Library · Formulas

Parallax budget (Woods)

An inverse solution from the shooting–screen geometry of Woods, Docherty and Koch (1993): the nearest point of the scene is placed exactly on the front limit and the farthest point exactly on the back limit.

b = (pos + neg) · Wc / (f · (1/Zn − 1/Zf)) 1/C = (pos/Zn + neg/Zf) / (pos + neg)

where: b interaxial, C convergence distance, Wc sensor width, f focal length, Zn and Zf the nearest and farthest point of the scene

pos and neg are the largest parallax allowed behind and in front of the screen (as a fraction of image width). As a result, the nearest point gets exactly −neg and the farthest point exactly +pos parallax; the whole budget is used.

The budget depends on the type of the selected screen. The nearest and farthest points sit on the two limits of the window; the main subject falls between them, depending on the depth distribution of the scene.

Assumptions

Parallel cameras with sensor shift (or horizontal image translation, HIT, in post-production) are assumed; the keystone and curvature of the converged rig are not taken into account.
Convergence is set by the depth of the scene; the main subject may not be on the screen plane.
Because the budget is given as a percentage, it does not by itself know the screen size. On a large screen the divergence limit must be checked separately; see Comfort zones.

It gives the same result as the Bercovitz formula; the small difference is Bercovitz's lens extension term.

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