Scheimpflug principle

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The Scheimpflug principle is a geometric rule that describes the orientation of the plane of focus of an optical system (such as a camera) when the lens plane is not parallel to the image plane. It is commonly applied to the use of camera movements on a view camera. 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.

Contents

[edit] Description of the Scheimpflug principle

Normally, the lens and image (film or sensor) planes of a camera are parallel, and the plane of focus (PoF) is parallel to the lens and image planes. If a planar subject (such as the side of a building) is also parallel to the image plane, it can coincide with the PoF, and the entire subject can be rendered sharply. If the subject plane is not parallel to the image plane, it will be in focus only along a line where it intersects the PoF, as illustrated in Figure 1.

Figure 1. With a normal camera, when the subject is not parallel to the image plane, only a small region is in focus.
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 2. The angles of the Scheimpflug principle, using the example of a photographic lens.
Figure 3. Rotation of the plane of focus.
Figure 3. Rotation of the plane of focus.
Figure 4. Depth of field when the PoF is rotated.
Figure 4. Depth of field when the PoF is rotated.

When an oblique tangent is extended from the image plane, and another is extended from the lens plane, they meet at a point through which the PoF also passes, as illustrated in Figure 2. With this condition, a planar subject that is not parallel to the image plane can be completely in focus.

Scheimpflug (1904) referenced this concept in his British patent; Carpentier (1901) also described the concept in an earlier British patent for a perspective-correcting photographic enlarger. The concept can be inferred from a theorem in projective geometry of Gérard Desargues; a simple proof is also given by Larmore (1965, 171–173). The implication is that there exists a homography between the subject plane and the image plane.

[edit] Changing the plane of focus

When the lens and image planes are not parallel, adjusting focus rotates the PoF rather than displacing it along the lens axis. The axis of rotation is the intersection of the lens’s front focal plane and a plane through the center of the lens parallel to the image plane, as shown in Figure 3. As the image plane is moved from IP1 to IP2, the PoF rotates about the axis G. The axis of rotation has been given many different names: “counter axis” (Scheimpflug 1904), “hinge line” (Merklinger 1996), and “pivot point” (Wheeler). If a lens with focal length f is tilted by an angle θ relative to the image plane, the distance J[1] from the center of the lens to the axis G is given by

J = \frac f {\sin \theta} .

For an essentially planar subject, such as a roadway extending for miles from the camera on flat terrain, the tilt can be set to place the axis G in the subject plane, and the focus then adjusted to rotate the PoF so that it coincides with the subject plane. The entire subject can be in focus, even if it is not parallel to the image plane.

The plane of focus also can be rotated so that it does not coincide with the subject plane, and so that only a small part of the subject is in focus. This technique sometimes is referred to as “anti-Scheimpflug”, though it actually relies on the Scheimpflug principle.

Rotation of the plane of focus can be accomplished by rotating either the lens plane or the image plane. Rotating the lens (as by adjusting the front standard on a view camera) maintains perspective in a vertical subject, such as a building, but requires a lens with a large image circle to avoid vignetting. Rotating the image plane (as by adjusting the back or rear standard on a view camera) alters perspective in a vertical subject, but works with a lens that has a smaller image circle. Rotation of the lens or back about a horizontal axis is commonly called tilt, and rotation about a vertical axis is commonly called swing.

[edit] Camera movements

Tilt and swing are available on most view cameras, often on both the front and rear standards, and on some small- and medium-format cameras with special lenses that partially emulate view-camera movements. On small-format cameras, such special lenses are often called “tilt/shift” lenses (e.g., the Canon 24 mm, 45 mm, and 90 mm TS-E) or “perspective-control”[2] lenses (e.g., the Nikon 24 mm PC-E Nikkor and 85 mm PC Micro-Nikkor).

The Lensbaby SLR lens is a low-cost alternative for providing tilt and swing for many SLR cameras, although the effect is somewhat different from a tilt/shift lens. Because of the simple optical design, aberrations are significant, and sharp focus is limited to a region near the lens axis. Consequently, the Lensbaby’s primary application is selective focus.

[edit] Depth of field

When the lens and image planes are parallel, the depth of field (DoF) extends between parallel planes on either side of the plane of focus. When the Scheimpflug principle is employed, the DoF becomes wedge shaped, with the apex of the wedge at the PoF rotation axis, as shown in Figure 4. 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.

[edit] Notes

  1. ^ The symbol J for the distance from the center of the lens to the PoF rotation axis was introduced by Merklinger (1996), and apparently has no particular significance.
  2. ^ The earliest Nikon perspective-control lenses included only shift; the 85 mm f/2.8D PC Micro-Nikkor (introduced in 1999) and the 24 mm f/3.5 PC-E Nikkor (introduced in 2008) also included tilt.

[edit] References

  • Carpentier, Jules. 1901. Improvements in Enlarging or like Cameras. GB Patent No. 1139. Filed 17 January 1901, and issued 2 November 1901. Available for download (PDF).
  • Larmore, Louis. 1965. Introduction to Photographic Principles. New York: Dover Publications, Inc.
  • Merklinger, Harold M. 1996. Focusing the View Camera. Bedford, Nova Scotia: Seaboard Printing Limited. ISBN 0-9695025-2-4. Available for download (PDF).
  • Scheimpflug, Theodor. 1904. Improved Method and Apparatus for the Systematic Alteration or Distortion of Plane Pictures and Images by Means of Lenses and Mirrors for Photography and for other purposes. GB Patent No. 1196. Filed 16 January 1904, and issued 12 May 1904. Available for download (PDF).

[edit] External links