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Angle of view

In photography, angle of view (AOV) describes the angular extent of a given scene that is imaged by a camera. It is used interchangeably with the more general term field of view.
It is important to distinguish the angle of view from the angle of coverage, which describes the angle range that a lens can image. Typically the image circle produced by a lens is large enough to cover the film or sensor completely, possibly including some vignetting toward the edge. If the angle of coverage of the lens does not fill the sensor, the image circle will be visible, typically with strong vignetting toward the edge, and the effective angle of view will be limited to the angle of coverage.
A camera's angle of view depends not only on the lens, but also on the sensor. Digital sensors are usually smaller than 35mm film, and this causes the lens to have a narrower angle of view than with 35mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (consumer SLR), to 2 (Micro Four Thirds ILC) to 4 (enthusiast compact cameras) to 6 (most compact cameras). So a standard 50mm lens for 35mm photography acts like a 50mm standard "film" lens even on a professional digital SLR, but would act closer to an 80mm lens (1.6 x 50mm) on many mid-market DSLRs, and the 40 degree angle of view of a standard 50mm lens on a film camera is equivalent to a 28 - 35mm lens on many digital SLRs.
==Calculating a camera's angle of view==
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. Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications. (In the case of a lens with distortion, e.g., a fisheye lens, a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion)〔http://www.the-digital-picture.com/reviews/canon-ef-15mm-f-2.8-fisheye-lens-review.aspx〕
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 (focused at infinity, see derivation), the angle of view (''α'') can be calculated from the chosen dimension (''d''), and effective focal length (''f'') as follows:
::$\alpha = 2 \arctan \frac$
$d$ represents the size of the film (or sensor) in the direction measured ''(see below: sensor effects)''. For example, for 35mm film which is 36 mm wide and 24mm high, $d = 36$ mm would be used to obtain the horizontal angle of view and $d = 24$ mm for the vertical angle.
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 $\alpha\approx \frac$ radians or $\frac$ 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. In this case, the magnification factor (''m'') must be taken into account:
::$f = F \cdot \left( 1 + m \right)$
(In photography $m$ is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find $f = 1.5 \cdot F$ and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.
A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (''P'') between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes:
::$\alpha = 2 \arctan \frac$
Angle of view can also be determined using FOV tables or paper or software lens calculators.〔(CCTV Field of View Camera Lens Calculations ) by JVSG, December, 2007〕

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