You can't catch X-rays from stars with an ordinary mirror: they pass through glass like light through a window pane. To reflect them, you need a mirror almost parallel to the beam: then the X-rays skim along the surface like a flat stone skipping on water, only slightly changing direction.
Japanese engineers grew such a mirror from nickel using electroforming — depositing metal onto a precise mold, like ice building up on a pipe in freezing weather. The result was a seamless bowl 60 mm in diameter. They sent it to the kilometer-long beamline at SPring-8, where the X-ray beam was spread into a wide parallel stream, like light from a distant star.
The center of the spot was even sharper: 0.7 arcseconds. For comparison, a human hair seen from 100 meters subtends an angle of about 1 arcsecond. This sharpness held even after assembling the mirror into a multi-layer module.
The mirror has already flown to space on the FOXSI-4 rocket, catching hard X-ray emission from solar flares. Now such mirrors are promised for CubeSats — satellites the size of a shoebox. Then a small spacecraft could see the Sun in X-rays as clearly as large observatories.
An X-ray mirror reflects rays only at very small angles — less than one degree. That's why it's shaped like a narrow cone, not a bowl like a reflecting telescope.
In the movie Interstellar, the heroes fly through a wormhole where X-rays distort space. Such mirrors could help us see accretion disks around black holes.