## 2 Materials and Methods  
### The Experimental Setup  
Our XUV CDI experimental setup, designed and developed at the Institute of Plasma Physics and Lasers (IPPL) [36], consists of four stages, depicted with letters A, B, C, and D as presented in Figure 1. The first stage, A, is the semi-infinite static cell filled with the gas target at pressures in the order of tens of mbar. The IR laser pulses have a central wavelength of 807 nm and are delivered by the Ti:Sa laser system (Amplitude Technologies) to the first stage of the setup with an energy of 1 mJ and a minimum pulse duration of 26 fs. The laser beam is focused by an \(f=38\) cm lens at the neighborhood of the exit of the semi-infinite cell, which ends in a 100 \(\upmu\)m thin copper foil attached to a 1.5\" aluminum tube. The foil is drilled by the laser beam, creating an exit pinhole of 50 to 100 \(\upmu\)m in diameter. The intense laser fields interact with the gas atoms, resulting in the generation of an XUV comb of higher-order harmonics that propagates along with the laser beam through the drilled pinhole to the second and third stages of the setup. The location of the laser beam focus in the neighborhood of the drilled pinhole area can be varied, by moving the lens micrometrically along the laser propagation axis. Moreover, the semi-infinite gas cell is equipped with a tube manifold for evacuating and filling it with a variety of gases, or even a mixture of gases if necessary, at accurately measured pressures during the experiment. Thus, the generated XUV radiation can be controlled and optimized with respect to the gas species and pressure, as well as to the location of the laser focus. In addition, the plasma formation inside the semi-infinite gas cell can be imaged by a CCD camera along with the corresponding XUV spectral images described below. This option is a powerful tool towards both the interpretation of the corresponding XUV spectral images characteristics, as well as the optimization of the coherent XUV generation at the predetermined wavelengths. The second stage, B, is a differentially pumped chamber, which separates the high-pressure first stage from the third and fourth low-pressure stages. The entry aperture is the laser drilled pinhole at the exit of the semi-infinite cell, the small size of which minimizes the gas throughput. The exit aperture has a diameter of 3 mm, which is wide enough to allow the propagation of the XUV radiation, but simultaneously blocks a large part of the more divergent IR laser beam. Stage B is pumped by a 150 L/s turbomolecular pump reaching pressure values of \(\sim\)10\({}^{-4}\) mbar in gas cell operation conditions. The third stage, C, is a 70 cm in diameter chamber that is pumped by a 350 L/s turbomolecular pump, thus reaching a background pressure of \(1\times 10^{-6}\) mbar or of \(\sim\)10\({}^{-5}\) mbar in gas cell operation. The chamber hosts all the necessary optical and optomechanical components for the automated optimization, filtering, and selection of the XUV wavelengths and propagation of the resulting XUV beam to the target area at the fourth stage. First, the mixed XUV and IR beam, upon entering the chamber, is filtered from the IR laser residual beam using a 400 nm-thick Al filter, while at the same time, the XUV radiation spectrum of interest (i.e., 30 nm to 50 nm) suffers only an overall reduction in intensity. The Al filter is mounted on a linear rod equipped with a vacuum-compatible motor that is externally controlled. Thus, the Al filter can be inserted in the XUV beam path at will. Figure 1: The XUV CDI experimental setup shown in a CAD design (**top**) and in the IPPL laboratory with zoom pictures for the stages of A, C, and D (**middle** and **bottom**). A: The first stage hosting the semi-infinite gas cell. B: The second stage hosting the differentially pumped region. C: The third stage hosting the XUV filtering, diagnostics, and wavelength selection. D: The fourth stage hosting the target and the recording of the CDI result. L: lens. AL-F: aluminum filter.