# Field of view

The image space and the field of view of a camera in the vertical dimension
The image space and the field of view of a camera in three-dimensional representation

Field of view ( english field of view , FOV ) is the area in the field of view of an optical device, a solar sensor , the scene of a camera (film or image sensor) or a review of displays , can be perceived within which events or changes and recorded.

In the case of a camera with a fixed focal length f of the lens, the focus is on an object in the object distance g by adjusting the extension, i.e. H. the distance between the lens and the image surface (image sensor), to the associated image distance b = b (g) = fg / (g - f) . However, due to the camera dimensions, there is a lower limit b min and an upper limit b max for the image distance b . The minimum image width b min is set to the focal length f and is used to take pictures of distant subjects. The maximum image distance b max corresponds to the minimum object distance (minimum object distance) g min :

${\ displaystyle g _ {\ mathrm {min}} = g (b _ {\ mathrm {max}}) = {\ frac {fb _ {\ mathrm {max}}} {b _ {\ mathrm {max}} -f}} }$.

Varies the lens image area space b in its maximum possible interval ( fbb max ), so the combination of the rectangular image areas provides the cuboid image space . In the case of optical imaging, the so-called field of view of the camera corresponds to this image space bijectively. The field of view is the area in the three-dimensional object space (object space, subject space) that can be sharply imaged with the camera. It is an infinite truncated pyramid, the pyramid tip of which lies in the object-side focal point F and in which the pyramid tip is cut off by the plane g = g min which is parallel to the lens plane .

The opening angles of this pyramid are referred to in photography as the angle of view of the camera. At a vertical height sensor S v and a horizontal sensor width S h the trigonometric calculation gives the vertical angle α v and the horizontal viewing angle α h to

${\ displaystyle \ alpha _ {v} = 2 \, \ arctan {\ frac {S_ {v}} {2f}}}$,
${\ displaystyle \ alpha _ {h} = 2 \, \ arctan {\ frac {S_ {h}} {2f}}}$.