# Optics of an all-sky camera

I'm curious about the optics of an all sky camera like this one or this one. My suspicion is that the sensor has an inherently wide field of view - the former has a lens that's 1.55, which doesn't seem that enourmous on it's own. And does the dome contribute anything?

Does anyone know of a model of one of these for any of the popular online optical calculators? I wouldn't mind building one using the sensor I have, although I haven't measured it's FOV yet.

• Isn't the fisheye lens doing the actual heavy lifting here? – probably_someone Nov 26 '18 at 14:36
• I believe so, but consider that the f number of the lenses in question are about the same as the lowest setting on a typical camera zoom lens, there's more to it than just that. – Maury Markowitz Nov 26 '18 at 14:37
• I don't think f number and field of view are related across different types of lenses. There is probably a relation between the two for fisheye lenses and another relation for ordinary lenses, but they may not be directly comparable. – probably_someone Nov 26 '18 at 14:43

In paraxial optics a ball lens like two convex lenses connected by a planar sheet. It's focal length and f-number are given in this Edumund Optics application note: $$f\approx \frac{n D}{4(n-1)} \\ NA = \sin(\theta)=\frac{1}{\sqrt{1+4\left(\frac{nD}{4d(n-1)}\right)^2}}\\ f\# = f/d$$
where $$D$$ is the diameter of the sphere, $$d$$ is the "entrance pupil" (which will be $$D$$ unless light is clipped somewhere), and $$n$$ is the index of refraction of the lens (I have assumed you are using the lens in air). Thus the typical relation $$f\approx\frac{1}{2NA}$$ holds for $$f\#$$'s bigger than 1.