Scheimpflug principle

The principle is named after Austrian army Captain Theodor Scheimpflug, who used it in devising a systematic method and apparatus for correcting perspective distortion in aerial photographs, although Captain Scheimpflug himself credits Jules Carpentier with the rule, thus making it an example of Stigler's law of eponymy.

But, when Carpentier and Scheimpflug wanted to produce equipment to automate the process, they needed to find a geometric relationship.

The concept can be inferred from a theorem in projective geometry of Gérard Desargues; the principle also readily derives from simple geometric considerations and application of the Gaussian thin-lens formula, as shown in the section Proof of the Scheimpflug principle.

[e] For some camera models there are adapters that enable movements with some of the manufacturer's regular lenses, and a crude approximation may be achieved with such attachments as the 'Lensbaby' or by 'freelensing'.

The DoF is zero at the apex, remains shallow at the edge of the lens's field of view, and increases with distance from the camera.

The shallow DoF near the camera requires the PoF to be positioned carefully if near objects are to be rendered sharply.

With some subjects, such as landscapes, the wedge-shaped DoF is a good fit to the scene, and satisfactory sharpness can often be achieved with a smaller lens f-number (larger aperture) than would be required if the PoF were parallel to the image plane.

If the PoF is to pass through more than one arbitrary point, the tilt and focus are fixed, and the lens f-number is the only available control for adjusting sharpness.

In a two-dimensional representation, an object plane inclined to the lens plane is a line described by By optical convention, both object and image distances are positive for real images, so that in Figure 6, the object distance u increases to the left of the lens plane LP; the vertical axis uses the normal Cartesian convention, with values above the optical axis positive and those below the optical axis negative.

From Figure 7, where u′ and v′ are the object and image distances along the line of sight and S is the distance from the line of sight to the Scheimpflug intersection at S. Again from Figure 7, combining the previous two equations gives From the thin-lens equation, Solving for u′ gives substituting this result into the equation for tan ψ gives or Similarly, the thin-lens equation can be solved for v′, and the result substituted into the equation for tan ψ to give the object-side relationship Noting that the relationship between ψ and θ can be expressed in terms of the magnification m of the object in the line of sight: From Figure 7, combining with the previous result for the object side and eliminating ψ gives Again from Figure 7, so the distance d is the lens focal length f, and the point G is at the intersection the lens's front focal plane with a line parallel to the image plane.

Tilt-lens photo of a model train. The lens was swung towards right, in order to keep the plane of focus along the train. The sensor plane, the lens plane and the plane along the train all intersect to the right of the camera.
A scientific camera with a Scheimpflug adaptor mounted between the lens and the camera, showing in stop-motion the potential movements the adaptor provides in the two axes (tilt and swing).
A scientific camera with a Scheimpflug adaptor mounted between the lens and the camera, showing in stop-motion the potential movements the adaptor provides in the two axes (tilt and swing).
Figure 1. With a normal camera, when the subject is not parallel to the image plane, only a small region is in focus.
Figure 2. The angles of the Scheimpflug principle, using the example of a photographic lens
Figure 3. Rotation of the plane of focus
Figure 4. Rotation-axis distance and angle of the PoF
medium format camera with built in tilt
Figure 5. Depth of field when the PoF is rotated
James McArdle (1991) Accomplices .
Figure 6. Object plane inclined to the lens plane
Figure 7. Angle of the PoF with the image plane