Distortion correction does not alter the focal length.
Yes, that's correct.
However, distortion
does alter the focal length. T...
No. Toothwalk is right that focal length is not affected.
You are using focal length as a proxy for (observed) angle of view, the observed angle of view is affected. But focal length is an optical property that is not affected by and corrections.
I agree that focal length is defined on the optical axis and this doesn't change.
However, if you look at the image at a point off the axis, it more closely matches the image you would get from a different focal length lens (without distortion). That was what I meant. The usual meaning of focal length is defined at the centre of the image only.
Corrections technically change field of view, not focal length, but....
On most of Canon's PowerShot cameras, raw capture is only available thanks to
CHDK . Thus, Canon never expected anyone would know about the "corrections" applied in their JPEGs. However, CHDK raws reveal that most of the PowerShots have zoom lenses that are roughly as marked on the long end, but are of much shorter focal length on the wide end. Why? Well, they heavily vignette and distort, so their field of view needs to be cropped to get an evenly-lit rectangle of the right proportions. The typical difference is roughly equivalent to calling a 24mm lens 28mm, and the camera silently upscales the cropped raw to a JPEG with the full marketing-claimed pixel count for the camera.
I.e., Canon quotes the effective focal length, computed from the delivered angle of view in JPEGs. I very much doubt other manufacturers do much different.
CHDK exposes the fact that Canon's cameras commonly report bogus values for many metrics. For example, the user ISO settings are deliberately not mapped into the correct internal APEX96 values for computing exposure: the high ISO numbers are commonly off by nearly a full stop.
In CHDK, this is known as "market" vs. "real" values for exposure parameters. My point isn't that Canon's being bad or somesuch, but that it is actually the industry norm to lie about these sorts of things either to look better for marketing purposes or to improve user intuition about things (e.g., half of 1/8s shutter speed is NOT 1/15s, but 1/16s, except at some point people apparently thought those oddly-rounded numbers more intuitive).