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Panoramic pivot point - tutorial article updated and expanded

Doug Kerr

Active member
When doing panoramic photography with a conventional camera, multiple, slightly overlapping shots of the overall scene are taken by pivoting the camera in steps, and the images are joined to make a single large-scope image. In order to be able to properly join the images, we must avoid parallax shift between them. To do so, the camera must be pivoted about the camera’s center of perspective, which turns out to be the center of the entrance pupil of the lens.

It is widely, but incorrectly, said that the proper pivot point is “the nodal point” of the lens.

This matter is discussed at length, with numerous illustrations (and almost no math), in my tutorial article, "The Proper Pivot Point for Panoramic Photography", which has just been extensively updated and expanded. It is available here:


Among the changes in this issue are:

- An appendix has been added that shows how the principles discussed work in the case of a reasonable-size aperture. (In the basic discussion, a "tiny" aperture is used to simplify and clarify the work. Some had been concerned that the conclusion reached that way lacked generality.)

- A set of test images are included that demonstrate, in a "real life" situation, that in fact rotation about the entrance pupil, and not about either nodal point, produces the desired result.


Active member
Hi Doug,

As I did this many times before, I'll do it yet again: thanks so much for sharing all this know-how selflessly with us. Much appreciated :).




New member

Interesting article, thanks.

I think the term Nodal point is misused, most people mean entrance pupil but don't realise it.

The quickest and most accurate way I found to set a lens' entrance pupil up is to use a 4' square sheet of steel mesh (1" grid spacing) and place it centrally about 10" in front of the lens. Adjust the camera position to minimise parallax errors in both planes and your ready to do 360 QTVRs.

Doug Kerr

Active member
Hi, Bart,

It's demonstrated in this PDF:
Nice piece, and a nice technique. Thanks.

However, it is important to note that we can usually find where the entrance pupil is by by looking at it (since it can be easily seen looking into the front of the lens) and estimating its location relative to some handy external lens feature.

People often scoff at this, saying, "Well, Kerr, you should realize that nothing you see looking into the front of the lens appears to be in its actual location".

True enough if we are speaking of physical things inside the lens, such as the aperture stop ("iris") proper.

But the entrance pupil is, by definition, "what the aperture stop appears to be [in both diameter and location] when viewed from the front of the lens". So we do (by definition) see it in its actual location (even though it is only an "optical illusion"!).

By the way, a colleague (anonymous at the moment, but a well-credentialed optical engineer) advises that he hopes to do a "sensitivity analysis" of the pivot point matter. This would allow us to calculate, for any postulated amount of "error" in locating the ideal pivot point, "how much parallax shift" would result. I have encouraged him to move forward on this, which I think would produce a valuable tool.


Best regards,