# Angle of view

As a picture angle that angle is referred to in the object space in photography, which is bounded by the edges of the recording format. In the conventional rectangular image format is meant by field of view is usually the belonging to the diagonal value. Horizontal and vertical angles are smaller and to designate a full length horizontal angle or vertical angle. In typically greater width and smaller height is the vertical angle of the smallest and the largest of the three diagonal angle.

Except by the image format - height, width and diagonal of the image - the image angle is essentially determined only the actual focal length of the camera lens. The following formula accordingly provides the diagonal angle of view and setting the lens to "infinity" ():

In figure closer objects, however, the image distance is greater than, whereby the angle decreases accordingly.

According to the formula can be a maximum of 180 ° angle of view, because the range of the arctangent function is bounded by -90 ° and 90 °. Fisheye lenses still have an excess of 180 ° reaching angle, but do not produce collinear figure, that is, straight lines are mapped curved so that the formula for the angle of view can not be applied here. For lenses with pronounced distortion the recording format corresponding local focal length of the lens at the edges or corners of the recording format must be used. Otherwise, the formula is fully applicable to collinear imaging lenses with image angles independent focal length.

## Directional dependence

Except a circular recording format of the image depends on the size of the angle of the direction - in relation to the horizontal plane of the recording medium - as in which it is determined.

The special significance of the diagonal angle of view is that the diagonal of a rectangle corresponds to its greatest extent. Thus, for a given focal length and recording format is the diagonal also always the largest angle.

The direction of the respective image angle to the horizontal is in the

- Horizontal angle of view: 0 ° or 180 °
- Vertical angle: ± 90 °
- Diagonal angle of view:

When comparing different recording formats is therefore important to note that the diagonal angle of view of the two formats differ in their direction. A comparison based on the diagonal angle of view is only meaningful if the have to be compared recording formats in approximately the same aspect ratios.

By cutting the ausbelichteten image or by restricting the recording format when recording through masks in front of the image plane arbitrarily shaped recording formats can be realized. In this case one refers when specifying the angle of view on an imaginary rectangle that the actual recording format just rewrites.

A special case is the circular recording format, here the angle of the direction is independent and constant. This also applies to the ( circular ) image circle.

## Field of view

As a field of view ( engl. field of view, FOV) is referred to that region of the object space, which is spanned by the horizontal and vertical angles.

## Maximum achievable angle

For a single converging lens or a pinhole, the maximum angle of view can theoretically be up to 180 °. With lenses but the light has to pass through successively more openings that act as diaphragms. This includes the lenses and their versions. Thus, the usable field of view is limited. Aberrations can further limit the actual sensibly usable angle. Special lens designs such as fisheye lenses can still picture angle of 180 ° - reflect - or even beyond. The maximum achievable angle of a lens is given in the technical data. From it results in the diagonal of the largest usable recording format:

The image circle diameter corresponds to the diagonal of the largest usable recording format.

## Normal viewing angle and normal focal length of a photographic lens

To view or angle of vision with natural impression one has of the scene, values between 40 ° and 55 ° can be specified. The viewing photos leads to the same impression when they were taken with the same large picture angle. As a rule of thumb is that the focal length of the lens is supposed to be about the same size as the diagonal of the picture format (). Under this assumption, there is a picture angle of about 53 °:

The matching normal focal length for the small picture size of 36 mm × 24 mm would be:

Naturalized but has the small -screen focal length, whereby the angle falls in the above range between 40 ° and 55 °:

The other two angle are:

In another aspect ratio as the miniature film obtained for the horizontal and vertical angle other ratios. Therefore, to compare different images usually resorted to the diagonal angle, as this always refers independent of the aspect ratio on the maximum image circle. In an image angle of 46.8 ° is obtained for infinite object distances regardless of the aspect ratio always a screen size that is larger by about 16% than the focal length.

A wide-angle lens has a much larger, a telephoto lens a much smaller angle than the normal angle.

The relative image scale refers to the actual image scale of an optical imaging on the image scale at the normal focal length of the optical system.

## Angular Field of View

Similar to the picture angle is defined on the object side of the visual angle as

Wherein the horizontal, vertical or diagonal dimension of the object to be imaged and the distance of the object (more precisely, the object distance ) is.

The visual angle (also apparent size ) describes the angle at which an object appears at a given extension and distance.

Intuitively, one can imagine the visual angle by reversing the beam path.

In order to fully represent an object on the recording medium, the horizontal and vertical angle must not be less than the corresponding visual angle, so it must be true:

If a subject at close range and with a lens with large aperture are imaged sufficiently sharp, so the object distance must also be the picture angle involved (see section Macro photography). The effective angle of view must not be smaller than the corresponding angle of view:

## Angle and angle of view in photography

Angle and viewing angle are the most important photographic design elements, with the former only by the focal length of the lens used and the recording format of the camera, the latter, however, depends only on the size and distance of the object to be photographed.

Accordingly, the photographer if he wants to change the angle of view, do this either by changing the focal length, eg by means of interchangeable lenses, converters, or by using a zoom lens, but alternatively by choosing another record, that h sensor or film format, subsequent trimming the recording or merging several individual images ( stitching) into an overall picture.

The rule is: If you change the recording format and the focal length by the same absorbed. Form factor, so the viewing angle will not change. This relationship follows directly from the definition of the angle of view:

The angle of view, however, can be influenced only by changing the size or distance of the object to. Thus, the visual angle is modified in approximately the trick Engineering and Architecture Photography that one instead of the object to be imaged - for example, a building or architectural details - the same a reduced (or enlarged ) model being photographed or filmed. The size of "real" objects, however, usually can not be influenced - here the photographer therefore usually only have the possibility to choose a different distance to the object, jokingly referred to as " foot - zoom ".

## Macro Photography

The definition of the angle of view refers to the focal plane. However, this does not necessarily fall with the image plane together. If an object at a short distance still keen to be mapped to a movie or a matte screen, either dimmed or the image plane will be moved backward. If the object distance is not greater than twice the focal length, it is called macro photography.

To the effective angle of view - based on the image plane - to get at close range, one must use instead of the focal length of the image distance in the definition, ie

Expressed by the focal length and object distance is obtained according to the lens equation:

Note: