Need help understanding dome port theory

[Ol Dirty Diver]

I just maxed out my credit card on the following dream rig:

• Nikon D700
• Nikon 16-35mm f/4 (better than the 14-24mm?)
• Sea & Sea MDX-D700 housing
• Zen 8" optical dome port
• Sea & Sea extension ring 40

I hoped that I would finally have a nice sharp image through to the corners, but apparently the rig still needs more optimization (see attached images taken at f/5.6 and f/11). Because the lens I'm using is so new I haven't been able to find any advice online from others using it underwater. In an effort to figure out what I need to do, I've been reading up on dome port theory online and while the terminology and math starts to get over my head, I think I get the gist. But there's still a few things I'm not sure about which I was hoping someone on here could answer:

• From this article I learned that it "must be such that the camera lens' primary principal plane ends up at the dome's centre of curvature. Positioning the lens in that manner ensures that its underwater field of view will be identical to its in-air field of view." Where exactly on the lens is its "primary principal plane"? I'm guessing this may be aligned with the outermost element of the lens (which I know moves in a zoom), but I can't be sure from the other resources I checked.
• If I should manage to align the lens' principal plane with the dome's center of curvature, does this actually yield the best possible image quality underwater for a particular lens/dome port? Is the issue of corner fuzziness eliminated assuming the lens' minimum focusing distance can handle the distance to the virtual image?
• It appears that dome ports are not actually complete half domes (as indicated in the dome port theory articles, such as this diagram), but instead only sections of a half dome. Indeed, the Zen website admits this about my dome port: "[it is] an 8" segment of a much larger BK7 crystal glass dome". Therefore, if I was trying to achieve positioning the lens' principle plane at the dome's center of curvature, should the front element of the lens be recessed in the housing and certainly not protruding into the dome port itself? What is the penalty of allowing the lens to protrude into the dome port? I'm guessing the problem of corner blurriness is exacerbated the further the lens protrudes inside the dome port (i.e., the closer the lens is to hitting the dome port itself)?

I suspect that this is the reason I'm dealing with corner blurriness. I really don't think it's an issue of the minimum focusing distance of my lens being too short to accommodate the distance to the virtual image. I can estimate that the virtual image (at infinity) is 3 x radius - 4 x dome thickness in front of the outer surface of the dome port (reference). In my case this is some distance greater than 12"; since my dome port is only a section of a half-sphere, the opening of which is 8" across, the radius of my dome must be something greater than 1/2 the 8" diameter of the opening (I emailed Zen to learn the exact radius). My lens has a minimum focusing distance of ~11", as measured from the sensor. With the D700/16-35mm I measured the distance from the sensor to outer edge of lens at ~7", meaning I can focus as close as 4" away from the outer edge of the lens, easily accommodated by the over 12" I have to work with outside the dome + the distance between the lens and dome. It seems that I have plenty of focusing distance to spare, so I really don't think I have any need to use diopters, which I'd prefer to avoid anyway to preserve image quality and depth-of-field.

So is my theory correct so far? Is it really in our interest to try to position the lens' outermost element (which I'm assuming to be the "primary principal plane" or close enough to it for my purpose) at the center of curvature of the dome port? If this is necessary for good corner resolution, then I can understand why my rig is failing in this regard: my lens protrudes too far into the dome port. I knew I'd need an extension ring, so I got the one recommended by Sea & Sea for the Nikon 17-35mm (extension ring "40"), which was also suggested by the vendor to be all I'd need (*note that the new 16-35mm is 0.7" longer than the 17-35mm). But if you look at the attached photo you'll see that I'm hardly using much of the real estate of that beautiful dome, due to the lens still coming so close to the inner face. I'd estimate that there is about an inch between the outer edge of the lens and inner face of the dome, and that the outermost element of the lens is receded ~3/4" inside the outer edge of the lens, so that there is probably 1.5 - 2" of space between the outer element of the lens and the inner face of the dome.

An obvious solution is simply to go ahead and buy another extension ring, or test someone else's out. The latter is not an option because I don't know other photographers with this sort of gear, and the former is not something I want to do carelessly since I am already so strapped having bought all this already. I want to be sure it would be the solution, and I figured if I could understand the theory I could perhaps precisely measure how much more extension I'd need. There are two options for the extension after all, the thinner "SX" extension ring, and putting on another thicker "40". It really looks to me like I could afford to double the extension, which would be unfortunate because the current amount of extension is already adding so much bulk. I know that another option still is to simply forget about using a rectilinear lens and opt for a fisheye, but it so happens that I have important assignment which requires images shot at 24mm and minimizing distortion.

If anyone actually read through this entire post and can advise me, I'd be much obliged. There's no doubt that this new Nikon lens will become very popular with underwater photographers, so I feel that my observations and whatever conclusions we arrive at regarding housing/dome port/extension ring combinations with this lens will be of great value to other photographers who acquire this lens in the future. Thanks in advance for your assistance.

[scottfiji]

Personally I would test it in the pool and try a +2 and +4 B&W diopter.

[davelew]

Experiments with different external diopters are likely to be the best way to solve your problem.

For the theory, I have been re-aquainting myself with my old optics textbooks for the last few months as I adapt water-corrected Nikonos lenses to a digital camera. I'm not familiar with the 16-35 lens of which you speak, but I can comment on the general theory of dome ports. I apologize in advance if I use too many three letter acronyms (TLAs) in my description.

The problem you face is that the dome port is an extra lens element that you're putting in front of a highly optimized lens. There is no best place to put the dome port, because the lens you have has already been optimized so that "bad" things from each element are cancelled out by other elements. Any dome port is going to curve the focal plane (resulting in soft corners) and cause vignetting (corners that are too dark), as well as introduce some chromatic aberration (purple fringing). I don't want to make it sound like a dome port will ruin your images; these issues are all manageable, and other problems like lighting or cloudy water are likely to be bigger issues in the real world.

Getting back to dome ports, most people believe that the dome port should be centered on the front nodal point (FNP) of the lens. There are a lot of descriptions of what FNP means, but I think the easiest way is to think about the angle of view (AOV) of the lens. Every angle has to have a vertex, and the vertex of the AOV of a lens is at that lens' FNP. If you center the dome on the FNP of the lens, you will have the same angle of ivew in water as in air, and will get sharp corners. Typically, the FNP is located inside the lens.

Unfortunately, there's a problem with centering a dome port on the FNP. In some lenses, this can cause vignetting, because you get a different effective f-stop for out-of-focus objects at the edges of the frame. It can also cause some weird perspective effects, but I've never seen these show up in a real-world photograph, the perspective shifts are mostly just interesting to us optics geeks. To make the vignetting problem go away, you need to center the curvature of the dome on the entrance pupil of the lens. The entrance pupil is the image of the aperture, as viewed from the front of the lens.

Since most underwater scenes don't have perfectly even light, the vignetting issues tends to go un-noticed, and the consensus seems to be to center the dome on the FNP of the lens.

Now for your next question, where is the FNP of your lens? I have no idea. It's possible to figure it out with a yardstick, tape measure, and tripod, but it takes a couple hours of work.