Converging fields of view

[P3D Neil Harrington <nharrington@xxxxxxxxxxxxx>]

Gregory J. Wageman writes:

>Neil Harrington writes:
>
>>>If I understand it right, the offset lenses simply cause the left image to
>>>have more information from the right side of the scene, and the right image
>>>from the left side of the scene.  
>
>>Beyond the window, yes.  You don't see that that means their angles of view
>>must converge?  (Of course I mean angles of view as if seen from the center
>>of each frame.)
>
>As John Bercovitz explained it, lines drawn from the center of the image
>through the center of the lens converge at the window, and then
>diverge.  

Right.  Any converging straight lines must, of course, diverge after they
cross.  
>I guess what I have a problem with is your use of the phrase
>'converging angles of view', which seems to imply some kind of angular
>rotation, when there is in fact none.  Yes, it is a matter of semantics,
>but sometimes the choice of semantics makes things much easier to
>exlain to a neophyte.  I prefer to think of the offset as a selective
>masking at the film plane.

You bet.  That's exactly what it is.  The only problem with settling for the
term "offset" is that, as we have seen here, it does not convey to everyone
the important fact that the fields of view do, in fact, converge.  Several
times others here have mentioned that in a stereo camera, the left frame
shows more of the right side of the subject, and vice versa.  Whenever I've
mentioned this I have added the qualifying "beyond the window," as requoted
above, because it is only beyond the window that this is true.  On the near
side of the window, the opposite is true: the left frame shows more of the
left side of the subject than the right lens does, etc.  _At_ the window
there is no difference at all; both fields of view in that plane are exactly
the same.

>From the responses here, I'm not sure everyone understands this.  Others
have written a number of times that the left frame takes in more of the
right side of the subject, without qualification, as though that were always
the case at all distances.  "Offset" may imply a lateral shifting of the
point of view while still looking straight ahead, as though that were the
reason for the left lens seeing more of the right side of the subject, and
this isn't true.  I suspect this is what led another user here to be
surprised that the film apertures were not _closer_ together than the lenses
in order for the left lens to take in more of the right side of the subject.

>If you think of it as the *apertures* being shifted *outward* from
>the center of the lenses, and remember that the images are inverted, it
>is easy to see the shifting the left aperture to the left causes that
>image to have more information from the right side of the scene.  If
>the lens didn't invert the image, shifting the left aperture left would
>cause it to capture more information from the *left* side of the scene,
>contrary to what you assert in another message.

You're right.  Actually I was being a little silly.  My point, really, was
just that it's the convergent fields of view that establish the window, not
the fact that lenses rotate the image at the focal plane.  If you imagine
the central line of view for each frame to be a plain hollow tube from the
center of that frame passing through the center of the corresponding lens,
those two hollow tubes would converge, the lines of sight crossing at the
window, which would be in the same place regardless of the fact that the
images seen through them were right side up.  But no, I don't really think
it would work that way if you did use some sort of erecting lens systems
instead.

>Let me try a painful ASCII diagram:
>
>    ---------------
>    | |         | |
>    | |  \ /    | |
>    | |   |     | |
>    | |  ---L   | |  "L" represents the center of the lens
>    | |   o     | |
>    | | r   l   | |
>    ---------------
>    ^ ^         ^ ^
>    | |         | |
>    | unshifted | unshifted aperture (lens centered)
>    shifted     shifted aperture (lens offset)
>
>Doing that on both sides in opposite directions creates the binocular
>disparity that positions the window closer than infinity.

No argument there.




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