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
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