Library · Formulas

Bercovitz

The formula published by Y. Bercovitz in 1998 gives the interaxial from the nearest and farthest distances and the focal length (SPIE 3295).

b = P / (L − N) · (L · N / F − (L + N) / 2) For L = ∞: b = P · (N / F − 1/2)

P: the desired total deviation (depth) on the film or sensor.
N, L: the nearest and farthest distance.
F: focal length.

In the letters used on the other pages: N = Zn, L = Zf, F = f. P here is the deviation on the sensor; do not confuse it with the screen parallax P.

The term (L + N) / 2 accounts for lens extension, that is, the image plane moving away from the lens at close focus; it can be neglected for distant shots.

In the calculator

The total deviation is taken from the selected parallax budget: P = (pos + neg) · Wc. Convergence is placed at the nearest point (C = N); the scene stays behind the screen.

The budget depends on the type of the selected screen: 3% in total for both screen types. Because convergence is at the nearest point, the whole budget is used behind the screen.

Relation to the other methods

It is the equivalent of the parallax budget solution when the focal length is very small compared with the nearest distance; the difference is about 1%, that is, the size of the lens extension term. The 1/30 rule is an approximation of this formula for 35 mm film, a normal lens and a scene extending to infinity.

Open in the calculator Parallax budget