How do I convert an equisolid fisheye field-of-view radius into pixels for cropping?

Question

I’m using an 8mm equisolid (equal-area) fisheye lens with a 180° field of view. I want to crop the image to a circular area defined by an angle from the lens axis/zenith (the center of the fisheye image).

For an equisolid fisheye, I believe the image radius on the sensor is:

R = 2f sin(θ/2)

where θ is the angle in radians from the center axis, f is the focal length, and R is the image radius on the sensor in mm.

How do I convert that sensor-plane radius into a radius or diameter in pixels so I can crop the image correctly?

user11924 · Accepted Answer

You're almost there. You just need to know the pixel pitch of your imaging sensor (that's usually in µm). If you can't find the sensor's pixel pitch, then you can calculate it by dividing the sensor's width (or height) by the total number of the sensor's horizontal (or vertical) pixels.

If you don't know the sensor's exact size, but you do know its format (i.e., 1/2.3" as an example), be aware that sensor sizes in terms of fractions of an inch are nomenclature, not dimensional. You can find dimensions for all sorts of sensor sizes at Wikipedia.

So given your image-plane measurement \$R\$ (in mm), then conversion to pixels is simply

$$ ext{Pixels} = {R\,\mathrm{[mm]} imes {1\over\mathrm{pixel\,pitch\,}\left[{\mathrm{\mu m}\over\mathrm{px}} ight]}} imes{1000\,\left[{\mathrm{\mu m}\over\mathrm{mm}} ight]}$$

How do I convert an equisolid fisheye field-of-view radius into pixels for cropping?

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