Correcting camera distance with zoom

[Kidphysics]

So I have four pinhole type cameras in my experimental setup. All of them have the same magnification and are placed at the same distance away at different locations except one which has a different magnification and zoom. This camera is 72.5% further and has 52.5% less magnification as the rest of the cameras. The magnification problem could be worked out in a photoshop by an appropriate 52.5% zoom (or so I naively assume) but how to correctly zoom to adjust the difference due to position seems to be a harder problem. I am only familiar with the lens-makers equation to tie in magnification levels with image distances etc, but a pinhole is not a lens and I am not sure how to fix the distance problem with zoom. Any ideas? I'd like to calibrate all of the cameras. Thanks

 

[schip666!]

The beauty of an -- ideal -- pinhole camera is that there is none of that focal length nonsense to obscure the relationship of image to object. The ratio of I-O distances should be the same as the ratio of I-O sizes. So you should be able to move the image plane on your more-distant camera to compensate. Note that you will still have a different viewing angle so the perspective of objects at various distances will not exactly match the other cameras, much like changing from wide-angle to telephoto lenses on a grown-up camera.

 

[Kidphysics]

The beauty of an -- ideal -- pinhole camera is that there is none of that focal length nonsense to obscure the relationship of image to object. The ratio of I-O distances should be the same as the ratio of I-O sizes. So you should be able to move the image plane on your more-distant camera to compensate. Note that you will still have a different viewing angle so the perspective of objects at various distances will not exactly match the other cameras, much like changing from wide-angle to telephoto lenses on a grown-up camera.

what if the pictures were already taken? Now I must use zoom to account for the distance, are you saying I can use the 72.5% further ratio and zoom by the same amount? Also what do you think of my idea to solve the magnification problem by an appropriate 52.5% zoom?

 

[schip666!]

Ah, I see... Yes, you should be able to just enlarge them by the right ratio. The proof will be in the pudding when you compare the same object in multiple photos. But as I said, the relative perspective will be off for objects at different distances.