Angle of view

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A camera's angle of view can be measured horizontally, vertically, or diagonally.

In photography, angle of view describes the angular extent of a given scene that is imaged by a camera. It parallels, and may be used interchangeably with, the more general visual term field of view.

1 Calculating a camera's angle of view
2 Lens types and effects
3 Common lens angles of view
4 Three-dimensional digital art
5 Cinematography
- 5.1 Video games
6 Notes
7 External links

[edit] Calculating a camera's angle of view

The angle of view of a camera is a function of three parameters:

The dimensions of the film format or image sensor;
The focal length of the photographic lens projecting the image; and
The kind and degree of distortion of the lens.

It follows that for lenses projecting rectilinear (non-spatially-distorted) images, the film format or image sensor dimensions completely define the angle of view for any given lens focal length.

Angle of view is usually measured one of three ways:

horizontally (from the left to right edge of the frame)
vertically (from the top to bottom of the frame)
diagonally (from one corner of the frame to its opposite corner)

For a lens projecting a rectilinear image, the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (ƒ)^[1] thus:

$\alpha = 2 \arctan \frac {d} {2 f}$ ^[2]

Note that the effective focal length can simply be set equal to the stated focal length of the lens (F), except in macro photography where the magnification factor (m) must be taken into account:

$f = F \cdot ( 1 + m )$

If the chosen dimension is to be the diagonal, then it can be calculated from the horizontal and vertical dimensions of the format through the use of the Pythagorean Theorem:

$d = \sqrt{h^2 + v^2}$

where h is the horizontal dimension of the image format and v is its vertical dimension. For example, the diagonal measurement of the image format for a full-frame 35 mm camera is:

$d = \sqrt{36^2+24^2} = 43.27\,\mathrm{mm}$

[edit] Lens types and effects

Lenses are often referred to by terms that express their angle of view:

Ultra wide-angle lenses, also known as fisheye lenses, cover up to 180° (or even wider in special cases)
Wide-angle lenses generally cover between 100° and 60°
Normal, or Standard lenses generally cover between 50° and 25°
Telephoto lenses generally cover between 15° and 10°
Super Telephoto lenses generally cover between 8° through less than 1°

Zoom lenses are a special case wherein the focal length, and hence angle of view, of the lens can be altered mechanically without removing the lens from the camera.

Longer lenses magnify the subject more, apparently compressing distance and (when focused on the foreground) blurring the background because of their shallower depth of field. Wider lenses tend to magnify distance between objects while allowing greater depth of field.

Another result of using a wide angle lens is a greater apparent perspective distortion when the camera is not aligned perpendicularly to the subject: parallel lines converge at the same rate as with a normal lens, but converge more due to the wider total field. For example, buildings appear to be falling backwards much more severely when the camera is pointed upward from ground level than they would if photographed with a normal lens at the same distance from the subject, because more of the subject building is visible in the wide-angle shot.

Because different lenses generally require a different camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground.

*An example of how lens choice affects angle of view. The photos below were taken by a 35 mm camera at a constant distance from the subject.*
28 mm lens	50 mm lens
70 mm lens	210 mm lens

Note that the angle of view of a given lens is frequently, and incorrectly, referred to as the angle of coverage, a term which describes the angle of projection by the lens onto the focal plane. Angle of coverage is only a consideration in technical photography involving view camera movements, in which the lens may be required to project an image circle much larger than the film dimensions. In cameras with fixed alignment between the lens and film (or sensor), it can generally be taken for granted that the center of the lens is aligned with the center of the frame, and the that image circle is large enough to cover the frame, and thus angle of coverage is not a consideration for the photographer.

A circular fisheye lens, as opposed to a full-frame fisheye, is an example of a lens where the angle of coverage has been narrowed relative to the other lenses in that system. In many cases the angle of view of the circular fisheye will be almost exactly the same as the nearest full-frame fisheye; however, the image projected onto the film is rendered circular because the diameter of the image projected is narrower than that needed to cover the widest portion of the film.

[edit] Common lens angles of view

This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, 135 film or full-frame 35mm digital^[3])

Focal Length (mm)	13	15	18	21	24	28	35	50	85	105	135	180	210	300	400	500	600	830	1200
Diagonal (°)	118	111	100	91.7	84.1	75.4	63.4	46.8	28.6	23.3	18.2	13.7	11.8	8.25	6.19	4.96	4.13	2.99	2.07
Vertical (°)	85.4	77.3	67.4	59.5	53.1	46.4	37.8	27.0	16.1	13.0	10.2	7.63	6.54	4.58	3.44	2.75	2.29	1.66	1.15
Horizontal (°)	108	100.4	90.0	81.2	73.7	65.5	54.4	39.6	23.9	19.5	15.2	11.4	9.80	6.87	5.15	4.12	3.44	2.48	1.72

[edit] Three-dimensional digital art

Displaying 3d graphics requires 3d projection of the models onto a 2d surface, and uses a series of mathematical calculations to render the scene. The angle of view of the scene is thus readily set and changed; some renderers even measure the angle of view as the focal length of an imaginary lens. The angle of view can also be projected onto the surface at an angle greater than 90°, effectively creating a fish eye lens effect.

[edit] Cinematography

Modifying the angle of view over time, or zooming, is a frequently used cinematic technique.

[edit] Video games

As an effect, some first person games, especially racing games, widen the angle of view beyond 90° to exaggerate the distance the player is travelling, thus exaggerating the player's perceived speed. This effect can be done progressively, or upon the activation of some sort of "turbo boost." An interesting visual effect in itself, it also provides a way for game developers to suggest speeds faster than the game engine or computer hardware is capable of displaying. Some examples include Burnout 3: Takedown and Grand Theft Auto: San Andreas.

Players of first-person shooter games sometimes set the angle of view of the game, widening it in an unnatural way (a difference of 20 or 30 degrees from normal), in order to see more peripherally.

[edit] Notes

^ Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications.
^ Because this is a trigonometric function, the angle of view does not vary linearly with the focal length. That is why a small change in the focal length of wide angle lenses produces a greater change in the angle of view than the same change would produce in a telephoto lens.
^ However, most interchangeable lens digital cameras do not use 24x36 mm photosensors and therefore produce narrower angles of view than set out in the table. See subtopic Digital camera issues in the article on wide-angle lenses for further discussion.