EOS Documentation Project

Image Controls: Tilt and Shift

by Jeff Conrad

Contents

• Background

  Camera Movements  Image Circle  Light Falloff  Depth of Field  Circle of Confusion 

• Tilt

  Plane of Focus  Setting the Correct Tilt  Setting the Lens f-number  Calculating the Required Tilt and f-number 

• Shift

  Rising/Falling Front  Lateral Shift  Panorama  Combined Rise and Lateral Shift 

• Further Reading

  Books  Web Resources 

• Revision History
• Comments

Background

Camera Movements

In addition to the larger image size, a great advantage of a view camera over most small- and medium-format cameras is the inclusion of camera movements that allow adjustment of the orientation of the lens relative to the image plane. Two types of movements usually are possible: displacement of the lens parallel to the image plane, and rotation of the lens axis relative to the image plane.

Parallel displacement allows the line of sight to be varied while controlling the relationship between parallel lines. When the motion is vertical, it is called rise or fall (or sometimes, rise or drop); when the motion is horizontal, it is called shift or cross. Canon refer to vertical and horizontal movements on tilt/shift lenses as shift.

Rotation of the lens axis allows of the part of the image that is acceptably sharp. Rotation about a vertical axis is called a swing; rotation about a horizontal axis is called a tilt. Canon refer to either movement on tilt/shift lenses as tilt.

Because they allow control of the image shape and the zone of sharpness, camera movements are also known as image controls, or sometimes, simply controls.

The Canon tilt/shift lenses provide functionality similar to view camera movements, although the range of movements is more limited and setting the movements is not as convenient. Swing and tilt, and rise and shift, cannot be set independently, but the tilt/shift mechanisms on the Canon lenses can be rotated about the lens axes to give essentially the same effect.

Image Circle

The image circle of a lens is the sharp circular image formed at the lens focal plane. On most small- and medium-format cameras, the image circle need only be large enough to cover the image format. With a tilt/shift lens, the circle must be larger than the image format to accommodate the lens movements. When the TS-E 24 mm f/3.5L is shifted more than 8 mm in the long direction, the corner of the image is outside the specified image circle, and vignetting may occur. The image circle often is slightly larger at greater f-numbers, so setting a greater f-number when using extreme movements will often produce better results, especially when the TS-E 24 mm f/3.5L is shifted in the long direction. Using a camera that shows 100% of the image in the viewfinder, such as the EOS-1, EOS-1n, EOS-1v, or EOS-1D, makes it easier to avoid vignetting.

Light Falloff

Within the image circle, the illumination decreases as the fourth power of the cosine of the angle from an object to the lens axis, although some lens designs can slightly reduce the falloff. When the TS-E 24 mm f/3.5L is shifted 11 mm in the long direction, the decrease in the corners is nearly three exposure steps even without vignetting.

Depth of Field

A camera can precisely focus on only one plane; a point object in another plane is imaged as a circle rather than a point. The farther the plane from the plane of focus, the larger the circle. If the circle is sufficiently small, however, it is perceived as sharp, so that a zone of acceptable sharpness exists between two planes on either side of the plane of focus. This zone is known as the depth of field (DoF). The closest plane is the near limit of the DoF, the farthest plane the far limit of the DoF. The diameter of a “sufficiently small” circle is known as the permissible circle of confusion, or simply as the circle of confusion (CoC).

The DoF depends upon the lens focal length, the object distance, and the lens f-number. The lens focal length and object distance determine the magnification, so that DoF depends on magnification and f-number; lesser magnification and greater f-number (smaller lens opening) give a greater DoF.

Circle of Confusion

The diameter of the “permissible” circle of confusion for the captured image (i.e., film or electronic sensor) depends upon three factors:

1. The distance at which the final image is viewed. The commonly assumed value is 250 mm, the approximate distance at which human visual acuity is maximum. A comfortable viewing distance is one at which the field of view is approximately 60 degrees, so that an especially small or large final image is likely to be viewed at a distance other than the standard 250 mm.
2. Human visual acuity. Under ideal conditions, the eye can just distinguish a point that subtends one minute of arc (1/60 degree), equivalent to 0.073 mm at the normal viewing distance of 250 mm. Under normal conditions, a more realistic value is about 0.1 mm; the spatial resolution threshold is twice this value, or 0.2 mm. This is a common value for final-image CoC, although 0.25 mm also is sometimes used. In angular terms, with the value of 0.2 mm at a distance of 250 mm, the final-image CoC would subtend 2.75 minutes of arc.
3. The enlargement of the captured image required to produce the final image. If a full-frame 35 mm image is enlarged to fit the short dimension of an 8" x 10" final image, the enlargement is approximately 8x, and the CoC for the captured image is then 1/8 of that for the final image.

Assuming a viewing distance of 250 mm, a final-image CoC of 0.20 mm, and 8x enlargement gives a permissible CoC of 0.025 mm on a full-frame 35 mm image. Commonly cited values are 0.025 mm to 0.033 mm; it should be obvious that the choice of CoC is somewhat arbitrary.

Other criteria are sometimes used to determine CoC. One approach is to relate the CoC to the format diagonal; it’s easy to apply, and works well when the captured image has the same aspect ratio as the final image. For example, with a final-image size of 8" x 10", and a final-image CoC of 0.2 mm, the CoC is 1/1625 of the image diagonal. Canon apparently use this approach, and choose CoC equal to 1/1250 of the 35 mm format diagonal to arrive at a CoC of 0.035 mm (see the end of the first paragraph under “Permissible circle of confusion” on page 193 of Canon’s Lens Work II). Relating CoC to format diagonal is less effective when the format (e.g., 6 x 17) differs markedly from the “standard” aspect ratio of 4:5.

Tilt

Plane of Focus

On a camera without movements, the lens axis is perpendicular to the image plane, and the plane of focus and the planes that define the near and far limits of the DoF are perpendicular to the lens axis. When great DoF is required, even the smallest lens opening may not be sufficient to render the entire scene acceptably sharp.

When the lens is tilted relative to the image plane, the plane of focus is inclined to the image plane. At the beginning of the 20th century, Jules Carpentier and Theodor Scheimpflug discovered that the plane of focus, a plane passing through the center of the lens, and the image plane intersect on a common line. This phenomenon has become known as the Scheimpflug principle, although it actually follows from a theorem of French mathematician Girard Desargues (1591–1661).

Scheimpflug also discovered that the plane of focus intersects a plane parallel to the image plane passing through the center of the lens. The distance of this intersection from the center of the lens depends on the lens focal length and the amount of lens tilt. The line formed by this intersection has been called the “hinge” line by Harold M. Merklinger because the plane of focus pivots about this line as the camera is focused. Merklinger describes the Scheimpflug principle and the “hinge” rule in detail in his book Focusing the View Camera. His web site includes several excellent diagrams, as well as copies of his articles that appeared in Photo Techniques, Shutterbug, and View Camera.

Robert Wheeler also describes the Scheimpflug principle in “Notes on View Camera Geometry,” available on his web site. The diagrams aren’t quite as good as Merklinger’s, but unlike Merklinger, he includes the derivation of most of the formulas. He also includes an explanation, in English, of Desargues’s theorem.

The planes that define the near and far limits of DoF are also inclined to the image plane; the three planes intersect at the “hinge” line, forming a wedge-shaped DoF, that when suitably aligned, may enable an entire scene to be rendered acceptably sharp.

The most common use of tilt is to get an entire scene acceptably sharp. For a scene that has depth but minimal height, such as a chess board without pieces, this often simply requires that the plane of focus and the ground plane coincide.

Setting the Correct Tilt

It is possible to focus the lens on the approximate center of the scene, tilt the lens, and then adjust the focus and the tilt until everything appears to be in focus. In practice, this is often quite difficult, even when using a view camera with a large ground glass. With a 35 mm camera and its much smaller viewfinder, it can be difficult to precisely judge the effects of tilt, especially with the TS-E 24 mm f/3.5L and TS-E 45 mm f/2.8 lenses.

In his article “Setting Up the View Camera,” in the May/June 1998 issue of Photo Techniques, Howard Bond described a method, that, although still trial and error, is more systematic. That method, in essence, is as follows:

1. Select a near point and a far point through which the plane of focus is to pass. The two points should contain sufficient detail to enable determination of sharp focus. Ideally, the two points would as far apart as possible in the viewfinder, but they need not be the same distances from the center of the viewfinder. The near and far points in the procedure below can be interchanged if desired.
2. Choose an initial value for the tilt, and repeat until the sharpness of the near point does not change:
   1. Focus on the far point.
   2. Slowly decrease the focus distance (i.e., focus closer); then
      • If the near point becomes sharper, increase the tilt; or
      • If the near point becomes less sharp, decrease the tilt; or,
      • If the change in the sharpness of the near point is difficult to determine,
        1. Refocus on the far point.
        2. Slowly increase the focus distance; then
           • If the near point becomes sharper, decrease the tilt; or,
           • If the near point becomes less sharp, increase the tilt.

This procedure usually requires only a few iterations to determine acceptable settings, regardless of the initial value of the tilt.

Setting the plane of focus to pass through two points will not always suffice to render a scene acceptably sharp, however. If a scene has height as well as depth (e.g., a chess board with pieces), adjustment of the camera is a bit more involved. If the scene height increases with distance from the camera (e.g., the pieces on a chess board are at the far end), the region of interest is approximately wedge-shaped, and it may be possible to set the plane of focus so that all important parts of the scene lie within the wedge-shaped DoF.

Unfortunately, the best orientation for the plane of focus isn’t obvious in many situations. One approach is to position the plane of focus approximately in the middle of a distant tall object; focus for the near point should be close to exact because of the relatively shallow DoF near the camera. Some trial and error may be required; the angular DoF decreases with increasing tilt, so in many instances using less tilt gives better results. Merklinger gives an example of such a situation in the Addendum to Focusing the View Camera. In some cases, the best results are obtained without using any tilt.

When there is substantial height near the camera, the region of interest isn’t wedge-shaped, and it may not be possible get everything acceptably sharp. In such cases, setting the tilt to zero and the focus to the hyperfocal distance usually gives the best results.

Setting the Lens f-number

The lens DoF scale can be used to determine the f-number with reasonable accuracy when the lens is tilted, but the indicated distances no longer correspond to camera-object distances. Focusing the lens changes the angle of the plane of focus rather than the distance of the plane of focus from the lens.

1. Focus on the point that is at the greatest angular distance above the plane of focus; note the indicated distance.
2. Focus on the point that is at the greatest angular distance below the plane of focus; note the indicated distance.
3. Set the focus so that it is exactly halfway between the two distances noted above
4. Observe the depth-of-field scale, and find an f-number whose marks are on or just outside the indicated near and far distances; set the lens to that f-number.

With the TS-E 90 mm f/2.8, the f-number markings are so close together that the method just described is difficult to apply, and a strictly visual assessment of what is sharp using the camera’s DoF preview may be easier.

Because the plane of focus pivots about the hinge line as the lens is focused, rather than moving toward or away from the camera, the points at the greatest angular distances above and below the plane of focus may not immediately be obvious, and finding them may require several attempts.

Although tilt is usually used to get the greatest part of a scene acceptably sharp, the opposite is also possible. By adjusting the tilt so that the plane of focus is as far away from most of the scene as possible the part of the scene that is within the DoF can be minimized. Again using the chess board as an example, the plane of focus could be oriented away from the plane of the board, perhaps emphasizing a single piece.

Calculating the Required Tilt and f-number

Scenes with Little Height

If the approximate position of the desired plane of focus is known, the required tilt is given by

tilt = arcsin(f /J),

where f is the lens focal length and J is the distance from the center of the lens to the “hinge” line. Some photographers, such as Merklinger, find it easy to envision the location of the “hinge” line; others do not. Merklinger covers the topic in great detail in Focusing the View Camera and on his web site.

In a manner analogous to Canon’s DEP automatic exposure mode, it’s possible to calculate the tilt and focus settings required to pass the plane of focus through two points if the distances from the camera and from the center of the image of the two points are known. The mathematics are straightforward but sufficiently tedious as to be impractical without a computer or advanced programmable calculator. Some view cameras, such as the Sinar f models, incorporate a scale to facilitate such calculations. Canon unfortunately offer no similar capability.

It’s also possible to calculate the tilt and focus settings required to pass the plane of focus through two points if the distances from the center of the lens and the angles from the line of sight to the points are known. The required measurements usually can be made to sufficient accuracy using the lens distance scale and a clinometer, with the clinometer pressed against the camera’s hot shoe when measuring the angle. It should be noted that the lens distance scale indicates distances from the image plane, whereas most calculations use the distance from the lens front principal point. For landscapes, the difference usually isn't important, but for close-ups the difference can be significant.

Wheeler describes both methods for calculating the tilt in “Notes on View Camera Geometry,” available on his web site. He has developed software, also available on his web site, that performs these and other calculations. The software runs on various handheld devices, including Palm™ computers. Excellent documentation for the software is available.

Scenes with Height As Well As Depth

When a scene contains height as well as depth, the optimum position of the plane of focus usually is far from obvious. It’s possible to calculate the required tilt and focus settings that give the smallest f-number that will place an arbitrary set of points within the DoF, but again, the calculations aren’t practical without a computer or programmable calculator. The Sinar e view camera incorporated sensors for making the appropriate measurements and used an attached computer to perform the calculations, but its cost and bulk made it impractical for most applications. As with trial-and-error methods, calculations sometimes indicate that best results will be obtained by setting the tilt to zero.

Shift

Rising/Falling Front

Parallel lines in a plane parallel to the image plane remain parallel in the image. When the object plane is not parallel to the image plane, parallel lines in the object plane converge. For example, when the camera is pointed up to include the top of a tall building, vertical lines in the building converge, making the top of the building appear small, and in some cases causing the building to appear as if it is falling over backward.

This convergence of parallel lines can often be avoided with a tilt/shift lens by keeping the camera back vertical and shifting the lens up. When the lens is shifted, the image framing changes but linear perspective does not.

Falling front can be used to avoid convergence when placing a building at the top of an image to emphasize the foreground. Falling front is also useful when looking down from a high vantage point, such as from a trail above a stream in a forest. Shifting the lens down avoids divergence of the tops of the trees.

Rising or falling front may be useful even on a subject with no apparent straight lines if the shape of the subject is very familiar, such as with El Capitan in California’s Yosemite Valley. When photographed by pointing an ordinary wide-angle lens up, such objects often have the appearance of falling over backward. Employing rising front with a TS-E 24 mm f/3.5L lens maintains the appearance with which viewers of innumerable published photographs are familiar.

Some objects may be too tall to photograph without pointing the camera up slightly, even with maximum shift. In some cases, completely avoiding convergence may look unnatural, and allowing slight convergence may be preferable. A common guideline is that when the line of sight to the top (or bottom) of an object is greater than 20 degrees, allowing some convergence usually gives a more pleasing result. The amount of convergence to allow is usually a matter of personal taste, and may vary from subject to subject.

An alternative may be to take the picture from an elevated floor of a nearby building, and using rising front to adjust the framing. The resulting image will not be quite the same as one taken from ground level, but the overall effect may be more pleasing. If a nearby building is not available, a ladder can sometimes be used to raise the camera position.

In some cases, it may be desirable to increase convergence of vertical lines. For a tall building, this can be done by shifting the lens down and pointing the camera up.

Lateral Shift

When photographing a highly reflective object, such as a mirror, that is directly in front of the camera, the camera will appear in the image. This can be avoided by moving the camera to one side and shifting the lens laterally until the image framing is the same as for the direct position. The relationship of foreground objects will not be exactly the same as for the direct framing, but convergence of horizontal lines will be avoided.

Sometimes it is desirable to eliminate a foreground object from a picture; in some cases this can be accomplished by moving the camera to the side away from the unwanted object, and shifting the lens in the opposite direction until the framing is the same as it was before moving the camera. As with the reflective object, the relationship of other foreground objects to the background will change, but convergence of horizontal lines will be avoided.

Panorama

A panoramic image can be created by fully shifting the lens to one side, taking a picture, fully shifting the lens to the opposite side, and taking a second picture. The resulting images can be combined to form a single image; with a 35 mm camera, the effect is equivalent to a 24 mm x 58 mm format.

Combined Rise and Lateral Shift

When photographing the front of a building, it’s often desirable to include part of the side of the building, while avoiding convergence of vertical or horizontal lines. This can be accomplished by a combination of rising front and lateral shift; with a tilt/shift lens, this is done by revolving the lens about its axis before shifting. Several attempts may be needed to get the best combination of rise and shift, and the amount of shift may not allow complete elimination of both vertical and horizontal convergence. When the TS-E 24 mm f/3.5L is revolved with maximum shift, vignetting may be possible, so the viewfinder should be carefully examined.

Further Reading

Nearly everything written on camera movements is intended for view camera users; however, subject to a few adaptations, much of the technique also applies to the Canon tilt/shift lenses.

Books

Merklinger, Harold M.

Focusing the View Camera. Self published, 1996 (2nd printing) ISBN 0-9695025-0-8

Simmons, Steve.

Using the View Camera. New York: Amphoto, 1987. ISBN 081746347X

Shaman, Harvey.

The View Camera. Rev. ed. New York: Amphoto, 1991. ISBN 0817463755 (pbk.)

Stroebel, Leslie D.

View Camera Technique. 7th ed. Boston: Focal Press, 1999. ISBN 0240803450 (alk. paper)

Tillmanns, Urs.

Creative Large Format: Basics and Applications. 2nd ed. Feuerthalen: Sinar AG, 1997. ISBN 3-7231-0030-9

Kodak Guide to Large Format Photography. Rev. ed.

Rochester: Silver Pixel Press, 1998. Kodak publication number O-18e. ISBN 0-87985-771-4

Lens Work II: Taking Great Pictures with EF Lenses.

Tokyo: Canon Inc., 1996. Canon publication number CT2-1508-000

Web Resources

Revision History

v1.2b 2002Sep04

jul: minor reformat

Version 1.2  3 Feb 2002

Revised section on circle of confusion; expanded description of camera controls

Version 1.1 30 Jan 2002

Original release

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