Most standard lenses can be approximated by a virtual pin-hole or
"nodal point". This is equivalent to reducing the aperture to almost
zero, or infinite f-stop. All rays of light striking the film appear
to pass through this point. This is illustrated in the following
The black box represents the simplified camera. The orange line
on the bottom represents the film being exposed. The gap at the top
represents the pin hole (nodal point of the lens). The blue circle
represents some object in view of the camera. Light reflected from
the blue object follows the gray line through the pin-hole and
strikes the film on the left side where an image of the object is
recorded on the film.
The view direction of the camera can be represented by an arrow
which is perpendicular to the film and passes through the pinhole,
as shown in the following diagram:
The view direction is represented by a red arrow. In this case,
the camera is aimed to the left of the blue object. Light reflected
from the blue object follows the gray line, passes through the
pinhole, and strikes the film to the left of the center.
The vertical bar on the right side represents the background
beyond the blue object. Following the gray line back beyond the blue
object leads to the point on the background which is hidden by the
The following image presents an example of these conditions. In
this case, the blue object in the diagram is represented by the back
of a chair placed close to the camera. The background contains a
fireplace and surrounding walls. Part of the chair lies in front of
the third tile over the fireplace, and a smal part of the fourth
The following diagram shows what happens when the camera is
rotated by a point behind the pin-hole.
In this case, the camera has been rotated to the right until the
view direction points to the right of the blue object. The axis of
rotation is located at the base of the direction arrow. Light
reflected from the blue object follows the green line through the
pin-hole and strikes the film to the right of the center of the
In this case, the green line is not the same as the gray line
representing the path of the light from the object to the camera for
the previous shot. As a result, for this shot, the camera sees the
blue object from a different direction compared to the previous
shot. In addition, following the green line back to the background
shows that the part of the background hidden by the blue object in
this shot is located to the left of the part of the background
hidden by the same object in the previous shot.
The following image shows what happens in a real scene.
In this case, the camera used to capture the previous image was
rotated to the right until the back of the chair was seen to move
from the right side of the image to the left side of the image. As a
result of the rotation of the camera, the entire scene has been
shifted to the left within this image, as expected. The back of the
chair, however, has moved to the left even more than the background.
Now the back of the chair covers parts of the second and third tiles
over the fireplace. The grout between the third and fourth tiles is
now completely exposed, and the grout between the second and third
tiles is completely hidden.
This shifting of the chair relative to the background is called a
parallax effect. Because of this parallax effect, this pair of
images is not suitable for merging together into a panoramic image.
It is not possible to align both the foreground (the chair) and the
background (the fireplace) to form a single image.
The parallax effect can be eliminated by rotating the camera
about the virtual pin-hole. This is illustrated in the following
In this case, the camera has been rotated by the same amount as
in the previous diagram. This time, however, instead of rotating the
camera about the base of the direction arrow, the camera has been
rotated about the virtual pin-hole. As in the original shot, light
reflected from the blue object follows the gray line, passing though
the pin-hole, and striking the film. Since this is exactly the same
path followed in the first shot, following this line back to the
background shows that the part of the background hidden in this shot
is exactly the same as the part hidden in the original shot.
The following image shows the result of rotating the camera about
the virtual pin hole instead of a point behind the pinhole:
In this case, the image of the chair has shifted to the left by
exactly the same amount as the background, no more and no less. The
portion of the background hidden by the chair in this image is the
same as is hidden in the orginal shot.
Having eliminated the parallax effect, this image is consistent
of coherent with the first image. These tow images may now be merged
into a single image representing part of a panoramic image. The
following image shows the result of merging the previous image with
the original image.
Calibrating the Mini Pan Head
The process of calibrating the PanoramIX Mini Pan Head consists
of adjusting the position and orientation of a camera on the Mini
Pan Head so as to minimize or eliminate the parallax effect. If you
have an SLR camera, or a digital film camera, you can use the
- Mount the camera on the Mini Pan Head. Keep the screw snug,
but to not tighten the screw.
- Mount the Mini Pan Head on the tripod. Tighten the screw that
connects the tripod head to the Mini Pan Head.
- Shift the position of the camera along the slot in the Mini
Pan Head until the lens is over the screw in the head of the
- If the mounting hole in the bottom of the camera is not in
line with the center of the lens, adjust the camera into a
diagonal orientation that allows the lens to be placed over the
mounting screw in the head of the tripod.
- Place a test object with sharp vertical features up close to
- Look through the viewfinder of an SLR camera or the preview
monitor for a digital camera, and rotate the camera until the test
object is visible on the right side of the image.
- Make a careful note of the background features directly behind
the vertical edges of the test object.
- Turn the camera to the right until the test object has been
shifted into the left side of the image.
- Notice how the test object has moved with respect to the
- If the test object appears to shift to the left with respect
to the background, then move the camera back (away from the tripod
head), and repeat the previous three steps.
- If the test object appears to shift to the right with respect
to the background, move the camera forward and repeat the previous
- If the test object does not shift with respect to the
background, yu are done. Tighten the screw holding the camera over
the slot in the Mini Pan Head and mark the position and angle of
the camera on the Mini Pan Head for future reference.
In order to calibrate the Mini Pan Head accurately, it helps to
exaggerate the parallax effect as much as possible. To do this,
place the test object as close to the camera as possible as long as
the camera can still focus on both the test object and the
background. Ideally, the distance from the camera to the test object
will be much less than the distance from the camera to the nearest
visible object in real scene to be captured for a panoramic
The calibration needs to be performed only once for a particular
camera. Do this once in your home, office, studio, or other
convenient place and mark the result on the Mini Pan Head. Then go
and shoot panramic scenes using the same calibration settings
If you have a non-SLR camera, like most "point-and-shoot" models,
then you cannot tell where the camera is being aimed. The non-SLR
viewfinder (rangefinder) has a large parallax error of its own, so
it is useless for calibration. In this case, you may need to shoot a
test roll of film, carefully noting how the camera was adjusted for
Instead of shooting a test roll of film, you may perform a crude
calibration of the Mini Pan Head by following the first four steps
listed above. In this case, although the parallax effect may not be
eliminated completely, it will be much less than would be
encountered if the camera were mounted directly on the tripod
without the Mini Pan Head.
All diagrams shown in this page were drawn by William Luken. All
images shown on this page where created by William Luken. All items
seen in these images are the personal property of William Luken.
Last modified Sept. 20, 1998.
Last updated January 11, 1999; October 11, 2001; January 27, 2006; June 5, 2013