A puzzle for three-eyed photographers

A few years back Barbara acquired a Kodak Stereo Camera, built some time around 1957. It loads 35mm film, and has two lenses on a coupled shutter release on the front. Unlike some other 3d stereo camera arrangements, this one makes a pair of square but full frame 35mm images for each click of the shutter release.

But the images aren’t next to one another on the film. They overlap.

I recall that before Barbara loaded film for the first time and developed the results, I spent a couple of days trying to figure out how the images would be arranged on the film. I knew that each pair overlapped a neighbor, so it wasn’t like this:

1122334455...

At least one 2 would appear between the two 1 images, I knew from what I read online. But… don’t they start overlapping in time?

For instance:

1.1
 2.2
  3.3 whoops

That totally doesn’t work, because the second 1 is overlapped by the 3. That sort of thing seems to happen a lot, actually, for various numbers of units between left and right images for one stereo pair, and offsets between subsequent pairs.

Finally, when the film was developed, I actually got to look at it, and the arrangement was:

1..1
  2..2
    3..3
      4..4
        5..5...

That produces a sequence like this:

1.2132435465…

But that wasn’t the only arrangement I was able to find by hand, before we saw the actual developed film. Here’s another one that “works”, in the sense that the photos don’t overlap one another:

1...1
   2...2
      3...3
         4...4
            5...5…

That one avoids double exposures, too, but it does so at the expense of some wasted film. The resulting pattern for that one on the roll would be something like this:

1..21.32.43.54.…

In other words, a good third of the film would have ended up wasted. That’s not very smart.

Then there were some irregular patterns I discovered, which used all the film but need some kind of weird mechanicals to advance the film a different number of steps at certain time-points. For instance, this one fills the entire roll (at least the front end), but does so at the expense of having to advance in a sequence like 1111511151115…

1...1
 2...2
  3...3
   4...4
        5...5
         6...6
          7...7…

So overall in my sketches I identified at least three factors I was concerned about:

1. I wanted to minimize the number of overlaps between exposures (of course),
2. I also wanted to minimize the amount of wasted film, and
3. also minimize the number of different step-sizes the mechanism needed to do

After all, this was well before the advent of powered film advancement, and there weren’t any landmarks a machine could rely on beyond the sprocket holes themselves.

Is the pattern actually used by the Kodak Stereo Camera the only optimal one, in terms of non-overlapping frames, minimal wastage, and consistent film advancement? I think so, but maybe you could check for me?

Sheet film is cheap

It strikes me that there would be another way to arrange stereo pairs on film, though the form factor of the camera would be quite different: We might be able to expose them in pairs on a sheet of film. Say we have a single sheet of film that’s 10-by-10 (square) images in size. Assuming we can “advance” the film as before, and also turn the film by 90°, is there a scheme that also

1. avoids overlapping frames
2. minimizes wastage
3. minimizes the number of times we need to turn the sheet or advance a weird number of steps?

Our alien colleague

A certain friend (I can’t say who for the moment—“Spoilers!” as the lady says) has a trinocular camera, with three simultaneously activated shutters.

How should their camera advance? Surprisingly, it’s still using a single spool of film. Not all three images need to be evenly spaced, in this case.

Here’s one that might work, based on the boring old two-eyed version Kodak used:

1...1...1
   2...2...2
      3...3...3
         4...4...4
            5...5...5…

Are there others?