Don't be ridiculous Ray,
Don't be ridiculous, Oscar. All images are cropped, whether in-camera or through post processing. If the telephoto image had not been cropped you'd see a circle with a very dark circumference, and that would be impossible to emulate by cropping the wide-angle shot.
.....you crop the wide-angle shot to an equivalent field-of-view or angle-of-view as the telephoto shot and because the angle of incident light is then equivalent, so is the apparent distortion. if you subsequently blow up the cropped wide-angle shot to the exact scale of the telephoto shot, it will exhibit the exact same compression.
Eh! ...the angle of incident light is then equivalent?? Surely the angle of incident light is/was always the same in respect of the same objects in the scene, whatever the lens used. It's not changed through cropping. What has changed are the reference points that provide the impression of distance. They've been removed and the ball game has consequently changed.
The compression and expansion are not constant over the frame. It expands because it becomes wider than what would be considered a normal lens, and it compresses when the angle is narrower for a telelens. In a telelens, as well as in the center part of the wide-angle lens, incident light rays are increasingly more parallel. Thus it will look more like a parallel projection.
That sounds a bit confused to me. Are you introducing the red herring of volume anamorphosis again? Let's just shift focal lengths upwards by a few mm, and compare a standard 50mm shot with a significantly telescopic shot.
The 50mm shot provides no sense of either compression distortion or extension distortion. It looks pretty close to what the eye sees in respect of the relative size and distances of objects in the scene.
We then make a crop of the central area of the 50mm shot to emulate the focal length of the telephoto lens. We don't
emulate the FoV. We make it exactly the same. It's not an
equivalent FoV. It's the same FoV. However, the same FoV results in a focal length of lens which is
equivalent to the telephoto lens used. We've demonstrated the principle that lenses of
equivalent focal length will produce an
identical sense of perspective from the same position.
I presume by
expansion you mean
extension. The
extension distortion in a wide-angle shot refers to the effect or impression of extended distances. The
compression distortion of a telephoto shot refers to the effect of shortened distances.
How do we make something that previously looked small (and distant) appear large and close? By removing the big things in the scene (through cropping) and magnifying the small things.
The principle here is that big and small are relative terms. Big is big only in relation to something that is small, and vice versa. Is an elephant big? Not compared with a whale.
