"A proposed space telescope would focus light primarily with a patterned sheet of metal rather than a large mirror or lens. The telescope would have amazingly sharp vision and could spot Earth-size planets around other stars, its backers say. The technique takes advantage of the wave nature of light, which causes light to bend around an object's edge. The same phenomenon, called diffraction, is the reason you can hear sounds coming from around the corner of a building. This means that light can be focused into an image simply by passing it through a certain pattern of holes carved in an opaque sheet. Such patterned sheets have long been used for focusing laser beams, but have so far not been used for astronomy. They are called Fresnel zone plates, after the French physicist Augustin-Jean Fresnel, who studied diffraction in the 1800s.
But a team led by Laurent Koechlin of the Observatoire Midi Pyrénées in Toulouse, France, says a powerful "Fresnel imager" could be made by launching a piece of metal foil, cut with the Fresnel pattern and attached to a solid frame, into space. A spacecraft equipped with a camera and other scientific instruments would sit at the focal point some distance away and record the observations.
Because it relies on a foil sheet rather than a massive mirror, it could be much more lightweight, and therefore less expensive to launch, than a traditional telescope.

Sadly a 3 1/2 meter demo was NOT selected as a 2015-2025 Top 10 mission finalist by ESA. Bummer.

Were I Paul Allen, I'd sponsor some form of terrestrial planet finder scop ahead of radio SETI.