Findclouds Manual 35
3 Appendix
3.1 Geometry of fisheye projection
This text takes attention to a fisheye lens, which maps a hemispherical view field conformal to an
image plane and produces a circular image. The radius of the image relates to the opening angle
(zenith angle). The following image shows the path of rays inside of a fisheye lens.
For an ideal fisheye lens the image radius relates linear to the view angle and the whole field of
view will be mapped to concentric circles. A real fisheye lens will produce some distortions,
especially for larger angles. There will be aberrations from linear ratio of view angle and image
radius. But for the moment we assume a linear, not distorted mapping.
A cloud cover can be seen like a two dimensional plane at a specific height in the sky, but when
using a fisheye lens for cloud monitoring, it maps a hemispherical view field to the image and not
the original plane.
The first part of the chart shows that for mapping of a plane in constant height h to an angular
dependent fisheye lens image, the distance d depends on the tangent of viewing angle. For zenith
