Zoom and magnify relation

Dave Martindale wrote:

Or the handwaving argument: you haven't doubled the FOV angle, but the
additional squares you can see are being increasingly foreshortened by
the very wide angle they are off-axis, so you get more of them in each
degree of extra visual angle. The two effects cancel, and you get
exactly twice as many squares in not twice as many degrees.

By the way, your argument would be correct if the squares were drawn on
a sphere centered on the lens, since the squares would always appear a
certain number of degrees wide everywhere in the field. But we're
assuming a flat subject, not a spherical one.

This is sort of like what is explained below... about the egghead
effect. There is no distortion of a flat field subject in a super wide
rectilinear view.

Paul Furman wrote:
Dave Martindale wrote:

Or the handwaving argument: you haven't doubled the FOV angle, but the
additional squares you can see are being increasingly foreshortened by
the very wide angle they are off-axis, so you get more of them in each
degree of extra visual angle. The two effects cancel, and you get
exactly twice as many squares in not twice as many degrees.

By the way, your argument would be correct if the squares were drawn on
a sphere centered on the lens, since the squares would always appear a
certain number of degrees wide everywhere in the field. But we're
assuming a flat subject, not a spherical one.

This is sort of like what is explained below... about the egghead
effect. There is no distortion of a flat field subject in a super wide
rectilinear view.

Except for the inevitable distortion that happens if you view a very
wide angle shot from a position where the image is encompassed by our
eye from a smaller angle (which it usually is), and which is a
widening of things at the edges. It's just a natural feature of
changing viewing geometry, nothing to do with lenses, happens with
pinhole wide angle views :-)

--
Chris Malcolm DoD #205
IPAB, Informatics, JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK
[http://www.dai.ed.ac.uk/homes/cam/]

David Ruether wrote:
"Chris Malcolm" wrote in message ...
Paul Furman wrote:
Dave Martindale wrote:

Or the handwaving argument: you haven't doubled the FOV angle, but the
additional squares you can see are being increasingly foreshortened by
the very wide angle they are off-axis, so you get more of them in each
degree of extra visual angle. The two effects cancel, and you get
exactly twice as many squares in not twice as many degrees.

This is sort of like what is explained below... about the egghead
effect. There is no distortion of a flat field subject in a super wide
rectilinear view.

Except for the inevitable distortion that happens if you view a very
wide angle shot from a position where the image is encompassed by
our eye from a smaller angle (which it usually is), and which is a
widening of things at the edges. It's just a natural feature of
changing viewing geometry, nothing to do with lenses, happens with
pinhole wide angle views :-)
--
Chris Malcolm

I have quite a bit on my web page on lens "distortion" (the articles
index is at www.donferrario.com/ruether/articles.html), but there
is really no distortion in super-wide images (which you *almost*
get to at the end of the above...;-), just an image with possibly
"unexpected/unfamiliar" appearance (I included a couple of samples
of these in the article below...;-). Paul Furman made a CAD drawing
of a hemisphere as imaged near the corner of a S-W WA image
that nicely demonstrates that for sections of "distorted" rounded
objects that are taken parallel with the sensor, there are no
deformations in the image (as you note above, using a different
process). The difference is in semantics - I don't call "distorted",
images that are really not...;-) The article that includes the photos
and drawing is at --
http://www.donferrario.com/ruether/l...erspective.htm

I had to try drawing it to convince myself based on David's description.
It's the way the wide angles 'chop up' 3D objects that creates
distortion but flat subjects are not distorted. Long lenses see 3D
objects more like as if it was an isometric view with close to the same
angle for nearer & further where wide angles have more difference in
angle of view.