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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.

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  • $\begingroup$ Isn't the fisheye lens doing the actual heavy lifting here? $\endgroup$ – probably_someone Nov 26 '18 at 14:36
  • $\begingroup$ 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. $\endgroup$ – Maury Markowitz Nov 26 '18 at 14:37
  • $\begingroup$ 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. $\endgroup$ – probably_someone Nov 26 '18 at 14:43
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The cameras you linked might some sort of custom lens, but a widely available variety is called a "ball lens" (a version for photographers evidently goes under the brand name "lensball"). They are just spheres of glass/optical-material.

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.

That said, you asked for ray tracing, which is probably what you need to understand non-paraxial optics (for example, rays coming from `extreme angles' will be imaged onto a sphere. I found a ball lens in this neat ray-tracer, and I don't know about 180deg field-of-view, but I can at least put an ideal lens behind the ball lens (with a lot of point-source "stars") and see what the image looks like.

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  • $\begingroup$ Actually, on second thought I'm not sure a ball lens can get you the type of image you posted. I will have to give it more thought. You could get a very large field of view by taking a picture of a "ball-mirror" (image coating a ball-lens in metal), albeit with small dark area looking straight back at the camera. $\endgroup$ – Green Apples Nov 26 '18 at 16:36

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