Extended hemispherical lens

The extended hemispherical lens is a commonly used lens for millimeter-wave electromagnetic radiation. Such lenses are typically fabricated from dielectric materials such as Teflon or silicon. The geometry consists of a hemisphere of radius $R$ on a cylinder of length $L$, with the same radius.

Scanning performance
When a feed element is placed a distance $d$ off the central axis, then the main beam will be steered an angle $γ$ off-axis. The relation between $d$ and $γ$ can be determined from geometrical optics:
 * $$ \frac{d}{L} = \tan \gamma. $$

This relation is used when designing focal plane arrays to be used with the extended hemispherical lens.