Is Zoom Factor Based On Focal Length Or AOV Ratios?

Inspired by Rein Raud's question in chat.

I remember having this same question a while back and deciding it was focal length.

One reason would be that, technically the stated AOV is dependent on the imager size, where as focal length makes no such assumptions.

So with this standard Fuji vari focal lens, with a stated zoom of 2.7x, we get 2.72x by using the focal length, then deciding which imager size we use we get 2.58x and 2.61x, for the 1/3" and 1/4" normal aspect ratio formats, respectively.

I have not done an exhaustive analysis by any means, and do welcome any counter-examples or corrections!

I don't think AOV is a reliable enough metric - different sensor sizes aside, it will also vary with the backfocus distance. Many (most?) C/CS-mount cameras have adjustable backfocus, so even that being different from one camera to another would affect "zoom factor". Different manufacturing tolerances from one manufacturer to the next may even mean the AOV on one 1/3" camera isn't the same as on someone else's 1/3"camera.

In IP cameras as well, software cropping for different resolutions could affect AOV measurements - the 3MP Dahua cameras we use are not only a "shorter" VAOV crop, but also a wider HAOV when set to 1080p vs. 3MP.

Zoom factor or range has traditionally been a metric of the lens itself - this applies to photographic and video cameras as well as CCTV. For that matter, most PTZs specifically list their zoom ratio in reference to the focal range as well.