# Is lens focal length specified considering the effect of barrel distortion on field of view?

Given a Nikon 14mm f/2.8D ED AF Ultra Wide-Angle Nikkor Lens on a full-frame sensor, in theory the field of view is HFOV: 104° x VFOV: 81°. However this lens exhibits noticeable barrel distortion increasing with the distance from the image center.

Is the lens distortion used to achieve the FOV of a perfectly rectilinear 14mm lens, meaning that the real focal length is slightly longer (i.e ~16mm Lens + Barrel Distortion = 14mm rectilinear lens) or distortion is not accounted in the computation and in practice the actual FOV is bigger then HFOV: 104° x VFOV: 81° (i.e 14mm Lens + Barrel Distortion = 12mm rectilinear lens)?

Surprisingly many websites and research papers on the topic explain lens distortion as either purposely built on fish-eye lenses or to be found only in cheap lenses due to construction errors such as misalignment. I don't think Nikon 14mm f/2.8D ED AF Ultra Wide-Angle Nikkor belongs to either of those groups.

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Except in the case of fisheye lenses barrel distortion is an unwanted side effect of wide angle lenses, something lens designers work hard to minimise. Typically the more expensive a lens the lesser the degree of barrel distortion but it's always there, even in small amounts.

There's two important things to bear in mind with regards to focal length as stated in the specification of a lens (e.g. Nikon 14mm-24mm f/2.8). Firstly manufacturers round the figure, generally in their favour, so the actual focal length might be more like 14.8mm, secondly the focal length is measured with the lens focused to infinity, and almost certainly by shining a light through the centre of the lens.

This means you can't use the quoted figure to calculate the exact field of view. It also means you can't say ~16mm Lens + Barrel Distortion = 14mm rectilinear lens. To get technical a lens with barrel distortion doesn't have a single focal length, the focal length will vary across the frame.

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Do you think the actual field of view is bigger due to lens distortion, or it's the same as the one stated in the specs? – memecs Feb 1 '13 at 10:07
It really depends on a lens and manufacturer. In some cases it's greater, it's some cases it's not. Besides, as told - it doesn't matter much in the end as you don't know true focal length of the lens at your focusing distance. – MarcinWolny Feb 1 '13 at 10:11

The “focal length” of a lens is a linear-optics notion, thus defined respective to a small bundle of rays that travels close to the optical axis. Then, a lens with barrel distortion will image small objects at the center of the field with the expected magnification, but the whole field of view will be larger than expected from the atan() formula.

However, if you want to draw conclusions about the FoV you can expect from a given lens, you need the proper specification of it's focal length. The number written on the barrel, as Matt Grum pointed out, is an unreliable approximation. You have to find the patent of the lens if you want the accurate focal length.

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The focal length isn't measured by examining the field of view; it's an optical property of the lens. For real-world camera lenses, it's measured from the center of a theoretical equivalent single-element lens (see this earlier question). So... no, barrel distortion is not taken into account.

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