Study of chromatic aberrations in x-ray crystal imagers for plasma diagnostics

Abstract

We investigate chromatic aberrations in x-ray crystal imagers. For on-axis point-to-point imaging, second-order astigmatism can be eliminated by the optimal choice of meridional and sagittal radii, but higher-order aberrations generally remain. In crystals and other diffractive reflectors these aberrations are termed chromatic because they couple to the spectral distribution of the reflected x-rays limited by the extent of the Bragg angles sampled across the reflector aperture. The aberrations can be suppressed by using an ellipsoid of revolution as the reflector shape, without reducing the reflector size, thereby improving imaging point spread function (PSF) [S. Stoupin, and D. Sagan, Rev. Sci. Instrum., 97, 053508 (2026)]. High-resolution imaging with ellipsoidal crystals becomes especially advantageous in close-to-backscattering geometries, where second-order aberrations from off-axis source points do not significantly limit the usable field of view. Here we present ray-tracing simulations of the PSFs for a representative close-to-backscattering geometry using the optimized toroidal and the equivalent ellipsoidal crystal reflectors. The PSFs were evaluated using a 1×1µm² Gaussian source positioned at the nominal center and at off-center locations. For on-axis point-to-point imaging using the toroid the maximum spread of rays in the detector plane as a function of the reflector’s aperture agrees with analytical aberration expressions for a specular reflector. By contrast, the ellipsoid produces a Gaussian image with no observable aberrations in agreement with theory. The differences between the simulated PSFs are discussed.