How Big Is That Fish Eye, Really?

I only recently started to understand the specs for fisheye lenses.

I’m big on fisheyes – especially for glass-and-steel city scenes.

But the 8mm fisheye I used for that photo is big and heavy. Recently I picked up a vastly smaller lens, the Pergear 10mm/F8 (it’s great). The coverage of the 10mm was somewhat less than that of the 8mm, as I expected. But not, as it turns out, for the reason I thought.

Some time later I decided to get a full-frame fisheye to use with my Nikon Z6. I chose the TTArtisan 11mm F2.8, a nice lens, more compact than the 8mm Rokinon despite being full frame. And here’s where I got confused. I’d just assumed the field of view was directly related to the focal length, like any other lens; so allowing for the 1.5x sensor size factor, I thought an 11mm FF lens would take in more than an 8mm APS-C. In fact, it took in a bit less.

Here’s the deal: a fisheye lens also has a field-of-view specification, in degrees, but I’d never paid attention to it. And that specification is the one that matters. The stated focal length only applies to the center of the lens; away from there, the image is increasingly distorted as the lens departs from that focal length. It’s that distortion that makes the lens a fisheye and allows it to take in something like a 180 degree field of view. So actually, who cares about the focal length of a fisheye? It just defines the perspective of a small area the very center of the photo.

Here are images from each of these 3 lenses, taken from the same spot, annotated with focal length, sensor size and field-of-view:

The difference is easiest to see at the top – the image from the 10mm lens with the 150 degree angle doesn’t include the distorted arc of the highest beam. But the 11mm FF and 8mm APS-C lenses take just about the same picture (the differences are mostly due to hand-held shooting).

Sure, it’s obvious when you think about it. I just hadn’t.