PanoTools:
Re: entrance pupil - nodal point
Rik Littlefield 2004-Nov-11 05:54:09
--- In #removed#, "Erik Krause" <#removed#>
wrote:
> On 10 Nov 2004 at 22:52, John Houghton wrote:
>
> > > On 10 Nov 2004 at 8:59, Erik Krause wrote:
> > > Sorry, but from optical geometry this can not be true.
> > > You don't change refraction by putting an aperture somewhere,
> > > hence you can not modify the location of nodal point
> > > with this technique.
> >
> > I did say that this did not change the position of the
> > nodal point. It is nevertheless the case that if you
> > experimentally determine the "no parallax" point,
> > it corresponds to the position of the aperture,
> > not the nodal point. Try it yourself.
>
> I'll do it, but first off all please tell me the exact settings
> you used. And please could you explain the theory why the
> "no parallaxe" point should corresponds to the position of the
> aperture? This is contradictory to all I learned about
> geometrical optics and what proved to be true all the time...
>
> BTW.: There is not only one aperture inside each lens. There
> are several designed to minimize stray light. Any of them
> could be the one limiting the diameter of the pencil of rays
> if you don't stop down. Would this mean that the "no parallaxe
> point" moves if I stop
I disagree with everybody ;-)
But I think I have figured out the problem -- there is not a standard
name for the point that we care about!
Let me explain...
What we care about is a geometric center of projection -- the point
(if one exists) around which we can rotate the lens & film as a unit
without getting parallax problems.
The entrance and exit pupils are often defined as images of the
aperture as seen through the front and back lens elements. (This
definition fails, by the way, for telecentric lenses, whose entrance
pupil is effectively at minus infinity.)
It is certainly true that all light rays must pass through these
pupils. However, the front-to-back locations of the entrance and
exit pupils depend not just on the lens elements, but also on the
exact location of the aperture stop. The lens designer has some
freedom about where to put that. It may be driven by mechanical
reasons in addition to optical -- where is there space for it?
Different placements of the stop would result in slightly different
front-to-back positions of the entrance and exit pupils. This would
not affect the geometric center of projection, which is determined
only by the lens elements in this case. So the location of the
entrance pupil is not always what we want.
The front and rear nodal points are defined as being the points on
the central axis of the lens through which light rays are displaced
without changing their angle. The rear nodal point has the property
that if the lens (not the camera) is rotated around it, then the
image of points at infinity do not move. (See
http://www.abdn.ac.uk/physics/px2505/lensnote.doc ) This is useful
for special landscape panorama cameras. There is a similar
relationship for the front nodal point, that again applies for points
at infinity.
But the nodal points cannot always be what we want either, because
they are fixed with respect to the lens while the geometric centers
can vary with focus. Suppose, for example, that I set up to do a
very close-up "panorama" at 1X magnification using a conventional
lens. Then symmetry requires that the point around which I can
rotate the lens without moving the image will no longer be the rear
nodal point but instead will be in the center of the lens, midway
between the two nodal points (and also between the entrance and exit
pupils).
So I think we need a new name -- I like the "no-parallax point" used
earlier in this thread -- to mean the geometric center of projection
for rotating the whole camera (lens+film).
Then we can accept that the no-parallax point is not necessarily the
entrance pupil or the front nodal point. Instead it is someplace
else that may be at or near those locations, or not, depending on
details of lens design and on variable conditions like subject-to-
lens distance.
And perhaps we can also agree that the standard calibration
techniques actually find the no-parallax point, which of course is
what we care about in the first place.
--Rik
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