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A large field of view is particularly relevant, for example, for astronomical telescopes which are used in stellar surveys.

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The field of view of an optical imaging instrument is often limited by an intentionally created field stop. This is an optical aperture, e.g. in the form of a diaphragm, which is placed in an image plane or close to such a plane, such that the edges of the field of view are sharply defined. However, in some cases one obtains vignetting effects, i.e., a gradual decrease of image brightness towards the edges of the field of view. This happens when the field of view is limited by an aperture which is not in an image plane. An example for that situation can be found in the article on field lenses, where we vignetting in an optical telescope is explained. In cases with vignetting, one may define different values for the field of view – for example, the field without any vignetting, the field up to the point of half-vignetting or (is the very maximum) up to the point where the intensity vanishes.

FOV to focal length

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The field of view of a photo camera depends on both the used photographic objective and the size of the photographic film or the image sensor. This is explained in Figure 1, which shows the optical configuration is a greatly simplified way: the objective is represented by a single lens, although it is usually a system containing multiple lenses. One can simply consider rays coming from object points and going through the center of the lens, where no ray deflection occurs.

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Field of view

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The field of view of a telescope or a photo camera, for example, is usually understood as the range of angular directions in which objects can be observed for a fixed orientation of the instrument. (One may of course observe a wider range by combining images from different instrument orientations.) It can be quantified in different ways:

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The field of view of the human eye is also not precisely defined. Maximum image resolution is only achieved in the central area, and the peripheral regions exhibit a substantially lower image quality. This is largely compensated by rapid eye movements for covering a wider angular range and accurately viewing objects of particular interest.

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The field of view of the eye may be restricted by various kinds of devices, for example by correction glasses of small size or by magnifying glasses. In some cases, the peripheral view is completely blocked, e.g. with some laser safety glasses; that can introduce additional hazards, e.g. of bumping into items which could not be seen.

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The field of view gets particularly small when using a tele-objective, while wide field objectives are by definition made for a large field of view. Extreme versions are called fish-eye objectives; they produce substantial image distortions, which are hardly avoidable in that regime.

Telescopes provide some magnification for viewing distant objects. The higher the magnification, the smaller is typically the field of view. However, there are optical designs which provide a larger field of view for given magnification. For example, a simple Keplerian telescope has a small field of view, which can be expanded by inserting an additional field lens.

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FOV to focal length calculator

Standard photographic objectives are made such that their field of view is similar to that of the human eye – with a full horizontal angle around 50°, when considering the range with reasonable sharp imaging.

For small angles, the full-angle field of view in radians is approximately the sensor diameter divided by the focal length; for obtaining a value in degrees, one has to multiply that with <$180\textdegree / \pi$>. For wide angle cameras, one has to use a more accurate formula:

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The term field of view is not only used for that field itself, but also for its magnitude. In some cases, for example for telecentric lenses, it is used for the viewed area on the object plane.

As mentioned above, the field of view of an instrument is often intentionally limited. This is often not motivated by its application, but rather because the image quality would be too much degraded by optical aberrations when permitting a larger field of view. Advanced optical designs, e.g. based on aspheric lenses or more refined combinations of lenses, can offer a wider field of view with good image quality. However, they are not always employed, e.g. for reasons of higher cost, size or weight of the instruments.

In some cases, the term angle of acceptance is used instead of field of view – particularly for non-imaging optical instruments.

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