## Monday, February 25, 2008

### Effect of Focal Length

In previous postings we examined the effect of the stereo base. Now we will see what happens if we change the focal length of the recording lens or the viewing lens (or viewing distance).

These effects are summarized in the Table here. Note that what matters for these effects is not the absolute value of the focal lengths of the individual lenses, but the relationship between the two.

If no lenses are used (as in the case of mirrors or projection) we can substitute the focal length of the viewing lens with the viewing distance. If the original film chips are magnified (as with prints) then the focal length of the recording lens must be multiplied by the magnification. A better way to treat this subject is to talk about angles. The condition for ortho stereo is that the scene is viewed from the same angle as it is recorded.

Why does this mismatch of recording/viewing affect the perception of depth?

One way to explain it is this: A longer focal length lens (which essentially magnifies the image) makes it look as if the camera was closer to the subject than it really was. When we view this picture we mentally compare it with the one recorded from closer. In this case, to be compatible with the reduced perspective (2d) and deviation (3d), the depth must be reduced. Hence the perceived depth compression.

Some people think that the focal length affects the perspective (relative size of near vs. far objects). This is not correct. Only the distance affects perspective. Let’s say that we record a scene with a wide angle lens, and then, without changing position, switch to a long FL lens and take another picture. If we then enlarge the picture from the wide angle lens to match the size of the objects in the picture from the long FL lens, the two pictures will be identical! The focal length acts only as a magnification factor and this is true both in 2d and 3d. What creates the compression/stretch “illusion” is the mismatch of the viewing distances. If both the wide angle and telephoto lens pictures are viewed from the same distance, then they will result in a different impression.

A Simple Experiment

Here is an experiment anyone can do right now: While viewing a stereo image (for example, freeviewing some of the images in this newsletter) move the image away and see how this affects the perceived depth. You should see the depth increase (“stretch”). By bringing the image closer, the depth should decrease (“squash”). The effect is rather subtle but most people notice it. Another experiment is to move back and forth during stereo projection. There appears to be more depth in the projected image when viewed from further away. Note that these effects are not perceived proportionally.

Seen Also in 2D

This effect is seen in both 2d and 3d images but it is more noticeable in stereo. In 2d it is the change in perspective with distance that creates this impression. Most of us are familiar with races in which, when filmed straight-on with long lenses, it appears that all the runners are in the same line and we are surprised to see how far apart they are when the camera changes angle of view. The reason the runners appear in the same line (depth compressed) is that their sizes are the same (zero perspective). That's the result of filming the race from far away and not the result of using long lenses, but the long lenses help get a larger image. To be more exact we should say that this compression is the result of viewing the image from much closer than it was recorded. We should always have in mind that it is not the recording lens or distance that creates the effect but the mismatch between the recording and viewing distances.