field of view

Field of view is how wide an angle of the world the camera sees through its lens — the angular size of the cone the image captures. A wide field of view (a wide-angle or fisheye lens) takes in a panoramic sweep but renders each object small; a narrow field of view (a telephoto lens) sees only a thin slice but magnifies it. It is the angular counterpart of focal length: they describe the same thing from two directions.

Precisely, field of view depends on both the focal length and the sensor size, through FOV = 2 arctan(d / (2 f)), where d is the relevant sensor dimension (width, height, or diagonal — so a camera has a horizontal, vertical and diagonal FOV) and f is the focal length in the same units. Equivalently in pixels, horizontal FOV = 2 arctan(image_width_pixels / (2 fx)). The inverse-tangent makes the relationship nonlinear: at long focal lengths small changes in f swing the angle a lot, while at very short focal lengths the angle saturates toward 180 degrees.

Field of view is the practical knob that decides what fits in frame and how distortion behaves. Wide fields of view stretch and curve the periphery and amplify perspective (near things loom huge), which is why fisheye and 360-degree cameras need special projection models beyond the simple pinhole. In computer vision, knowing the FOV is equivalent to knowing the focal length in pixels, so it is a convenient human-readable handle for the same intrinsic information used by SLAM, stereo and 3D reconstruction.