## Monday, February 25, 2008

### Effect of Focal Length on Stereoscopic Deviation

What happens to the stereoscopic deviation as we increase the focal length? We have mentioned that the focal length acts as a magnification factor and magnifies the stereoscopic deviation, per the formula: p = FB (1/Imin – 1/Imax) (1)

So, according to (1), if we double the focal length, the stereoscopic deviation will be doubled. This assumes that the distances of the near and far objects do not change as we change the focal length. Now, what are the chances of this happening? Pretty slim, I think. Unless if the near and far objects are in the line of sight near the center, as we zoom into the scene we will be moving past near objects, thus keeping the deviation under control. I first noticed this while watching zooming during digital stereo projector. As our projectionist was zooming into the scene, the range of depth changed and the deviation and sense of depth seemed well-balanced and under good control.

Constant Magnification

So far we have examined the effect of the focal length with a fixed distance from the subject. What happens if we change both the focal length and the distance to the subject so we can have the subject fill the frame? “Fill the frame” implies constant magnification. In this case we can either use a short FL lens and come close to the subject or use a long FL lens and stay far back. There are many situations (wild life photography, portraits, etc) where we use long FL lenses in order to stay further from the subject and still fill the frame. In the case of constant magnification, instead of using (1) we should go back to the original formula: p = M B (2)

This formula shows that if the magnification remains the same, the stereoscopic deviation is independent of the focal length. This formula assumes that there is infinity in the picture. But in many real situations not only there will not be any infinity, but the scene will have a rather narrow depth range.

Narrow Depth Range

From (1) we have: dp = F B dI / I**2 (dI is the depth range). Substituting M = F/I, we get:

dp = M**2 B (depth) / F (3)

This formula shows that for constant magnification and a narrow depth range, the stereoscopic deviation varies inversely to the focal length. So, if we want to maintain the same amount of deviation, while we are increasing the focal length, we need to increase the stereo base. This is the basis of the “PePax” principle.