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Convergence

Convergence means two cameras, like two eyes, pointing at the same point. The convergence distance is the distance in the scene that falls at zero parallax. Everything at this distance appears on the screen plane; nearer things sit in front of the screen, and farther things behind it.

Two camera rigs

Convergence is set in one of two ways (Woods, Docherty, Koch 1993):

Converged rig (toe-in): the cameras are rotated toward each other by equal angles; their central rays cross at the convergence distance. The toe-in angle of each camera is β = atan(b / 2C).
Parallel rig and sensor shift: the cameras stay parallel; the sensors or the images are shifted horizontally. The shift of each sensor is h = f·b / 2C.

If the shot is made parallel and convergence is to be set in post-production, the images are shifted horizontally (HIT, horizontal image translation). The total shift is f·b / C on the sensor and f·b / C · N_px / Wc in pixels.

Interaxial 100 mm, 35 mm lens, Super 35 sensor. As the convergence distance changes, objects move in front of or behind the screen; the depth range does not change.

Parallax formula

In a parallel rig with shift, the parallax of a point at distance Z from the camera, as a ratio of image width, is:

d = (f · b / Wc) · (1/C − 1/Z)

where: d parallax as a ratio of image width, f focal length, b interaxial, Wc sensor width, C convergence distance, Z distance of the point from the camera

For Z = C the parallax is zero. The parallax of a point at infinity is f·b / (C·Wc).

Convergence does not change the depth range

The parallax difference between the nearest and the farthest point does not depend on convergence:

d_far − d_near = (f · b / Wc) · (1/Zn − 1/Zf)

where: Zn the nearest point of the scene, Zf the farthest; C does not appear in the formula

Convergence only determines where the scene sits relative to the screen. The amount of depth is determined by the interaxial, the focal length and the scene itself. This is why HIT is the tool in mastering for moving the scene forward or back without altering the depth.

Converged rig and keystone distortion

In a converged rig the two image planes are rotated relative to each other, so vertical parallax, that is, keystone distortion, appears in the corners of the frame, along with curvature of the depth plane (Woods et al. 1993). Keystone distortion is corrected in mastering by rotating each image back about its own center. The corrected image has the same geometry as an image shot parallel with shift, with the same interaxial and convergence.

In the Cerit Triangle the cameras are always converged; their central rays meet at the main subject, at the convergence point.

Interaxial In the glossary Try in the calculator