[en] There is continued interest in developing a diffraction-limited soft or hard x-ray source. Candidate paths include the storage-ring-based free-electron laser (FEL) and the linac-based self-amplified spontaneous emission (SASE) FEL for the two regimes, respectively. As previously discussed, target beam parameters are σ_x,y ∼ 10 microm, σ_x',y' = 1 microrad, and σ_t ∼ 1 ps (0.1 ps for the linac case). The authors report the use of few- to sub-angstrom radiation emitted by a 7-GeV beam transmitting a 198-period diagnostics undulator and a bending magnet to characterize the particle beam. A particle beam divergence as low as σ_y' = 3.3 microrad was measured using an x-ray monochromator. Additionally, a particle beam size of σ_y < 45 microm and a bunch length of σ_t = 28 ps with 4-ps resolution were measured using an x-ray pinhole camera with a unique synchroscan and dual-sweep x-ray streak camera as the detector. The adjustable pinhole aperture was varied by more than a factor of 100 to assess spatial resolution and dynamic range issues in the system. These diagnostics demonstrations should scale to next-generation applications