## Sunday, February 10, 2008

### Limit to Stereo with Translation – Converge or not Converge?

As the magnification increases, translation cannot be used effectively any more. Consider for example M = 5 (5 times magnification).

I = 1.2F, I' = 6F, Cropping = 5B

How much should I translate? My rule of thumb B = I/20. Assuming F = 100mm, B = 6mm. But cropping = 30mm. If we use 35mm film, all we have is 36mm to record the image. If we crop 30mm, we have very little image to work with. We need to work this the other way around. Let’s say we need to maintain half the film width. Then cropping = 18mm, B = 1.8mm. We can only translate by 3.6mm, not 6mm we originally had planned. That might not be enough and result to a flat image.

In practical terms, we are forced to converge the lenses or use tilt instead of translation for magnifications of 10x or higher. I mentioned earlier that you should avoid convergence because it leads to keystone distortion. As it turns out, at high magnifications the working distance becomes equal to F and the extension equal to MF. Because of the large extension, perspective is minimized, which means that we can use tilt with no problem. (I will try to explain this “perspective is minimized” in a subsequent post.)

The same is true of very long focal length lenses are used. Perspective is minimized and convergence is not only acceptable, but also the only practical way to record the image.