Finding the Nodal (Focal) Point of a Lens

As shown in the figure on the left, lenses transform light rays converging on a point to parallel light rays that can be captured by film or electronic sensors in cameras. The point at which the rays would converge if the lens were removed is called the Nodal Point of the lens. For a simple (1-element) lens, the Focal Length (f) is the distance between the Nodal Point and the lens, but camera lenses are more complicated. (Note: In optics, this point is called a "Focal Point" of the lens and the term "Nodal Point" has a different meaning, so it may be best to call this the "Focal Point" when talking to lens manufacturers.)

To build panoramas, we want to capture all of the light rays that converge on a point in space. To do this, we want to stitch together images that have the same Nodal Point. If we try to stitch together images that have different Nodal Points, the relative positions of some objects will be different in each image. This effect is called Parallax and is illustrated in the figure on the right.

The figure on the right also illustrates how we can find the Nodal Point of a lens. To find the Nodal point, we pick a far object and a near object that is on the line formed by the tripod and the far object. Then we take two images containing the reference objects, one with the camera rotated to the left and another with the camera rotated to the right. If the relative positions of the objects change in the two images, the rotation point is not the Nodal Point. The point of rotation of the camera can be adjusted by using a special plate to move the camera forward and backward on the tripod. We can keep moving the rotation point and comparing images until we find a pair of images that do not show parallax.

In practice, the distant object is usually the edge of a building or a tree or telephone pole, and the near object is usually a post or a telephone pole. We can usually look through the viewfinder of SLR cameras or at the preview images on digital cameras to find forward and backward camera positions that clearly show more parallax than positions in between. (If nothing else, we can try limiting rotation positions to those between the front of the lens and the back of the camera.) Then we can take a few (4 to 8) pairs of images at rotation positions equally spaced between the forward and backward limits for the rotation point. After we look at the initial images on the computer, we'll find new forward and backward limits for the rotation point. We can continue taking images and refinining the rotation point until we are within 1mm or so of the Nodal Point.

The figure at the left shows a trick that might help to find parallax in images. Instead of looking at two objects with parallel vertical lines, choose the close object so that it is slightly tilted with respect to the far object. This may help because it is sometimes easier to compare the height at which the lines meet than it is to compare the closeness of parallel lines.

When capturing these images, save them in an uncompressed format since it is important to have clearly defined edges. JPEG compression might be okay for the first set of images when the rotation positions are far apart, but you'll probably want to use an uncompressed format when the rotation positions are closer.

As an example, we can describe how we found the rotation position to use with our equipment, a Nikon 14mm lens on a Nikon D-100 camera mounted on a spherical tripod head from Kaidan. First, we put the tripod in a location that aligned the edges of close and far telphone poles with the center of the tripod. Then, by looking through the viewfinder, we could see that the positions with least parallax could be found when the edge of the mounting plate was between 90mm and 130mm, so we took pairs of images at every 5mm between 90mm and 130mm. After looking at these images on the computer, we narrowed the range to between 105mm and 125mm. Then we went to a parking lot and aligned a close post that was slightly tilted with the edge of a distant building and we took pairs of images at every 1mm between 105mm and 125mm. We found that the plate position with the least parallax was at 115mm.