Panoramic pivot point - demonstration images

For some while, there was a widespread belief that the proper pivot point for panoramic photography ("P5") was an axis through "the nodal point of the lens". Now one thing that should have made one suspicious of that is that of course any lens we are likely to encounter has two nodal points. And in fact, there are some "nodal point" enthusiasts who know that and believe that the P5 is the first nodal point, and some who believe it is the second nodal point.

But in fact, the P5 is actually an axis through the entrance pupil of the lens - the "virtual image of the aperture stop from in front of the lens". It is fact the entrance pupil we "see" when we look into the lens and see the aperture stop iris.

I just took a series of test shots, using my Canon EOS 20D, that illustrates the situation. Of course, the criterion here - critical to the effective "stitching" of multiple-frame panoramic images - is that there should be no parallax shift as the camera is "panned". That is, if a near and far object have a certain apparent alignment on the image when they both appear near the right edge of the frame, they should keep that alignment when they appear (in the next "pane") at the left edge of the frame.

The test was baldly intended to show that yes, the P5 is an axis through the entrance pupil, and no, an axis through either nodal point won't do (unless of course the entrance pupil happens to be collocated with the first nodal point, which is not uncommon).

To make the distinction more clear (to avoid approaching the situation of accidental collocation), I equipped the test lens (a Canon EF 50 mm f/1.4) with a "displaced aperture stop/entrance pupil" - an aperture stop in front of the entire real lens (in a filter mount, as a matter of fact).

The test objects were a pair of nail polish bottles, see here intentionally not aligned:



In each test run, the objects were placed so that they were aligned in the camera frame when the camera aim placed them in the left-to-right center of the frame.

Then, two images were taken, one with the camera aimed to the left of "neutral" so the two objects appeared near the right edge of the frame, and one with the camera aimed to the right of "neutral" so the two objects appeared near the left edge of the frame.

Here, we will see the two images of a pair, cropped so that most of the frame is gone (but with the objects still near the pertinent edge of the remaining frame).

The two objects were at distances from the front of the lens of about 20" and 40". Focus was at a distance of 30"; thus, neither object was in "perfect focus". (Of course, both couldn't be.) The displaced aperture stop/entrance pupil had a relative aperture of f/8.0.

Here, we see the "left" and "right" panes with rotation about an axis through the (displaced) entrance pupil:



[continued in part 2]

(Part 2)

Here, we see the two panes with rotation about an axis through the estimated location of the first (front) nodal point. (It is difficult to actually determine where the first nodal point is, and I don't have the needed apparatus.)



You can see that this approach results in a substantial amount of parallax shift.

Here, we see the two panes with rotation about an axis through the estimated location of the second (rear) nodal point. Its location is readily calculated very closely from the focal length and the current focus distance. (Of course, to determine the precise focus distance we must use, we need to know the location of the first nodal point. But a small error in guessing that doesn't have a big impact on the calculation.)



You can see that this approach results in a even greater amount of parallax shift.

An extensive discussion of this matter and the theoretical principles involved can be found in my tutorial article, "The Proper Pivot Point for Panoramic Photography", available here:

http://doug.kerr.home.att.net/pumpkin/index.htm#PanoramicPivotPoint