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:
formula_1 
This relation is used when designing focal plane arrays to be used with the extended hemispherical lens. 
References.
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