Panoramic photography - choice of pivot axis

[Doug Kerr]

The matter of the choice of an appropriate pivot axis for multi-shot panoramic photography is often confused by the interaction between two separate misconceptions:

Misconception 1: The pivot axis that avoids parallax shift as the camera is rotated passes through the nodal point of the lens.
[Of course in general, a lens has two nodal points. Some believers in this concept don't think about that, some believe that it is the first nodal point that is meant, and some believe it is the second nodal point.

Fact: The pivot axis that avoids parallax shift as the camera is rotated passes through the entrance pupil of the lens.

Misconception 2: The well-known test used in this area (see description later) gives us the location of "the nodal point" of the lens. [Which one?]

Fact: The well-known test used in this area gives us the location of the entrance pupil.

We sometimes hear, from those aware of the real fact in matter 1, that "since the difference is inconsequential in most cases of interest, I will just use an axis through the nodal point, since I can determine where that is, and I can't readily determine where the entrance pupil is."

Wow, how do you determine the location of "the nodal point"? Well, usually it is meant through the "well-known test".

But of course that yields the location of the entrance pupil. So there is no compromise in doing the only thing that is really doable in the field! (The test to locate either nodal point requires laboratory apparatus.)

I suspect that this whole misunderstanding came about since the "well-known test" for the location of the entrance pupil sounds a little like (if you don't pay attention to the details) the test to determine the location of the second nodal point of the lens.

So you can see what I mean, I'll give simplified explanations of both tests here.

Test for the location of the entrance pupil

The lens is tested on a camera. The camera regards two test objects at different distances, roughly aligned vertically from the camera position. Using a "candidate" pivot axis (we assume here a vertical one), a test frame is taken with the camera aimed so the images of the test objects are near one side of the field of view, and another with the camera aimed so the images of the test objects are near the other side of the field of view.

We check to see if there is any difference in the relative alignment of the two objects between the two frames (a parallax shift). If there is, we change the pivot axis and repeat the test, until there is no parallax shift as the camera is rotated. The pivot axis at that time passes through the entrance pupil. (And, of course, is the preferred axis for panoramic photography).

Test for the location of the second nodal point

The lens alone is mounted in a fixture that provides for its rotation about a changeable axis. The lens regards a point object at infinity.

The aerial image of the point created by the lens is observed though a microscope, focused on the focal plane. (The microscope is stationary; it does not "swing" with the lens.)

The lens is rotated about a "candidate" pivot axis, and we observe if there is any sideways movement of the image point. If there is, we we change the pivot axis and repeat the test, until there is no shift of the image as the camera is rotated.

The pivot axis at that time passes through the second ("rear") nodal point of the lens.

Test for the location of the first nodal point

We turn the lens around so its rear faces the test object. It second ("rear") nodal point in this situation is actually what would be its first nodal point in its ordinary use.

We conduct the test described above. The result is the location of the actual "first" nodal point of the lens in its normal use.

***********

Note that all these two tests are quite different. They both involve swinging something and observing something about the image. Thus it is not surprising that one may be confused with the other.

 

[Cem_Usakligil]

Hi Doug,

An excellent post, thanks.


Cheers,

 

[Doug Kerr]

Swinging-lens panoramic cameras

Adding to the confusion over the matter of the pivot axis for multi-shot panoramic photography is the situation of the swinging lens panoramic camera, where it is (correctly) said that the pivot axis should pass through the second nodal point of the lens.

In this type of camera, the lens, in a cylindrical "turret", swings smoothly across the scene in the course of the shot. The film is held in a curved track, cylindrical and concentric with the pivot axis.

The rear of the lens turret is an opaque container except for a narrow vertical slit at the lens axis. Among other things, it serves as a "focal plane shutter" as it passes across the film.

If we are to avoid smearing of the image on the film (owing to lateral motion of the image as the turret moves, over the period that any given point on the film is uncovered by the slit), we must have the lens turret rotate about an axis through the second nodal point of the lens. The optical principle involved is exactly the same one upon which we rely in the test to locate the second nodal point of a lens.

If we arrange for that axis, it would seem that we have compromised our criterion for the avoidance of parallax shift (which would call for an axis through the entrance pupil). But in this situation, objects at any given azimuth in the scene (sch as our famous near and far objects) are only in the picture (to make a bad pun) very briefly during the entire process, owing to the vary small lateral field of view of the camera at any given time, which in turn comes from the masking effect of the slit.

This is unlike the situation in multi-image panoramic photography, where our famous objects appear in two consecutive frames, with the camera angle quite different between them.

Thus here there is no opportunity for parallax shift to manifest, and that issue becomes inconsequential. So the use of a swing axis through the second nodal point is the clear choice.

It is likely that the situation in this kind of camera is in part responsible for the incorrect belief that the appropriate pivot axis for multi-image panoramic photography should pass through "the" nodal point of the lens. (In fact, some authors have said that it should pass through the second nodal point of the lens, which is probably a direct misapplication of the situation in the swinging-lens camera.)

Best regards,

Doug

 

[Jim Galli]

Doug, we can take this off-line so as not to bore everyone here but I'm having trouble understanding how to do the math with my Cirkut camera. I've lost the original lens that the camera was balanced with. It was a Turner Reich convertible of 10 1/2, 18, and 24 inch. I'm most interested in the 18 inch but if I use a modern lens where the node is somewhere in the middle around the aperture the physical length of the set-up is different than the old TR that used a single group behind an aperture. The result has been that the image is unsharp I believe from bad centering over the axis. Distance from the lens and speed of travel was done by "gears" with numbers. I have the set that matched the original lens. Perhaps my only solution is to just look on Ebay for a TR lens. They weren't terribly sharp though, especially the single groups.

 

[Doug Kerr]

Hi, Jim,

I'll send you a wire with my thoughts and maybe a request for some more background.

Can you e-mail me so I have your e-mail address. I'm at:

doug.kerr@att.net

Thanks.

Best regards,

Doug

 

[Jack_Flesher]

If we are to avoid smearing of the image on the film (owing to lateral motion of the image as the turret moves, over the period that any given point on the film is uncovered by the slit), we must have the lens turret rotate about an axis through the second nodal point of the lens. The optical principle involved is exactly the same one upon which we rely in the test to locate the second nodal point of a lens.

If we arrange for that axis, it would seem that we have compromised our criterion for the avoidance of parallax shift (which would call for an axis through the entrance pupil). But in this situation, objects at any given azimuth in the scene (sch as our famous near and far objects) are only in the picture (to make a bad pun) very briefly during the entire process, owing to the vary small lateral field of view of the camera at any given time, which in turn comes from the masking effect of the slit.

So now we have it both ways? Seems to me it depends on the projection chosen, not the capture methodology

 

[Doug Kerr]

Hi, Jack,

So now we have it both ways?

Quite.

One technical consideration applies to one technique, and another to another technique, leading to two different choices of axis for the two techniques.

This is discussed in some detail in my recent message (which you in part quote).

The projection to which we ultimately transform the captured image or image set does not affect this matter, nor in fact does the "native" projection of the capture technique.

With the multi-shot technique, regardless of the native or ultimate projection, the presence of parallax shift in the image capture is undesirable. A camera pivot axis passing through the entrance pupil avoids parallax shift. There is no issue of smearing at the focal plane.

With the swinging lens technique, regardless of the native or ultimate projection, "smearing" at the focal plane is undesirable. A lens pivot axis passing through the second nodal point avoids smearing at the focal plane. There is essentially no issue of parallax shift.

Best regards,

Doug

 

[Doug Kerr]

Swinging lens panoramic cameras

I should probably mention that, in a swinging lens panoramic camera, the choice of an axis through the second nodal point to eliminate image smearing is only precisely valid for objects at a great distance.

If our principal subject is at a moderate distance (and we assume that we focus on it, so that there is the potential for best sharpness for it), then smearing is avoided (for images of that object) by rotation of the lens about an axis slightly forward of the second nodal point.

The ideal location can be readily calculated, but doing so requires knowledge of the location of the first nodal point as well.

Further complications occur with respect to how the nodal points of the lens move axially as the lens is focused (which depends on the focusing system used). I would expect that by clever design, the matter of the ideal pivot axis shifting with object distance could perhaps be automatically compensated for as we focus at different distance.

As an example, if the lens employs "all element" focusing (in which the entire optical portion of the lens is just shifted forward and back, as in a Canon FD 50 mm macro lens), then the displacement of the rear nodal point with focusing is in the wrong direction for such compensation.

Those familiar with swing lens panoramic cameras may know if this is the case for any of them (I don't have any).

Best regards,

Doug

 

[Jack_Flesher]

The projection to which we ultimately transform the captured image or image set does not affect this matter, nor in fact does the "native" projection of the capture technique.

Hmmmm... So the Cirkut swing-lens camera which has a curved film plate has the same parallax issues as say the horizon swing lens camera with a flat film plate?

 

[Doug Kerr]

Hi, Jack,

Hmmmm... So the Cirkut swing-lens camera which has a curved film plate has the same parallax issues as say the horizon swing lens camera with a flat film plate?

Well, the usual swing lens camera does not have a parallax issue of any consequence. And they do not in general, so far as I know, have flat film plates (although I guess some might).

And I believe that in a Cirkut camera, the entire camera rotates (which is not what I mean by a swing lens camera). It in effect practices a third technique. And I wasn't aware that it has a curved film plate.

So I have to remind myself exactly how a Cirkut camera works before I really jump on the matter.

It may well be that the slit I believe it it has makes the parallax issue inconsequential, as on a swinging lens camera.

But I in fact plan to review its details soon anyway in connection with a question from Jim Galli, and when I have, I'll pick up on the interesting point you raise.

Thanks.

Best regards,

Doug

 

[Jack_Flesher]

And I believe that in a Cirkut camera, the entire camera rotates (which is not what I mean by a swing lens camera). It in effect practices a third technique. And I wasn't aware that it has a curved film plate.

The Cirkut camera uses a clockwork to rotate the camera in total *and* advances the film across the film plane and past an aperture slit at the same time and at the same speed as the rotational speed of the film at the film plane. This nets it the same thing as a fully curved film plane the full width of the negative in a significantly smaller box than would otherwise be needed if the film remained stationary.

An ancillary note: It is possible (and is now somewhat common) for the same person to appear twice in a Cirkut photo -- they simply wait until the lens passes their initial position then quickly run to a new position faster than the lens gets there and get recorded a second time ;-)

 

[Doug Kerr]

Hi, Jack,

In a Cirkut camera, the entire camera rotates. As I thought I recalled, there is a fixed mask in front of the focal plane, and as the camera rotates, the film, which is loaded a roll, is pulled past the slit.

I don't think there is anything about the film path that is "curved". Since only a very short section of the film is active at any particular time (owing to the slit), it wouldn't seem to have any significance to do so.

You can rather see that here:

The ratio between the angular rotation of the entire camera and the linear motion of the film past the slit is chosen to avert any image blurring (as well as to prevent geometric distortion). I know that the needed numerical ratio is affected by the focal length of the lens and perhaps the distance to teh subject as well. I know that there were various gear sets available to cater to the specific setup of interest.

As in the case of the swinging lens camera, there is essentially no issue here of parallax shift. If we wanted to eliminate any possibility of an effect, we could theoretically arrange for the camera to rotate about the entrance pupil, but I think there is no physical provision for that in the Cirkut mount and azimuth drive arrangement. (This is after all a bellows camera, and the lens moves substantially with focusing.)

There is no issue of second nodal point either, as the lens does not"scan" the film through its rotation with respect to the body.The equivalent consideration, regarding image smear on the film, is addressed by the ratio I spoke of earlier.

I will probably be reconstructing the math involved in connection with Jim's inquiry, and I'll report the results here.

Best regards,

Doug

 

[Jack_Flesher]

In a Cirkut camera, the entire camera rotates.

Yes, see my explanation in my post above

There is no issue of second nodal point either,

Nor is there of entrance pupil to begin with...

As you indicated, a change in focus on these cameras makes a correspondingly large change in either the nodal or entrance pupil locations and is not accounted for. Here the very narrow FoV imparted by the aperture slit combined with a fixed distance to the film plane does all the parallax elimination work; which is in fact a parallax adjusted projection method

Cheers,

 

[Jim Galli]

An ancillary note: It is possible (and is now somewhat common) for the same person to appear twice in a Cirkut photo -- they simply wait until the lens passes their initial position then quickly run to a new position faster than the lens gets there and get recorded a second time ;-)

Called a "Pizza Run". No one can seem to resist doing this.

Also of interest, modern vss. ancient, Cirkuts were used for large groups of people and each person had to hold still for roughly the same amount of time as a 1/10th second exposure. I have nightmares thinking of stitching a group photo that comprised maybe 6 to 8 seams together.

 

[Jack_Flesher]

called a "pizza run".

lolololol!!!!! I did not know that, too funny!

 

[Doug Kerr]

Gear ratio for Cirkut camera

Hi, Jim,

Of course I can't give the final answer to the gear ratio matter for your Cirkut camera since I don't know the details of the whole gear train, the diameter of the film drum, and so forth. But here's the underlying math from which you should be able to proceed:

Proper operation is attained by gearing that produces this result:

(57.3 s)/A = Q

where s is the distance the film moves during rotation of the camera through angle A, and Q is the distance from the lens (precisely, the second nodal point, but with view camera lenses being relatively "thin", that's not a big deal) to the film, with A in degrees and s and Q in consistent units (both mm, both inches, etc.).

Q can be measured if you wish (with the lens focused at the subject distance of interest), or can be calculated thus:

Q = (Pf)/(P-f)

where P is the distance from the subject to the lens (precisely, the first nodal point of the lens, but . . .) and f is the focal length, all in the units we want to have for Q.

Aren't you glad you asked!

Best regards,

Doug

 

[Doug Kerr]

Yes, see my explanation in my post above

Nor is there of entrance pupil to begin with...

None at all if the slit is of zero width; negligible in any practical case.

Here the very narrow [lateral] FoV imparted by the aperture slit [actually a field stop slit] .. .

Best regards,

Doug

 

[Jim Galli]

Hi, Jim,

Aren't you glad you asked!

Best regards,

Doug

Thanks Doug. I'm not sure "glad" is the word I'm searching for. I'll keep looking for the TR. J