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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 <paul-@-edgehill.net> 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/]

On Apr 17, 8:03 am, "David Ruether" <druet...@twcny.rr.com> wrote:
> "Chris Malcolm" <c...@holyrood.ed.ac.uk> wrote in messagenews:...
> > Paul Furman <pa...@-edgehill.net> 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 atwww.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 --www.donferrario.com/ruether/lens-angle-of-view-and-perspective.htm
> --
> David Ruether
> d_ruet...@hotmail.com
> www.donferrario.com/ruether

One way to envision a distortion-free lens is to map out the image a
pinhole camera produces. Any ray entering a pinhole lens MUST
continue in a straight line, since there is nothing in the lens to
deviate it. When distortion happens, the chief ray is not following
the normal "thin lens" mapping that requires the chief ray to transit
the lens and aperture undeviated.

As long as the chief ray transits the lens undeviated there is no
actual distortion in the lens design sense of the word.

David Ruether wrote:
> "Chris Malcolm" <> wrote in message news:...
>> Paul Furman <paul-@-edgehill.net> 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.