Confused/Curious - Fisheyes

I have the Rokinon 8mm FE, and love it, so this is more of a question about AOV/FOV between different fisheye lenses.

The Rokinon gives an AOV on crop of 180° - according to their specs
The Canon 15mm FE also gives an AOV of 180°- according to Canon's specs
Then there's others, like the Sigma 10mm, the Nikon 10.5mm, The Sigma 4.5mm, Minolta 16mm - all which are reported to give a 180° AOV/FOV

How does that work? It's my understanding that an XXmm lens, lives and XX° AOV, and that an XX° AOV is achieved with an XXmm Lens. Yet, here are various focal lengths from 4.5mm to 16mm that all give a 180° AOV.


I'm sure it have to do with the 'fisheye' effect, but I can't understand the how/why of it. Anyone have an understanding and can relay that in layman's terms?

I believe the 180 degree figure is the diagonal FOV. The horizontal/vertical FOV probably varies with focal length??

I stand to be corrected...

Your belief that xxmm gives xx AOV is for rectilinear lenses...ie, lens that are distortion corrected (in laymans terms)

Bob

1. Rokinon 8mm FE works on a APS-C sensors(crop) and Canon 15mm designed for Fullframe. Rokinon will give a small round image on a full frame.
When using lens on crop, FL works as it's mutipiled by 1.6. So 8mm is about 13mm.

2. There are diagonal fiseye and forgot the word.. not diagonal. Difference is how people measure that 180 degrees. Horisontaly or diagonal. DIfference is that with diagonal fisheye you'll get a non-blacked image(no black corners) and with another one you'll have a round image in your frame.

UPD: It's named Circular fisheye!
Circular makes circle on a frame. Like this: Sigma 8mm on a full frame http://www.juzaphoto.c​om …fish_fullframe/​8-full.jpg
And diagonal like this:Sigma 15mm on a full frame http://www.juzaphoto.c​om …ish_fullframe/1​5-full.jpg
In 1st photo it's 180 degree vertically(short side), on 15mm it's 180 degree diagonally.

Canon 8-15mm fisheye combines both.
So for Full frame you need 8 or 15mm. Divide it by 1.6 for a crop cameras.