Fig. 1: Experimental setup and operation scheme of the laser-plasma amplifier with diagnostics.

a A series of infrared pump beams (see Methods) creates a plasma waveguide, excites nickel-like Kr⁸⁺ and creates population inversion of the 3d⁹4d state, forming a laser-plasma amplifier. Here, only dipole-allowed transitions involved in the amplification process are shown (level scheme inset³³). The HHG seed at a 32.8 nm wavelength is coupled into the plasma channel and is amplified by stimulated emission (4d–4p transition in Kr⁸⁺). b Schematic setup of the experiment. c The emitted radiation is refocused using multilayer mirrors onto the sample consisting of a regular hole pattern (C depicts an SEM image). Ptychography is performed using a spiral scan pattern (indicated in yellow) with a CCD recording a coherent diffraction pattern at each scan point. The relation between the scan map and probe size is marked with a red circle. d The recorded diffraction patterns using ptychography can be reconstructed to retrieve the coherent complex-valued illumination function (probe) (d depicts the amplitude of the reconstructed illumination function)