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The field of view (also field of vision) is the angular
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 extent of the observable world that is seen
Visual perception

Visual perception is the ability to interpret information from visible light reaching the eye. The resulting perception is also known as eyesight, sight or vision....
 at any given moment.

The range of visual abilities is not uniform across a field of view, and varies from animal to animal. For example, binocular vision
Binocular vision

Binocular vision is Visual perception in which both eyes are used together. The word binocular comes from two Latin roots, bini for double, and oculus for eye....
, which is important for depth perception
Depth perception

Depth perception is the visual perception ability to perceive the world in three dimensions. Although any animal capable of moving around its environment must be able to sense the distance of objects in that environment, the term perception is reserved for humans, who are the only beings that can tell each other about their qualia of dist...
, only covers 140 degrees of the field of vision in humans; the remaining peripheral 40 degrees have no binocular vision (because of the lack of overlap in the images from either eye for those parts of the field of view).






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The field of view (also field of vision) is the angular
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 extent of the observable world that is seen
Visual perception

Visual perception is the ability to interpret information from visible light reaching the eye. The resulting perception is also known as eyesight, sight or vision....
 at any given moment.

The range of visual abilities is not uniform across a field of view, and varies from animal to animal. For example, binocular vision
Binocular vision

Binocular vision is Visual perception in which both eyes are used together. The word binocular comes from two Latin roots, bini for double, and oculus for eye....
, which is important for depth perception
Depth perception

Depth perception is the visual perception ability to perceive the world in three dimensions. Although any animal capable of moving around its environment must be able to sense the distance of objects in that environment, the term perception is reserved for humans, who are the only beings that can tell each other about their qualia of dist...
, only covers 140 degrees of the field of vision in humans; the remaining peripheral 40 degrees have no binocular vision (because of the lack of overlap in the images from either eye for those parts of the field of view). The aforementioned birds would have a scant 10 or 20 degrees of binocular vision.

Similarly, color vision
Color vision

Color vision is the capacity of an organism or machine to distinguish objects based on the wavelengths of the light they reflect or emit. The nervous system derives color by comparing the responses to light from the several types of Cone cell in the eye....
 and the ability to perceive shape and motion vary across the field of view; in humans the former is concentrated in the center of the visual field, while the latter tends to be much stronger in the periphery. This is due to the much higher concentration of color-sensitive cone cell
Cone cell

Cone cells, or cones, are photoreceptor cells in the retina of the eye which function best in relatively bright light. The cone cells gradually become sparser towards the periphery of the retina....
s in the fovea
Fovea

The fovea, also known as the fovea centralis, is a part of the eye, located in the center of the macula region of the retina.The fovea is responsible for sharp central Visual perception , which is necessary in humans for reading , watching television or movies, driving, and any activity where visual detail is of primary importance....
, the central region of the retina
Retina

The vertebrate retina is a light sensitive tissue lining the inner surface of the eye. The optics of the eye create an image of the visual world on the retina, which serves much the same function as the film in a camera....
, in comparison to the higher concentration of motion-sensitive rod cell
Rod cell

Rod cells, or rods, are photoreceptor cells in the retina of the eye that can function in less intense light than can the other type of photoreceptor, cone cells....
s in the periphery. Since cone cells require considerably brighter light sources to be activated, the result of this distribution is that peripheral vision is much stronger at night relative to binocular vision.

Conversions


Many optical instruments, particularly binoculars or spotting scopes, are advertised with their field of view specified in one of two ways: angular field of view, and linear field of view. Angular field of view is typically specified in degrees, while linear field of view is a ratio of lengths. For example, binoculars with a 5.8 degree (angular)
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
 field of view might be advertised as having a (linear) field of view of 305 ft per 1000 yd or 102 mm per meter. As long as the FOV is less than about 10 degrees or so, the following approximation formulas allow one to convert between linear and angular field of view. Let be the angular field of view in degrees. Let be the linear field of view in feet per 1000 yd. Let be the linear field of view in millimeters per meter. Then, using the small-angle approximation:


Astronomy

In astronomy the field of view is usually expressed as an angular area viewed by the instrument, in square degrees, or for higher magnification instruments, in square arc-minutes. For reference the Wide Field Channel on the Advanced Camera for Surveys
Advanced Camera for Surveys

The Advanced Camera for Surveys is a third generation axial instrument aboard the Hubble Space Telescope . The initial design and scientific capabilities of ACS were defined by a team based at Johns Hopkins University....
 on the Hubble Space Telescope
Hubble Space Telescope

The Hubble Space Telescope is a Space observatory that was carried into Low Earth orbit STS-31 in April 1990. It is named after the American astronomer Edwin Hubble....
 has a field of view of 10 sq. arc-minutes, and the High Resolution Channel of the same instrument has a field of view of 0.15 sq. arc-minutes. Ground based survey telescopes have much wider fields of view. The photographic plates used by the UK Schmidt Telescope
UK Schmidt Telescope

The 1.2 metre UK Schmidt Telescope is operated by the Anglo-Australian Observatory, and located adjacent to the 3.9 metre Anglo-Australian Telescope at Siding Spring Observatory, Australia....
 had a field of view of 30 sq. degrees. The 1.8 m (71 in) Pan-STARRS
Pan-STARRS

Pan-STARRS is a planned astronomical survey that will conduct astrometry and photometry of much of the entire sky on a continuous basis. By detecting any differences from previous observations of the same areas of the sky, it is expected to discover a very large number of new asteroids, comets, variable stars and other celestial objects....
 telescope, with the most advanced digital camera to date has a field of view of 7 sq. degrees. In the near infra-red WFCAM on UKIRT has a field of view of 0.2 sq. degrees and the forthcoming VISTA
VISTA (telescope)

VISTA is the Visible & Infrared Survey Telescope for Astronomy, a 4.1m telescope which is being built at Paranal Observatory in Chile. It is expected that it will be operational at the beginning of 2009....
 telescope will have a field of view of 0.6 sq. degrees. Until recently digital cameras could only cover a small field of view compared to photographic plates, although they beat photographic plates in quantum efficiency
Quantum efficiency

Quantum efficiency is a quantity defined for a photosensitive device such as photographic film or a charge-coupled device as the percentage of photons hitting the photoreactive surface that will produce an electron?hole pair....
, linearity and dynamic range, as well as being much easier to process.

Photography

In photography, the field of view is that part of the world that is visible through the camera at a particular position and orientation in space; objects outside the FOV when the picture is taken are not recorded in the photograph.

Although related, FOV is not exactly the same as angle of view
Angle of view

In photography, angle of view describes the angle 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....
; FOV is measured in linear, spatial dimensions (feet, inches, metres, etc) whereas AOV (more properly called the angular field of view) is measured in (dimensionless
Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantity which do have units, in such a way that all the units cancel out....
) degrees of arc. FOV increases with distance, whereas AOV does not. FOV changes as the camera rotates, AOV does not. Thus, while AOV is used for lens design specification, FOV is more useful to the photographer "in the field".

Calculating the FOV enables the photographer to frame a shot without using a viewfinder
Viewfinder

In photography, a viewfinder is what the photographer looks through to compose, and in many cases to focus, the picture. Most viewfinders are separate, and suffer parallax, while the more complex single-lens reflex camera lets the viewfinder use the main optical system....
. This is especially useful where the camera set-up requires planning. For example: where the working distances are logistically huge or awkward (eg. architectural and landscape photography) or restricted (eg. low cloud in aerial photography, turbidity in underwater photography, or lens' minimum focus distance and depth of field
Depth of field

In optics, particularly as it relates to film and photography, the depth of field is the portion of a scene that appears sharp in the image. Although a lens can precisely focus at only one distance, the decrease in sharpness is gradual on either side of the focused distance, so that within the DOF, the unsharpness is imperceptible under nor...
 in close-up and macro photography).

Technically: the photographic term field—as in "field of view", "depth of field" and "field curvature"—is a customized version of the object plane concept in optics. All points (or objects) within the field appear perfectly in-focus on the film plane
Film plane

A film plane is the area inside any camera where the individual frame of film or digital sensor is positioned during exposure. It is sometimes marked on camera body with the 'F' symbol where the vertical bar represents the exact location....
. However, field curvature describes how this "plane" is actually curved rather than flat; depth of field
Depth of field

In optics, particularly as it relates to film and photography, the depth of field is the portion of a scene that appears sharp in the image. Although a lens can precisely focus at only one distance, the decrease in sharpness is gradual on either side of the focused distance, so that within the DOF, the unsharpness is imperceptible under nor...
 permits objects positioned slightly behind or in front of the plane to appear to be in perfect focus; and the field of view describes how the lateral extent of the (otherwise unlimited) field is 'cropped' to a rectangular or circular 'window on the world'. Just as depth of field
Depth of field

In optics, particularly as it relates to film and photography, the depth of field is the portion of a scene that appears sharp in the image. Although a lens can precisely focus at only one distance, the decrease in sharpness is gradual on either side of the focused distance, so that within the DOF, the unsharpness is imperceptible under nor...
 describes the (min/max) objective distance(s) along the optical axis where an object appears to be 'in-focus', the field of view describes the objective distance perpendicular to the optical axis where an object (at a given object distance) appears to be 'in-frame'.

A camera's rectangular FOV is bounded by a virtual image
Virtual image

In optics, a virtual image is an image in which the outgoing ray from a point on the object never actually intersect at a point. A simple example is a plane mirror where the image of oneself is perceived at twice the distance from oneself to the mirror....
 of its field stop (usually the film gate
Film gate

The film gate is the rectangular opening in the front of a motion picture camera where the film is exposed to light. The film gate can be seen by removing the Photographic lens and rotating the shutter angle out of the way....
 or edges of the image sensor). A lens' FOV is a virtual image of its image circle. If the diameter of the image circle is not larger than the diagonal dimension of the film frame, vignetting
Vignetting

In photography and optics, vignetting is a reduction of an image's brightness or saturation at the periphery compared to the image center. A similar effect occurs when filming projected images or movies off a projection screen, the so-called hotspot, defining a cheap home-movie look where no proper telecine is used....
 will occur. The "FOV formula" is derived from similar triangles and can be used for (amongst other things) calculating the 'dimension' of the FOV at a given distance: where:
  • f is the film distance (from lens to film plane). When the lens is focussed to infinity, this distance is equal to the effective focal length of the lens. Treating f as equal to the focal length is adequate for most purposes.
  • d is the object distance (or "working distance" from lens to object along the optical axis).
  • o is the object dimension (or "field of view" perpendicular to and and bisected by the optical axis).
  • i is the image dimension (or "field stop" perpendicular to and and bisected by the optical axis).
  • The dimensions for o and i must be in the same diagonal, horizontal or vertical plane; so the horizontal object dimension corresponds to the horizontal image dimension, overtical to ivertical, and odiag / d = idiag / f.


So for example, a 135 film
135 film

The term 135 was introduced by Kodak in 1934 as a designation for Film cartridge film 35 mm wide, specifically for still photography. It quickly grew in popularity, surpassing 120 film by the late 1960s to become the most popular photographic film format....
 frame has i dimensions of 36 mm horizontal by 24 mm vertical and 43.3 mm diagonal. Thus, the horizontal field of view using a 50 mm lens would be d × i / f = d × 36 / 50 = d × 0.72. At a working distance of 10 metres, the horizontal field of view is therefore 7.2 metres; at a distance of 100 feet, the horizontal field of view is 72 feet, etc. (The horizontal AOV is about 39.6º at any distance).

From this we can see that i / f is another (dimensionless) expression for the angle of view
Angle of view

In photography, angle of view describes the angle 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....
 (AOV = 2 arctan(i /2 f)), but without the trigonometry required to translate linear dimensions to degrees of arc (and back again). While i / f is directly proportional to the measurable distances and dimensions, AOV is not; so for example, focal length × 2 does not equal AOV / 2. The FOV formula is therefore much easier (to do in your head) and more useful in practical photographic situations.

The same inaccuracies can be caused in both the AOV
Angle of view

In photography, angle of view describes the angle 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....
 and the FOV formulae by the quirks of a particular lens design: Close-focusing may reduce the FOV (by increasing f), and radial distortion means that the diagonal, horizontal and vertical FOVs will not be rectilinearly proportionate to each other or to a given focal length.

The DSLR crop factor
Crop factor

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 digital cameras, relative to 135 film as a standard....
 is also derived from this i / f factor : (2/3 × i) / f = i / (1.5 × f)

See also

  • Field of view (image processing)
  • Perimetry
    Perimetry

    Perimetry or Campimeter is the systematic measurement of differential light sensitivity in the visual field by the detection of the presence of test targets on a defined background....
  • Peripheral vision
    Peripheral vision

    Peripheral vision is a part of visual perception that occurs outside the very center of gaze. There is a broad set of non-central points in the field of view that is included in the notion of peripheral vision....
  • Visual perception
    Visual perception

    Visual perception is the ability to interpret information from visible light reaching the eye. The resulting perception is also known as eyesight, sight or vision....