# Does "Field of view" include radial lens distortion?

When manufacturers state the "field of view" of a camera, is that including lens distortion or not? I work a lot with CCTV and dashcam footage which always has barrel distortion. For a given focal length and sensor size, you can calculate the theoretical field of view that a perfect lens, or a pinhole camera, would reveal. However, in reality, we see that light rays way outside the theoretical field of view get bent in towards the camera sensor and are visible in the final image, especially at image corners.

When manufacturers state FOVh and FOVv, does this ever include camera distortion? For example, do they simply look at the footage from the camera from a known position, figure out where the pixel on the left-middle edge of the frame is in 3D space, calculate FOVh from that, and then do the same with the upper-most middle pixel to get FOVv? I feel that I have seen some specs where that appeared to be the case.

Thank you!

Edit: As an example I wanted to include some specs from these dashcams.

Take the 750 series cameras. After a camera calibration using computer vision techniques, I find the theoretical field of view for the undistorted image to be:

FOVh = 85.4 deg, FOVv = 54.9 deg, and FOVd = 93.3 deg.

But, the listed specs are:

FOVh = 116 deg, FOVv = 61 deg, and FOVd = 139 deg.

The only way that these field of view specs make any sense is if they are for the distorted image. Is that correct? And therefore, you cannot calculate the focal length knowing sensor size from these FOV values.

• They certainly do include the distortion in the advertised field of view of fisheye lenses for interchangeable lens cameras. It's their main selling point, really. I'd imagine it's the same for CCTV and dashcam cameras, but can't say for sure. Nov 18, 2022 at 2:15

They can do whatever they want... there is no standard/requirement that I know of.

The sensor that camera uses records a 16:9 aspect which is 1.78. The aspect they report as being recorded is 1.9; so it must include some barrel distortion **along the horizontal median line. The aspect you determined is 1.5 and would also include distortion; this time pincushion distortion.

** assuming no significant distortion recorded on the vertical aspect of a 16:9 rectilinear image.

• Thanks. But how did you get your aspects? Isn't the aspect ratio w/h = tan(FOVh/2)/tan(FOVv/2)? I am getting 1.777... for my determined aspect and 2.7168 for the listed aspect. Nov 29, 2022 at 21:55

You said (emphasis mine):

For a given focal length and sensor size, you can calculate the theoretical field of view that a perfect lens, or a pinhole camera, would reveal. However, in reality, we see that light rays way outside the theoretical field of view get bent in towards the camera sensor and are visible in the final image, especially at image corners.

A "perfect lens" (if there is such a thing) is not necessarily modeled by the pinhole projection formula. Dashcams like the one you linked to typically have wide angle distortions in order to capture more of the scene. Similarly, many lenses specifically aren't pinhole projection, such as fisheye lenses.

Lens manufacturers typically report the angles that the lens can see, which includes the projection distortion.

And therefore, you cannot calculate the focal length knowing sensor size from these FOV values.

Well, if you know the projection model of the lens, then the projection function needs to be incorporated into the FoV calculations.