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For my knoledge, the radome design is an art rather than a tecnique. Only few factories around the world know it.
There are almost 2 starting considerations:
1) The radome should protect the antenna from external weather regardless the attenuation and beam distorsion. Rugged construction is looked for. Mechanical resistance is the primary keyword (aircraft, missile etc.).
2) The radome protect the antenna but it's loss is negligeable and it's isotropic (radio astronomy and deep space communications).
For 2) look for Gore-Tex (Microwave division) data sheets and application bulletins.
Generally speaking lower is the dielectric constant, lower is the attenuation and the reflection but also the mechanical resistence is lower. Pure PE (Polietylene) and pure PTFE ( "Teflon") are used.
Gore-Tex has dielectric constant lower than PTFE and, due too the wowen nature, is weather resistent enough. Gore-Tex (or other air mixed PTFE) is probably the best material but also the most expensive.
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