Definitions

# 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.

Different animals have different fields of view, depending on the placement of the eyes. Humans have an almost 180-degree forward-facing field of view, while some birds have a complete or nearly-complete 360-degree field of view. In addition the vertical range of the field of view may vary.

The range of visual abilities is not uniform across a field of view, and varies from animal to animal. For example, binocular vision, which is important for depth perception, 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 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 cells in the fovea, the central region of the retina, in comparison to the higher concentration of motion-sensitive rod cells 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) 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 $A$ be the angular field of view in degrees. Let $L$ be the linear field of view in feet per 1000 yd. Let $M$ be the linear field of view in millimeters per meter. Then:

$A = 0.0191 times L$
$A = 0.0577 times M$
$L = 52.43 times A$
$M = 17.15 times A$

### 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 on the Hubble Space Telescope 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 had a field of view of 30 sq. degrees. The 1.8 m (71 in) Pan-STARRS 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 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, 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; 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) 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. 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 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. However, field curvature describes how this "plane" is actually curved rather than flat; depth of field 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 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 of its field stop (usually the film gate 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 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:

$\left\{o over d\right\} = \left\{i over f\right\}$
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 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 (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 and the FOV formulae by the quirks of a particular lens design: Close-focussing 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 is also derived from this i / f factor : (0.75 × i) / f = i / (1.5 × f)