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. Photography (fә'tɒgrәfi or fә'tɑːgrәfi (from Greek φωτο and γραφία is the process and Art of recording pictures by means of capturing In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called A camera is a device used to capture images either as still Photographs or as sequences of moving images ( Movies or Videos. It parallels, and may be used interchangeably with, the more general visual term field of view. The field of view (also field of vision) is the angular extent of the observable world that is seen at any given moment

It is important to distinguish the angle of view from the angle of coverage, which describes the angle of projection by the lens onto the focal plane. For most cameras, it may be assumed that the image circle produced by the lens is large enough to cover the film or sensor completely. ^[1] If the angle of view exceeds the angle of coverage, however, then vignetting will be present in the resulting photograph. In Photography and Optics, vignetting is a reduction of an image's brightness or saturation at the Periphery compared to the image center For an example of this, see below. In Photography, angle of view describes the angular extent of a given scene that is imaged by a Camera.

Calculating a camera's angle of view

In 1916, Northey showed how to calculate the angle of view using ordinary carpenter's tools. ^[2] The angle that he labels as the angle of view is the half-angle or "the angle that a straight line would take from the extreme outside of the field of view to the center of the lens;" he notes that manufacturers of lenses use twice this angle.

For lenses projecting rectilinear (non-spatially-distorted) images of distant objects, the effective focal length and the image format dimensions completely define the angle of view. In Photography, a rectilinear lens is a Photographic lens that yields images where straight features such as the walls of buildings appear with straight lines as The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light. Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications.

Angle of view may be measured horizontally (from the left to right edge of the frame), vertically (from the top to bottom of the frame), or 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 (f) as follows:^[3]

d represents the size of the film (or sensor) in the direction measured. For example, for film that is 36 mm wide, d = 36 mm would be used to obtain the horizontal angle of view.

Because this is a trigonometric function, the angle of view does not vary quite linearly with the reciprocal of the focal length. However, except for wide-angle lenses, it is reasonable to approximate radians or degrees.

The effective focal length is nearly equal to the stated focal length of the lens (F), except in macro photography where the lens-to-object distance is comparable to the focal length. Macro photography is close-up Photography; the classical definition is that the Image projected on the "film plane" (i In this case, the magnification factor (m) must be taken into account:

(In photography m is usually defined to be positive, despite the inverted image. Magnification is the process of enlarging something only in appearance not in physical size ) For example, with a magnification ratio of 1:2, we find and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.

Example

Consider a 35 mm camera with a normal lens having a focal length of F=50 mm. 35 mm film is the basic Film gauge most commonly used for both still Photography and Motion pictures, and remains relatively unchanged since its In Photography and Cinematography a normal lens is a lens that generates images that generally look "natural" to a human observer under normal The dimensions of the 35 mm image format are 24 mm (vertically) × 36 mm (horizontal), giving a diagonal of about 43. 3 mm.

Now the angles of view are:

• horizontally, 39. 6°
• vertically, 27. 0°
• diagonally, 46. 7°

Derivation of the angle-of-view formula

Consider a rectilinear lens in a camera used to photograph an object at a distance S₁, and forming an image that just barely fits in the dimension d of the frame (the film or image sensor). This article is mainly concerned with Still photography film For Motion picture film please see Film stock. An image sensor is a device that converts an optical image to an electric signal Treat the lens as if it were a pinhole at distance S₂ from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil^[4]):

Now α / 2 is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. The pinhole camera model describes the mathematical relationship between the coordinates of a 3D point and its Projection onto the image plane of an ideal Pinhole In Photography, a rectilinear lens is a Photographic lens that yields images where straight features such as the walls of buildings appear with straight lines as In an optical system the entrance pupil is a virtual aperture that defines the area at the entrance of the system that can accept light In Optics, the term optical axis is used to define a direction along which there is some degree of Rotational symmetry. Here α is defined to be the angle-of-view, since it is the angle enclosing the largest object whose image can fit on the film. We want to find the relationship between:

the angle α (half of the angle-of-view)

the "opposite" side of the right triangle, d / 2 (half the film-format dimension)

the "adjacent" side, S₂ (distance from the lens to the image plane)

Using basic trigonometry, we find:

which we can solve for α, giving:

To project a sharp image of distant objects, S₂ needs to be equal to the focal length F, which is attained by setting the lens for infinity focus. The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light. In Optics and Photography, infinity focus is the state where a lens or other optical device forms an image of an object an Infinite distance Then the angle of view is given by:

where f = F

Macro photography

For macro photography, we cannot neglect the difference between S₂ and F From the thin lens formula,

. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging

We substitute for the magnification, m = S₂ / S₁, and with some algebra find:

Defining f = S₂ as the "effective focal length", we get the formula presented above:

where . Magnification is the process of enlarging something only in appearance not in physical size

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. In Photography, a fisheye lens is a Wide-angle lens that takes in an extremely wide hemispherical image A zoom lens is a mechanical assembly of lens elements with the ability to vary its Focal length (and thus Angle of view) as opposed to a fixed focal

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. In Optics, particularly as it relates to Film and Photography, the depth of field (DOF is the portion of a scene that appears sharp in the image 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. In Photography and Cinematography, perspective distortion describes one of two phenomena – the appearance of a part of the subject as abnormally large relative In Photography and Cinematography a normal lens is a lens that generates images that generally look "natural" to a human observer under normal 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. In Photography and Cinematography, perspective distortion describes one of two phenomena – the appearance of a part of the subject as abnormally large relative

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

28 mm lens, 65. 5° × 46. 4°	50 mm lens, 39. 6° × 27. 0°
70 mm lens, 28. 9° × 19. 5°	210 mm lens, 9. 8° × 6. 5°

Circular fisheye

A circular fisheye lens (as opposed to a full-frame fisheye) is an example of a lens where the angle of coverage is less than the angle of view. In Photography, a fisheye lens is a Wide-angle lens that takes in an extremely wide hemispherical image The image projected onto the film is circular because the diameter of the image projected is narrower than that needed to cover the widest portion of the film.

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 using width 36 mm, height 24 mm, and diagonal 43. A full-frame digital SLR is a Digital single-lens reflex camera (DSLR fitted with an Image sensor that is the same size as a 35 mm (36x24 mm film frame 3 mm for d in the formula above^[5]).

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. 3D computer graphics (in contrast to 2D computer graphics) are graphics that use a three-dimensional representation of geometric data that is stored in the computer 3D projection is any method of mapping three-dimensional points to a two-dimensional plane 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.

Cinematography

Modifying the angle of view over time, or zooming, is a frequently used cinematic technique. See also Filmmaking Cinematic techniques are methods employed by film makers to communicate meaning entertain and to produce a particular emotional or

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. A point of view shot also known as POV shot or a subjective camera) is a short Film scene that shows what a character (the subject is looking at (represented 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. A game engine is a software system designed for the creation and development of computer and video games Typical PC hardware A typical Personal computer consists of a case or chassis in a tower shape (desktop and the following parts Motherboard Some examples include Burnout 3: Takedown and Grand Theft Auto: San Andreas. Burnout 3 Takedown is the third game in the Burnout series of video games Grand Theft Auto San Andreas is a sandbox-style action-adventure computer and Video game developed by Rockstar North

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. A first-person shooter ( FPS) is an action Video game from the Shooter game The initial development of Maze War

References and notes

1. ^ One exception is technical photography involving view camera movements, in which the optical axis of the lens may not be aligned with the center of the frame. The view camera is a type of Camera first developed in the era of the Daguerreotype and still in use today though with many refinements The photographer must ensure that the angle of coverage of the lens is large enough to cover the frame in this case.
2. ^ Neil Wayne Northey (Sept. 1916). "The Angle of View of your Lens". The Camera 20 (9). Columbia Photographic Society.  
3. ^ Ernest McCollough (1893). "Photographic Topography". Industry: A Monthly Magazine Devoted to Science, Engineering and Mechanic Arts: 399–406. Industrial Publishing Company, San Francisco.  
4. ^ Kerr, Douglas A. (2005). The Proper Pivot Point for Panoramic Photography (PDF). The Pumpkin. Retrieved on 2007-01-14. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1129 - Formal approval of the Order of the Templar at the Council of Troyes.
5. ^ However, most interchangeable-lens digital cameras do not use 24x36 mm image sensors and therefore produce narrower angles of view than set out in the table. An image sensor is a device that converts an optical image to an electric signal See crop factor and the subtopic digital camera issues in the article on wide-angle lenses for further discussion. In Digital photography, a crop factor is the ratio of the dimensions of a camera's imaging area compared to a reference format most often this term is applied to

See also

• 35 mm equivalent focal length

External links

• Angle of View comparison photographs
• Angle of View on digital SLR cameras with reduced sensor size
• Focal Length and Angle of View

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