Optics: building a camera with quasi-hemispherical recording surface, what lens?

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jdanforth
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I make Daguerreotypes (http://en.wikipedia.org/wiki/Daguerreotype) and I have decided that I want to move from the standard flat-plane photography and make images on silver domes instead.

I have domes that are 1.85" in diameter and I want to replicate the effect that a garden gazing ball gives you (reflecting everything around it in a sphere).
I have no problem with the chemical side of things, that's easy. What I can't figure out is what kind of lens to put on this thing!

Based on what I have read so far, I'm thinking that I should have a single-element positive (condensing) meniscus lens on the front and that it should have a curvature on the convex side that is sufficient to pick up a 120-180 field of view. Where can I find or how do I specify such a thing?

If I want to end up with the opposite of the Petzval Effect (http://www.astrosurf.org/lombry/Physique/aberration-curvature-dwg.gif ) and project my image on to the convex side of a dome instead of the concave side, is this the right way to go?

Are there any optical engineers that can help me with this?!

The camera diagram thus-far: http://www.danforthsource.com/pics/sphere_cam.gif
 
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My suggestion would be to direct this question to a company that specialises in making custom lenses. I find that most companies are very willing to aid you in designing the lens you want for your application, without any sort of commitment to purchase.

Claude.