# What is an Angle of View?

## This establishes the disc of best definition required for the lens

This term is often confused with angle of field and field of view. The angle of field is the angle subtended at the lens rear nodal point by the diagonal of the format itself. In a rectilinear image this is the same as the angle of view, but not for anamorphic images such as those produced by fisheye lenses. ‘Field of view’ simply describes the area covered in a scene. For example, although the angle of view of a fisheye lens is 180 degrees, its angle of field may be as low as 90 degrees. The field of view may be described as ‘horizon to horizon’. For a standard (prime) lens the angle of field is typically 50-55 degrees, the same as the angle of view, and the field of view is roughly the same as that of the eye in a normal viewing of a scene or a picture.

For lenses projecting rectilinear (non-spatially-distorted) imagery of far-off objects, the operative focal segment and the image format dimensions completely identify the angle of view. Calculations for lenses producing non-rectilinear images are a lot supplementary intricate and in the end not very useful in most hands-on applications.

Angle of look at may be measured horizontally (from the left to righteous perimeter of the frame), vertically (from the top to substructure of the frame), or obliquely (from one back into a corner of the frame to its opposite corner).
For a lens projecting a rectilinear image, the angle of view (a) can be calculated starting the selected dimension (d), and in effect main length (f) as follows:
d represents the bulk of the capture on film (or sensor) in the direction measured. For example, for haze so as to is 36 mm wide, d = 36 mm would be used to take the horizontal twist of view.
since this is a trigonometric function, the aim of position does not be different pretty linearly amid the common of the important length. However, not including for wide-angle lenses, it is rational to approximate radians or degrees.

### Calculating a camera's angle of view

These photos were shot with a Sigma APO 50-500mm F4-6.3 DG EX DG Lens
from the exact same spot Angle of view 50mm Sigma 50-500mm Lens Angle of view 100mm Sigma 50-500mm Lens Angle of view  200mm Sigma 50-500mm Lens Angle of view 300mm Sigma 50-500mm Lens Angle of view 400mm Sigma 50-500mm Lens Angle of view 500mm Sigma 50-500mm Lens

The helpful focal part is not quite equal to the stated focal time taken of the lens (F), except for in macro cinematography where the lens-to-object expanse is comparable to the focal length. In this case, the enlargement issue (m) must be in use hooked on account:
(In photography m is more often than not distinct to be positive, despite the inverted image.) For example, in addition to a intensification ratio of 1:2, we locate and in this fashion the angle of prospect is reduced by 33% compared to focusing on a far object with the same lens.
Angle of view can moreover be determined by FOV tables or paper or software lens calculators.

### Example

Consider a 35 mm camera with a normal lens having a focal length of F=50 mm. The dimensions of the 35 mm image format are 24 mm (vertically) × 36 mm (horizontal), giving a diagonal of about 43.3 mm. A camera's angle of view can be measured horizontally, vertically, or diagonally. In 1916, Northey showed how to calculate the angle of view using ordinary carpenter's tools. 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.

Now the angles of view are:

horizontally, 39.6° vertically, 27.0° diagonally, 46.8°

### 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). 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):

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. 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 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. 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,.

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

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

where .

### Measuring a camera's field of view

Schematic of collimator-based optical apparatus used in measuring the FOV of a camera.
In the optical instrumentation industry the term field of view (FOV) is most often used, though the measurements are still expressed as angles. Optical tests are commonly used for measuring the FOV of UV, visible, and infrared (wavelengths about 0.1–20 µm in the electromagnetic spectrum) sensors and cameras.

The purpose of this test is to measure the horizontal and vertical FOV of a lens and sensor used in an imaging system, when the lens focal length or sensor size is not known (that is, when the calculation above is not immediately applicable). Although this is one typical method that the optics industry uses to measure the FOV, there exist many other possible methods.

UV/visible light from an integrating sphere (and/or other source such as a black body) is focused onto a square test target at the focal plane of a collimator (the mirrors in the diagram), such that a virtual image of the test target will be seen infinitely far away by the camera under test. The camera under test senses a real image of the virtual image of the target, and the sensed image is displayed on a monitor.

Monitor display of sensed image from the camera under test
The sensed image, which includes the target, is displayed on a monitor, where it can be measured. Dimensions of the full image display and of the portion of the image that is the target are determined by inspection (measurements are typically in pixels, but can just as well be inches or cm).

D = dimension of full image d = dimension of image of tarBest Prices for the collimator's distant virtual image of the target subtends a certain angle, referred to as the angular extent of the target, that depends on the collimator focal length and the target size. Assuming the sensed image includes the whole target, the angle seen by the camera, its FOV, is this angular extent of the target times the ratio of full image size to target image size.

The target's angular extent is:

where L is the dimension of the target and fc is the focal length of collimator. The total field of view is then approximately:

or more precisely, if the imaging system is rectilinear:

This calculation could be a horizontal or a vertical FOV, depending on how the target and image are measured.

### 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 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. 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 43.3 mm for d in the formula above).

 Focal Length (mm) Diagonal (°) Vertical (°) Horizontal (°) 13 15 18 21 24 28 35 43.3 50 70 85 105 135 180 200 300 400 500 600 800 1200 118 111 100 91.7 84.1 75.4 63.4 53.1 46.8 34.4 28.6 23.3 18.2 13.7 12.4 8.25 6.19 4.96 4.13 3.1 2.07 85.4 77.3 67.4 59.5 53.1 46.4 37.8 31 27 19.5 16.1 13 10.2 7.63 6.87 4.58 3.44 2.75 2.29 1.72 1.15 108 100.4 90 81.2 73.7 65.5 54.4 45.1 39.6 28.8 23.9 19.5 15.2 11.4 10.3 6.87 5.15 4.12 3.44 2.58 1.72

Five images using 24, 28, 35, 50 and 72mm equivalent zoom lengths, portrait format, to illustrate angles of view Five images from the Ricoh Caplio GX100, using 24, 28, 35, 50 and 72mm equivalent step zoom function, to illustrate angles of view