Soft-X-ray nanobeams formed by aberration-reduced elliptical mirrors with large numerical aperture

X-ray focusing mirrors often employ the Kirkpatrick-Baez (KB) geometry, which sequentially crosses two elliptic-cylindrical mirrors in grazing-incidence configurations. However, KB mirrors do not satisfy the Abbe sine condition and thus potentially expand the focus size with severe coma aberration. Satisfying the Abbe sine condition complicates mirror shapes or increases the number of ultraprecision mirrors required. The present study shows that the focal length and mirror length of KB mirrors have to be shortened to simultaneously achieve a large numerical aperture and reduced aberration. Such ultracompact KB (ucKB) mirrors are examined using a simulation that combines ray tracing and wave propagation. The focus intensity distributions show that ucKB mirrors suppress the aberration produced by their rotation errors and that they robustly achieve diffraction-limited focusing. The simulation results are confirmed in a synchrotron radiation experiment. ucKB mirrors can be advantageous for soft-X-ray nanoprobes, which require focusing devices to achieve a large numerical aperture.