviation from the virtual image with increased image distance from the optical axis (center) - this is quite the mouthful and could be helped with some labeled points (with letters A to C and b and c) and lines (one would correspond to the object plane of the camera lens) being drawn on one of your figures. A on axis, B a little off of axis, and C a bit more off axis in the lens focus plane, a.k.a object plane, line. There would be corresponding b and c points on the virtual image line. No need for an "a" as it would be the same as A. Line Aa would thus have length = zero. Line Cc would be longer than line Bb. These lines are the deviation I referred to above.
I am also curious as to focused distances in the tests. I bring this up because the shape of the virtual image varies with distance from the dome. The virtual image is only spherical for an infinite object distance. It is otherwise aspherical. The source for this fact is Chapter 8 in Optical Fundamentals of Underwater Photography by Gomer T. McNeil, 2nd Ed., 1972.
Edited by Tom_Kline, 30 March 2015 - 04:56 PM.
Thomas C. Kline, Jr., Ph. D.
Oceanography & Limnology
Currently used housed digital cameras: Canon EOS-1Ds MkIII, EOS-1D MkIV, and EOS-1DX; and Nikon D3X. More or less retired: Canon EOS-1Ds MkII; and Nikon D1X, D2X, and D2H.
Lens focal lengths ranging from 8 to 200mm for UW use. Seacam housings and remote control gear. Seacam 60D, 150D, and 250D, Sea&Sea YS250, and Inon Z220 strobes.