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 5055 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 (nonspatiallydistorted) imagery of
faroff objects, the operative focal segment and the image format dimensions
completely identify the angle of view. Calculations for lenses producing
nonrectilinear images are a lot supplementary intricate and in the end not very
useful in most handson 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 wideangle lenses, it is rational to approximate radians or
degrees.
Calculating a camera's angle of view
These photos were shot with a Sigma APO 50500mm F46.3 DG EX DG Lens
from the exact same spot
Angle of view 50mm
Sigma 50500mm Lens
Angle of view 100mm
Sigma 50500mm Lens
Angle of view 200mm
Sigma 50500mm Lens
Angle of view 300mm
Sigma 50500mm Lens
Angle of view 400mm
Sigma 50500mm Lens
Angle of view 500mm
Sigma 50500mm 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 lenstoobject 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 halfangle 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 angleofview 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 angleofview, 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 filmformat 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 collimatorbased 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 wideangle lenses, also known as fisheye lenses, cover up to 180° (or even wider in special cases)
 Wideangle 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 wideangle 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 fullframe 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
fullframe 35mm digital using width 36 mm, height 24 mm, and diagonal 43.3 mm for d in the formula above).
Focal Length (mm) 
13 
15 
18 
21 
24 
28 
35 
43.3 
50 
70 
85 
105 
135 
180 
200 
300 
400 
500 
600 
800 
1200 
Diagonal (°) 
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 
3.10 
2.07 
Vertical (°) 
85.4 
77.3 
67.4 
59.5 
53.1 
46.4 
37.8 
31.0 
27.0 
19.5 
16.1 
13.0 
10.2 
7.63 
6.87 
4.58 
3.44 
2.75 
2.29 
1.72 
1.15 
Horizontal (°) 
108 
100.4 
90.0 
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
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