first off, ionizing radiation is blocked by our planet's atmosphere, which is for the best. to measure high energy photons like X-rays and gamma rays coming from astronomical objects, you need a satellite. but there's one problem.
they punch through mirrors.
low-energy or "soft" x-rays can be reflected with some effort. like skipping stones from the surface of a lake, you have to ensure they hit the surface of the mirror at low angles. that's done with grazing mirrors, which are cylinders built to focus x-rays. they have a much lower surface area than a normal bowl-shaped mirror, so you have to nest them into layers. the more layers you have the more light you gather, but it's impossible to keep that many mirrors well aligned, so the resolution drops as well. the Chandra X-ray telescopes has probably the best resolution out there because it only has 4 mirrors, but it's much worse at detecting dim sources. Then there's instruments like the XRISM, which has 203 mirrors
when you get into higher energies you just have to be content with the fact that you can't build a mirror. you can make something akin to a geiger counter and deal with only getting a single pixel image, or you can do some wild shit like Fermi LAT which uses a particle collider style instrument to track the travel paths of high energy particles.
then there's coded aperture masks. you make some patterned plate that you put on top of a detector, and the plate casts a shadow in the image that you can use to figure out where the light comes from. to be specific, you deconvolve the raw data with the shape of the plate, so how you arrange the holes does affect how noisy the final image comes out. turns out you have to make some pretty intricate masks!
finally, there's something you can do on earth! really high energy gamma rays create tiny bursts of light when they enter the atmosphere called Cherenkov radiation, and you can measure these with purpose-built regular telescopes.
