• Please use real names.

    Greetings to all who have registered to OPF and those guests taking a look around. Please use real names. Registrations with fictitious names will not be processed. REAL NAMES ONLY will be processed

    Firstname Lastname

    Register

    We are a courteous and supportive community. No need to hide behind an alia. If you have a genuine need for privacy/secrecy then let me know!
  • Welcome to the new site. Here's a thread about the update where you can post your feedback, ask questions or spot those nasty bugs!

The Proper Pivot Point for Panoramic Photography

Doug Kerr

Well-known member
My recent work on the geometry of tripod heads lead me to the area of panoramic heads, and I was reminded of the almost universal appearance of a misconception about the proper location of the "pivot point" for multi-image panoramic photography. So I concluded that it was time again for my periodic lecture on this topic.

Parallax shift

The issue here is the avoidance of parallax shift in multi-image panoramic photography. That is the phenomenon in which the relative alignment of near and far object points, on the image, shifts as we rotate the camera from shot to shot (considering point pairs that fall with the frame on consecutive shots). The result is that it becomes difficult to "stitch" the consecutive images into a consolidated image.

The basic cause of the problem is that the point of perspective of the camera - where the camera appears to be "looking at the world from" - moves from side-to-side (or up-and-down) as we pivot the camera. This is avoided if the pivot axis passes through the point of perspective (both axes for multi-row panoramic photography, where there is up-and-down movement of the camera as well as side-to-side movement).

But where is the point of perspective? It is at the center of the entrance pupil of the lens.

The entrance pupil

The entrance pupil is formally defined as the virtual image of the aperture stop from in front of the lens. In practical terms, when we look into the front of the lens, we "see" the aperture stop (iris), but not with its actual diameter or at its actual location along the lens axis. This is a result of the effect of the lens elements in front of it. It is a phantom - an optical illusion.

But what we seem to see is, by definition, the entrance pupil - it actually is right where the iris seems to be, and its actual diameter is the diameter the iris seems to have. It is a "recognized, card-carrying phantom."

Why is this the point of perspective of the camera? Because it is the "peephole" through which the camera sees the world. If I look at the world through a knothole in the fence, then, from a standpoint of perspective, where am I "looking from"? The knothole.

Why does it work that way? Consider the camera to be a "black box". We know nothing about what happens to rays of light as they pass through the various lens elements. Although the entrance pupil is (most commonly) located "inside" the lens, it is an "external" creature of the camera.

Any ray of light from the scene that, arriving at the camera, is not headed for "inside the entrance pupil" will not make it through the lens. What that means, if we could see inside the camera, is that such rays, refracted by the lens elements in front of the iris, would not make it through the iris. So the entrance pupil is the "exterior" (in the sense I described above) proxy for the iris.

Since only rays that would pass through the entrance pupil enter the camera proper, the entrance pupil is the peephole through which the camera views the world. And, as in the example of looking through the fence, that peephole is where the camera appears to be, when looking at the world, from a perspective standpoint.

Locating the entrance pupil

How can we determine the location of the entrance pupil? One way is by testing for parallax shift. With the camera mounted in some way on our "panoramic head", we swing it from side to side, looking in the viewfinder or in live view for a shift in the relative positions of a near and a far scene object. We adjust the camera longitudinally on the "slide" of the mount until, when we swing the camera, there is no such relative movement. We have then positioned the camera so the axis of the head passes through the camera's point of perspective (and thus through the entrance pupil).

Another way is we can just look and see where it is! We look into the front of the lens, and confirm which circle we see is the aperture stop (iris), perhaps by closing it with the DoF preview feature, or by firing a shot.

Where the iris appears to be is the actual location of the entrance pupil. (Remember, it is not a physical thing - just a "virtual image" - an optical illusion, as it were. But where it seems to be, it is.) We judge its location and set the camera on the rail so that falls over the head axis.

The misconception

So, what's the misconception I referred to at the outset?

We most often read that "the panoramic axis should pass through the nodal point of the lens". That's just not true (although it is not uncommon for the first nodal point of the lens to be at very near the same location as the entrance pupil - a case of "better lucky than right").

One hint that this statement is not correct is that of course almost any lens has two nodal points, so which one is meant here, anyway? Of course, it is neither.

Often, people I explain this to say,"but that can't be. I used the well-known test for finding the location of the nodal point (meaning the procedure I described above), mounted the camera accordingly, and get perfect results."

Of course. That's because that is not the test to find (either) nodal point - it is the test to find the entrance pupil! So of course it works.

There is a (quite different) test to locate the lens nodal points. And at first glance, it seems a little like the test we speak of here. That might be one reason behind the misconception.

For more information

Those who are interested in further information on this matter may want to read my technical article, "The Proper Pivot Point for Panoramic Photography", available here:

http://dougkerr.net/Pumpkin#PanoramicPivotPoint
 

Doug Kerr

Well-known member
Another matter that may contribute to the misconception as to the proper axis for multi-image panoramic photography relates to the "swinging-lens" panoramic camera

In that, the body is stationary, as is the film, which lies in a curved track. The lens is in a cylindrical turret (evocative of the side machine gun turrets in some World War I tanks). It has a vertical slit at its rear (which is the aperture stop and exit pupil). The turret rotates about a vertical axis, "spraying" the image through the slit onto the film.

In these cameras, the rear nodal point of the lens is located at the turret axis. It is not that, in this situation, that location eliminates parallax shift - it doesn't. But it eliminates a more deadly phenomenon: "smearing" of the image on the film. (This happens when the image does not move across the slit one way at the same rate the slit moves across the film the other way, so any little piece of the image is stationary as it falls onto the film.)

This choice of a rotation axis (not at the entrance pupil) means that parallax shift is not eliminated. It occurs, and in this situation results in a small lateral blurring, and a small lateral geometric distortion (narrowing), for nearby scene objects.

The "smearing" consideration is in fact identical to the phenomenon observed in the actual optical laboratory test to locate the rear nodal point of a lens. It will only locate the rear nodal point; to locate the front nodal point, we have to turn the lens end-for-end and have the front nodal point play the role of the rear one to become "found"!

Best regards,

Doug
 

Doug Kerr

Well-known member
In my report above, I mention the well-known technique for determining, in the field, the proper location of the pivot axis (axes) for multi-shot panoramic photography. It involves observing, though the finder or on live view, aligned near and far scene objects while rotating the camera about the "trial" axis. When the proper axis is in effect, the near and far objects retain their alignment.

Sometimes there are not any handy "near" objects, so we must arrange for some. A useful technique is to use something like a light stand, or the stand portion of a music stand.

Belgian photographer Alain Hamblenne suggests a technique that can be useful in some cases. He suggests hanging a panel of coarse wire mesh a short distance in front of the camera. This provides a convenient array of "near objects", whose alignment with distant building, trees, and so forth can be easily observed as the camera is moved.

The technique is well described in his paper, available in English here:

http://www.outline.be/quicktime/tuto/TheGrid.pdf

ou en français ici:

http://www.outline.be/quicktime/tuto/LaGrille.pdf

Brother Hamblenne is to be commended for correctly identifying the lens feature to be located by the test as the entrance pupil (pupille d'entrée) rather than "the" nodal point (point nodal).


Best regards,

Doug
 

Doug Kerr

Well-known member
For those who are interested in what a "nodal slide" really is, here is an illustration of Rudolf Kingslake's apparatus (c. 1932) for determining focal length, beginning with the location of the (rear) nodal point of the lens (one can of course find the front nodal point just by putting the lens in the rig backwards):

Kingslake_T-slide-01R.gif

Kingslake "T-slide" apparatus (c. 1932).​

The nodal slide is the part with the nodal point adjustment on it (duh!).

The "T-slide" is a part of the apparatus that automatically maintains a certain critical distance if the lens is rotated through a substantial angle (as is needed for a complete examination of the properties of the lens).

One of our colleagues here (I am embarrassed by not remembering who) was involved, as part of an alumni project, in the refurbishment of the original apparatus, which was discovered in storage in Rochester.

Best regards,

Doug
 

Ben Rubinstein

pro member
I tried the 'look for iris' method with my 16-35L at 16mm using the DOF button, it seems to be somewhere along the focus ring but it's almost impossible to be accurate to within a mm and when I try to rotate round that point it looks way out.

Edit, seems to work in vertical (holding camera in vertical) though not in horizontal, wonder why?
 

Doug Kerr

Well-known member
Hi, Ben,

I tried the 'look for iris' method with my 16-35L at 16mm using the DOF button, it seems to be somewhere along the focus ring but it's almost impossible to be accurate to within a mm and when I try to rotate round that point it looks way out.
Yes, it is sometimes hard to see. Maybe you have not nailed the right hole.

Edit, seems to work in vertical (holding camera in vertical) though not in horizontal, wonder why?
Well, that is curious!

Do you mean finding it, or rotating the camera to see what that does?

Best regards,

Doug
 

Ben Rubinstein

pro member
Tried it again, seems to work now in both vertical and horizontal. I was talking about rotating using the near/far technique with the point I found using the iris method.
 
Top