PanoTools:
Re: Re: entrance pupil - nodal point
Dan Slater 2004-Nov-12 07:11:51
Rik Littlefield wrote:
>Can you clarify a couple of fine points for me?
>
>1. I'm having trouble with the precise definitions here. I'm getting
>that the entrance pupil -- the virtual image of the aperture stop --
>is an outline enclosing an area, but the center of perspective is a
>dimensionless point. Apples and oranges, on the surface.
>
>Is it more correct to say that the center of perspective is the
>intersection of the lens axis and the plane containing the entrance
>pupil?
>
>
This gets a bit esoteric but here goes: The center of perspective is
really just a concept that assumes that the perspective is viewed from a
single infinitely small point. A real world lens approximates this very
closely if the lens is stopped down and does not have significant pupil
aberration. A pinhole lens would be a good example of a lens that very
closely approximates the true center of perspective. A wide angle or
fisheye lens does not have a simple center of perspective but one that
is generally good enough for our application. In a real world case, the
"center of perspective" location changes as a function of the angle from
the optical axis. For a typical fisheye lens, the center of perspective
moves forward with increasing angle from the optical axis by about an
inch or so. This number can vary from about 1/2 inch to several inches
for typical fisheye lenses and a bit less for rectilinear wide angle
lenses. Physically smaller and less wide angle lenses generally have
less pupil shift with angle than larger or wider angle lenses.
>2. What happens in the case proposed by Erik Krause, where at full
>aperture the limiting stop is not the variable iris? If the center
>of perspective is exactly tied to the image of the aperture stop,
>then it seems the center of perspective will suddenly shift from one
>place to another as the lens stops down. Possible, I guess, but it
>does not seem likely.
>
>What I imagine will happen is that the center of perspective will
>stay at the same place. I also imagine that place will be very near
>the image of the iris, but perhaps *slightly* displaced from it
>depending on the exact placement of the iris. (I think it cannot be
>displaced very much, or the lens would vignette when stopped down.)
>
>
What you are describing is vignetting. This does change the location of
at least part of the aperture. As the entrance pupil is the image of the
aperture stop, part or all of the entrance pupil location (perspective
center) must be changed. This rapidly become somewhat esoteric but if
you think in terms of the entrance pupil being nothing more than the
virtual image of the actual, in this case, multiple surface stop, it
becomes a bit easier to understand.
The bottom line is that if you are interested in a precise perspective
center with a fisheye or wide angle lens, you should determine the
entrance pupil location at the angle (and fstop if you have
*significant* vignetting problems) that you will be stitching at. You
really only need to be very precise if you have very close objects and
minimal image overlap. The other advantage is that stitching is
simplified with a well controlled perspective center. On the other hand,
after going through various rotator mounts, virtual tripods, etc., I
have switched almost completely over to shooting only hand held using
significant overlap and putting a bit more work into stitching.
Dan
[Non-text portions of this message have been removed]
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