# No-parallax point

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If you rotate your camera around some randomly chosen point, your images may show parallax and be difficult to stitch.

With most lenses, there is one special point around which you can rotate your camera and get no parallax. This special "no-parallax point" is the center of the lens's entrance pupil, a virtual aperture within the lens. In the panorama photography community, this special point is often called the "nodal point", but it is in fact unrelated to the actual nodal points of the lens.1,2 The actual nodal points are other points on the optical path, which are of no significance to most photographers. The no-parallax point is also the "center of perspective", but this term is not commonly used and does not describe why the no-parallax point is important.

The entrance pupil is the image of the limiting aperture or diaphragm, as seen through the front of the lens. The image seen may be magnified by the effect of the lens elements in front of it, and the image is displaced from the actual position of the aperture. It is the center of this image about which the camera must be rotated to avoid parallax. Interestingly, the entrance pupil is important in another way: the f-number[*] of a lens is actually the ratio of the focal length to the diameter of the entrance pupil, not to the diameter of the physical aperture inside the camera.

Everything considered, the best term for the no-parallax point may be (surprise!) the "no-parallax point". "Entrance pupil" is correct although a bit imprecise to a geometry purist; it makes a good term for searching the literature and would be preferred in formal writing. "Nodal point" is commonly-used, but incorrect and leads to confusion. It should be avoided when writing and interpreted with caution in reading the literature.

Regardless of what you call the no-parallax point, it is easily found by trial and error. Just adjust the rotation point so that foreground and background points stay lined up.

Some lenses, notably fisheyes, do not have a single no-parallax point. Instead, they have a range of what we might call "least-parallax points" that depend on the angle away from the lens axis. Such lenses can be recognized easily — just look into the front of the lens and observe that the location of the entrance pupil moves forward or backward as you rotate the lens off-axis. With such lenses, it is good to pick one angle at which you like to stitch, and rotate your camera around a point that gives no parallax at that angle.

To facilitate finding the no-parallax point for other people, please fill the measurements you have found for your Camera / Lens / Focal Length combination in the Entrance Pupil Database[*]

## See also

- NPP adapters[*]
- Entrance Pupil Database[*]

## References

1. Kerr, Douglas A. "The Proper Pivot Point for Panoramic Photography" The Pumpkin (2005). Accessed 2011-02-02.
2. van Walree, Paul "Misconceptions in photographic optics", Item #6. Accessed 2011-02-02.

## Links

#### In theory

- Paul van Walree, Center of Perspective
- Rik Littlefield, Theory of the "No-Parallax" Point in Panorama Photography
- John Bercovitz 1998, Image-side Perspective and Stereoscopy (SPIE proceedings vol. 3295). See section "3. Image-side perspective point" in particular for formulae relating entrance pupils, focal lengths and gaussian nodal points.
- R. Barry Johnson 2008, Correctly making panoramic imagery and the meaning of optical center SPIE Proc. 7060: 70600F.1–70600F.8. ISSN 0277-786X. OCLC 278726950

#### Locating the NPP(s) of a specific lens

- John Houghton, Finding the No-Parallax Point.
- Big Ben's Panorama Tutorials, Determining the Nodal Point of a Lens.
- Kaidan, How to Find Your Camera's Nodal Point.
- Alain Hamblenne, The Grid.
- Bill Claff, Finding the entrance pupil.
- Michel Thoby, especially Nodal point location for the SIGMA 8mm f:4 lens, which describes an interesting approach using a laser pointer.
- "Use an SLR as a rangefinder ..." See section "5. Miscellanea" of John Bercovitz 1998, Image-side Perspective and Stereoscopy (SPIE proceedings vol. 3295).

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