non-linear film path for constant f

[JamesHarr]

I have been lurking for a while and thinking on and off about designing a pinhole camera. I looked at a lot of photos and accompanying designs and liked the look of the curved-path images, but there was something that started to bug me. The question eventually boiled down to "How would the film path look if I wanted to keep the f value constant?" The problem is that as you turn a pinhole so that the angle of view gets shallower, the pinhole gets smaller. So I asked a mathemetician friend to give me the equation of the lateral diameter of the pinhole as it relates to the angle of view. This is what he gave me:
EA = x - y*tan(theta)
where EA is the effective aperture (lateral diameter). I know that this is an approximation since the pinhole is not circular when viewed at any angle other than 90deg, but bear with me.
x is the diameter of the pinhole
y is the thickness of the material
theta is the angle of view.
Given the relationship focal length = aperture * f, I calculate a series of focal lengths for a series of apertures (starting with my desired 0.3mm, going to 0mm) and a constant f = 215.
Then using the equation above, I calculated theta for an aperture material 0.1mm thick. Here are the results (attached).
Doing a quick sketch, it looks like an ovular shape. Obviously, there will be some serious magnification/distortion as the film plane approaches he pinhole, but I don't really plan getting all that close. I am thinking of a 6x12 format.

Am I crazy?

James

[Isis]

Crazy No, over concerned yes..

[JamesHarr]

Trained as a scientist, working in information management, there is no detail so insignificant that it doesn't warrant some exploration/experimentation.

[Jimmy G]

Way to suck the joy out of pinhole photography!
Just kidding. Welcome aboard!
Is your goal to eliminate light fall off? A curved film plane is nothing new, what does your analysis bring to the design? A steeper curve to compensate for the light fall off..maybe I don't get it 100%?

[JamesHarr]

Jimmy,

There are sqrt(4) kinds of people in the world... those who like math and those who don't.

Actually, I don't know what (if anything) this will bring to the design. The original thought was to eliminate light fall-off (which a circular plane already does adequeately but not perfectly), but the more I thought about the geometry of the pinhole itself, the more I wondered about the extreme angles where the apparent aperture gets very small (only really a concern with wide formats). At that point I had spent so much time thinking about it that it seemed silly not to do the experiment and see what happened. So I will be constructing my camera soon and will post results here.

[JoeVanCleave]

Welcome to F295, James. I hope you stick around, build a camera or twelve, and post many fine images. I've found over the years that I learn at least as much from newcomers as they learn from us oldsters.

Your question is interesting. To eliminate the problem of increased focal distance at off-axis angles with a flat film plane, you could build a circular film plane, which would maintain the same focal length at all parts of the film off-axis from the center-line. But then you still have the problem that the pinhole appears, off-axis, as an ellipse, further decreasing the light intensity at off-axis angles. So, you'd have to make the curve of the film plane such that at off-axis angles the distance from the film to the pinhole is actually shorter than the on-axis center-line focal distance, with increased off-axis angles needing proportionally shorter focal distances to the pinhole, to compensate for the increasingly elliptical appearing pinhole. Which sounds to me, back of the envelop calculation, like your suggestion of an elliptical shape would be right on.

I look forward to seeing the results from such a camera, if you build it. Which I'm hoping you do.

~Joe

[Jim Jones]

To keep the f/number constant on the film, the film would need to be something approaching a sphere, not cylinder. This is inconvenient, but not entirely impractical with liquid emulsions applied to the interior of the appropriately curved surface of transparent material. Even then, maintaining a constant f/number won't eliminate all fall-off. As the light's angle of incidence changes from 90 degrees at the center of the image to something less towards the edge, the emulsion will reflect more and absorb less of the light. Some fall-of near the image edges isn't all bad. I often deliberately burn in edges for effect.

[JamesHarr]

I agree that fall-off and vignetting isn't bad. I fully expect to also build a flat plane camera at some point. Unless they are cropped, those images have that immediate "pinhole" look that we love. The 'constant-f' camera is merely a flight of fancy on my part and I am just self-indulgent enough to go for it and see what happens. Thanks for the input everyone, and Merry Christmas.

James

[Isis]

Good luck with it James, pushing the envelope is how we get somewhere. Just because people like me say you don't need to bother it doesn't mean you shouldn't.
All the best.

[scheimfluger_77]

Sounds like a fascinating project, I look forward to seeing your results. My guess is that with your 6x12 format and your unique shape, and film latitude being what it is... any exposure variance will never be seen from a galloping horse. :-)

Welcome to f295.

Steve