Cerit Triangle
The shooting formula Erkan Cerit has used in the field since 2010. Converged, symmetric cameras; C = main subject. Interaxial: in-focus range limits = comfort window limits.
The result: everything that looks sharp stays within the depth the viewer can comfortably fuse; whatever extends beyond that depth is blurred.
Model
- A perpendicular axis extends from the center of the rig; the convergence point lies on this axis.
- The two cameras stand at equal distances from the center of the rig and are converged at equal angles. Their central rays meet at the main subject, at the convergence point. The cameras are always converged.
- Optical focus is the plane the lenses see sharply. In the field it follows the convergence point; on a robotic rig it can be set separately.
- The composition is set up first, and the lens is chosen to suit it. The interaxial can be opened up to several meters, depending on the composition; it is not fixed as in the human head.
- Depth of field is an aesthetic choice. At the chosen depth of field, the interaxial is set so that the in-focus range limits fall on the comfort window limits. This is an advantage for being able to use the S3D effect in an exaggerated way: everything that is sharp stays within the comfort window, and whatever extends beyond it becomes blurred.
Formula
Right triangle. Sides: the distance from the center of the rig to a camera (b/2) and the distance from the rig to the convergence point (D).
where: b interaxial; D distance from the rig to the convergence point, the same as the convergence distance C on the other pages
Lens and composition. Wf is the width that enters the frame in the plane of the convergence point. When the lens is chosen, the composition follows from this relation; when the composition is chosen, the lens follows from it.
where: Wc sensor width, f focal length
Screen parallax depends on the frame width at the focus, independently of the lens:
where: Z distance of the point from the rig
Depth of field. Thin lens; N aperture, c accepted circle of confusion, Do optical focus.
where: H hyperfocal distance; Dn and Df near and far limits of the in-focus range; N aperture (f-number), c circle of confusion, Do optical focus distance
Interaxial. The in-focus range limits are set on the comfort window limits; pos and neg are the back and front limits of the window.
where: pos and neg back and front limits of the comfort window, as a fraction of image width
The calculator solves for this value with the converged geometry, without the small-angle approximation.
Result
- Every point inside the in-focus range is inside the comfort window.
- Every point outside the window is outside the in-focus range, that is, blurred.
- As the aperture opens, the in-focus range narrows and the interaxial grows.
Example
Convergence point 3.5 m, Super 35 sensor, 35 mm lens (Wf 2.49 m), Sky budget, TV 55":
| Aperture | In-focus range | Interaxial b | Toe-in angle β |
|---|---|---|---|
| f/1.4 | 3.23 – 3.82 m | 302 mm | 2.47° |
| f/2.8 | 3.00 – 4.20 m | 151 mm | 1.24° |
| f/5.6 | 2.63 – 5.24 m | 75 mm | 0.62° |
| f/11 | 2.12 – 10.0 m | 38 mm | 0.31° |
Three variables in the field
Depth of field is a dramatic and aesthetic decision made in the field by the director of photography and the director. The field crew manages cause and effect with three variables: depth of field (aperture), interaxial and lens. If excess diplopia occurs when the depth of field widens and near and far objects come into focus, the cameras are moved closer together or the lens is changed. Having few variables gives the field crew flexibility; fine adjustment is done in post-production.
The distance between the rig and the main subject can also change in the field, and it directly affects the depth of field. When the rig moves forward or back, the scene stays in place; the distances of the nearest and farthest objects from the rig also change by the same amount.
The method set
The Cerit Triangle is the field part of the Erkan Cerit Method: the formula used in the field + S3D Mastering = Final Mastering. The keystone of a converged shot is corrected in mastering; which screens the same shot fits with a single master is calculated on the Mastering page.