Hi Gang
Welcome to the nodal-pupil-panoramic club
First we'll use principal or nodal points as being equivalent when the entrance and exit media are air. The question of panoramic stiching underwater will be left for another time ;-)
Struan and Helen have explained almost everything with pure ASCII text. A true challenge indeed.
Now it is time for diagrams and images.
Let us start with a geometricall ray tracing (see attached pdf file).
The problem is to define what we want in panoramic stiching with a regular camera.
We want that two points B1 and B2 "aligned" on view #1 (two points are always aligned !! so we should add "aligned with something in the camera") stay aligned on view #2 after rotating the camera. But what is the meaning of 'aligned' on film ?
When "B1 and B2 show as aligned on view #1", it means that, focusing on B1, the centre C'2 of the blurred image of B2 coincides with B'1, sharp image of B1 on film. The centre of the blurred image C'2 is located on the ray that connects the centre of the exit pupil P' with the sharp image B'2.
So the only way that the alignement on film is not destroyed is that in object space, B1, B2 and the centre of the entrance pupil P stay aligned while rotating the camera.
This condition can be fulfilled only if we rotate the camera around P.
P is located close to a H when the pupillar magnification ratio is close to unity.
The pupillar magnification ratio is fixed when the position of the iris relative to the position of the lenses does not change when focusing the camera.
This applies to all lenses without moving groups like view camera lenses and most traditional fixed focal lengths lenses. However in zoom lenses or macro lenses with floating elements, the pupillar magnification ratio can, of course, change, but not if we simply move the whole lens for focusing. The trouble is that is most modern zoom lenses, groups move also when focusing, not only when zooming... My understanding is that this change of pupillar magnification ratio, and hence the position of the entrance pupil, can be dramatic in a trans-standard zoom lens, changing from >1 in wide-angle-retrofocus position to <1 in long-focal-tele posistion.
Fortunately, we LF users ignore those trans-standard kind of zoom lenses as being unacceptable for our purpose ;-) So we escape from the dramatic situation of a diabolic entrance pupil that moves according to its fantasy !!
The change in pupilar magnification ratio is probably very minor in a floating-element macro lens.
I have plotted an arbitrary case with a pupilar magnification ratio equal to 1.5, this is the case for modest retrofocus lens designs. A kind of lens unknown to large-format users so I hope that the moderators will forgive me ;-)
In this case I have chosen to place the exit pupil half a focal length (f.l.) in front of H', therefore everything else is fixed, the position of the entrance pupil has to be 1.33 times the f.l. in front of H and the entrance pupil diameter 1.5 times smaller that the exit pupil.
Please note the weird ray tracing connecting the edges of the pupil together through the principal planes.
The green dashed ray is there only to tell us where the sharp image B'2 is located. It crosses the principal points H=N and H=N' and exits at the same angle as the entrance angle.
If there is a key-statement in this delicate question, this is the one: H=N and H'=N' have little to do with parallax issues. "little' since the position of the sharp image B'2 defines the conical projection for the blurred image C'2 ; so actually the position of H and H' plays, of course, a certain role in the question.
What about panoramic cameras like the Noblex®
They simply do not fulfill the parallax-free condition.
They are designed for far-distant objects and the axis of ratation should be located close to the rear nodal point to keep the image sationnary w/respect to film.
If a similar camera was designed for macro work, the rotation point shoud be different.
For example at 1:1 ratio with a perfectly symmetric lens, the proper rotation axis for a stationnary image on film should be the centre of symmetry of the lens, located mid-way between H=N and H'=N', not H'=N' like for far-distant objects. And this still-to-be-designed camera would not satisfy the parallax-free condition either, since in this case the entrance pupil is located in H=N (symmetric lens). Except when H' and H are close together, a situation that actually occurs not only for the single thin lens element, but also in some "thick" coupound lenses like the 150 mm Zeiss Sonnar (again off-topic, sorry).
Now that we are convinced that the centre of the entrance pupil is the right place to rotate for parallax-free panoramic stitching, it is time for an example "how precise should we be"
Sorry again if this is not large format, but Mr Carlos Manuel Freaza has done the test for a twin lens rolleiflex. He manages to show the parallax effects with objects located close to the camera, a few metres, and he is able to show that the Rolleiflex should not be rotated around the regular tripod socket, but a few centimetres in front, where the entrance pupil is located and where Rollei engineers in the old times had purposedly (God bless Them) placed the rotation point of the (long discontinued) Rollei panoramic attachment.
See images here, the title could be : "The Ultimate Quest for the Panoramic Parallax-Free Guitar"
"Rolleiflex 2.8C rotation axis: Technical folder, test"
http://www.rollei-gallery.net/itar/folder-5285.html
As a conclusion.
A kind of Secret of the Old Masters, lost for decades, unveiled and re-discovered thanks to the Internet. Am I kidding ? Certainly yes, however it should be mentioned (sotto voce) that Hasselblad brochures had to be updated to correctly mention the entrance pupil and its proper position for panoramic stitching, after initially mentioning incorrectly the entrance nodal point.
Do not ask me why this was corrected some day ;-);-)
To actually see the diagram, you should click on the thumbnail below, the pdf diagram will open readable in the pdf viewer attached to your browser.
Bookmarks