Parallax

Parallax demo © Bernhard Vogl (GIF animation must be turned on)

If you shoot the same scene from a slightly different point of view, the foreground will be shifted in relation to the background, as in this example image.

Parallax occures in panoramic photography if camera and lens are not rotated around the Entrance pupil of the lens. A difference caused by parallax will be visible in the overlap between two adjacent images.

Parallax errors are sometimes very hard to retouch, since necessary background details might be obscured by foreground details. A useful way to fix these kinds of errors is to 'invent' some background details.

Parallax depends on the object distance $d\,$, the displacement of the nodal point $r\,$ and half the rotation angle between two shots, the off axis angle $\alpha \,$. Then the half parallax angle $\beta \,$ will be: $\beta =atan{\frac {r*sin(\alpha )}{d-r*cos(\alpha )}}$

Since $d\,$ usually is far larger than $r\,$ this could be abbreviated to $\beta =atan{\frac {r*sin(\alpha )}{d}}$