Doug Kerr
Well-known member
Recent traffic in these esteemed pages suggests that it is time for the monthly delivery of the Annual Nodal Point Lecture.
A lens has two nodal points, normally on the lens axis. (In the fictional "thin lens" these two are at the same place, but not otherwise).
These have an important significance in geometric optics.
In the situation of common interest to us (where the object and image spaces are in the same medium, namely air), these coincide with the two principal points of the lens. These also have an important, but different, significance in geometric optics.
In connection with multi-shot panoramic photography, in which the entire camera is rotated between successive shots, we become interested in the matter of a location for the pivot axis (axes). The objective is usually for the camera to pivot about its point of perspective. The motive is to avoid parallax shift between the shots, which can make for paradoxical stitching between the shots.
It is often said that the appropriate pivot axis "passes through the nodal point of the lens". We should immediately be suspicious, since there are two nodal points. In any case, this is just plain not true.
In fact, the point of perspective of a lens will only by accident fall at either nodal point.
Where it does consistently fall is at the center of the entrance pupil. This is defined as the virtual image, from in front of the lens, of the aperture stop. It is in effect the "port" through which the lens accepts light. It is however not (except in some special places) a physical thing.
Often I hear that, "Well, the nodal point [which one] must be the proper location for the pivot axis. I use the well-known test to find the nodal point, and then when I use that location for my pivot axis, I have the proper result."
The joke here is that this "well-known test" is in fact not the test to find [either] nodal point, but rather to find the point of perspective (and thus the location of the entrance pupil).
So people often do the right thing, but describe it inaccurately. It's like the guy who really needs to know the circumference of a tree, but in error tells the field worker to find the diameter, which he thinks he can find by wrapping a tape measure around it.
Further helping this confusion is that the actual test to find the (second) nodal point sounds a little bit like this test, in that it involves rotating something while watching for some result in the image.
A further basis for the confusion comes from the matter of the revolving-lens continuous panoramic camera (in which the film is held in a curved track, the center of whose curvature is the pivot axis for the revolving lens and its associated aperture slit) . Two separate criteria suggest conflicting locations for the pivot axis:
• Consideration of the matter of parallax shift suggest rotation about the entrance pupil.
• Consideration of the matter of "smearing" of the image on the film suggest rotation about the second principal point (and thus about the second nodal point).
Various clever lens designs have been devised to reconcile these two conflicting matters (some very problematical to implement), but in practice the "smearing" issue wins, meaning that the lens/slit assembly is rotated about an axis through the second principal point of the lens. The very small lateral field of view (at any given instant) makes the impact of parallax shift relatively minor.
One nice thing about our actual interest being in the location of the entrance pupil is that this can often be determined by visual inspection. We look into the lens from the front (perhaps needing to have the aperture stopped down so we can easily identify what looks like the aperture stop).
What looks to us to be the aperture stop is (in diameter and longitudinal position) the entrance pupil - by definition. If we can estimate its axial location, that's the place we need to put our pivot axis.
Those who have not been paying attention might say, "But, but, we don't see the aperture stop where it really is, owing to the effect of the lens elements in front of it." Right. And we are not interested in the location of the aperture stop. We are interested in what and where it appears to be - which is, by definition, the entrance pupil.
Best regards,
Doug
A lens has two nodal points, normally on the lens axis. (In the fictional "thin lens" these two are at the same place, but not otherwise).
These have an important significance in geometric optics.
In the situation of common interest to us (where the object and image spaces are in the same medium, namely air), these coincide with the two principal points of the lens. These also have an important, but different, significance in geometric optics.
In connection with multi-shot panoramic photography, in which the entire camera is rotated between successive shots, we become interested in the matter of a location for the pivot axis (axes). The objective is usually for the camera to pivot about its point of perspective. The motive is to avoid parallax shift between the shots, which can make for paradoxical stitching between the shots.
It is often said that the appropriate pivot axis "passes through the nodal point of the lens". We should immediately be suspicious, since there are two nodal points. In any case, this is just plain not true.
In fact, the point of perspective of a lens will only by accident fall at either nodal point.
Where it does consistently fall is at the center of the entrance pupil. This is defined as the virtual image, from in front of the lens, of the aperture stop. It is in effect the "port" through which the lens accepts light. It is however not (except in some special places) a physical thing.
Often I hear that, "Well, the nodal point [which one] must be the proper location for the pivot axis. I use the well-known test to find the nodal point, and then when I use that location for my pivot axis, I have the proper result."
The joke here is that this "well-known test" is in fact not the test to find [either] nodal point, but rather to find the point of perspective (and thus the location of the entrance pupil).
So people often do the right thing, but describe it inaccurately. It's like the guy who really needs to know the circumference of a tree, but in error tells the field worker to find the diameter, which he thinks he can find by wrapping a tape measure around it.
Further helping this confusion is that the actual test to find the (second) nodal point sounds a little bit like this test, in that it involves rotating something while watching for some result in the image.
A further basis for the confusion comes from the matter of the revolving-lens continuous panoramic camera (in which the film is held in a curved track, the center of whose curvature is the pivot axis for the revolving lens and its associated aperture slit) . Two separate criteria suggest conflicting locations for the pivot axis:
• Consideration of the matter of parallax shift suggest rotation about the entrance pupil.
• Consideration of the matter of "smearing" of the image on the film suggest rotation about the second principal point (and thus about the second nodal point).
Various clever lens designs have been devised to reconcile these two conflicting matters (some very problematical to implement), but in practice the "smearing" issue wins, meaning that the lens/slit assembly is rotated about an axis through the second principal point of the lens. The very small lateral field of view (at any given instant) makes the impact of parallax shift relatively minor.
One nice thing about our actual interest being in the location of the entrance pupil is that this can often be determined by visual inspection. We look into the lens from the front (perhaps needing to have the aperture stopped down so we can easily identify what looks like the aperture stop).
What looks to us to be the aperture stop is (in diameter and longitudinal position) the entrance pupil - by definition. If we can estimate its axial location, that's the place we need to put our pivot axis.
Those who have not been paying attention might say, "But, but, we don't see the aperture stop where it really is, owing to the effect of the lens elements in front of it." Right. And we are not interested in the location of the aperture stop. We are interested in what and where it appears to be - which is, by definition, the entrance pupil.
Best regards,
Doug
