# An Easy Technique for Focus Characterization and Optimization of XUV and Soft X-ray Pulses
## 1 Introduction  
For a high spatial resolution on the micrometer scale [1, 2], as well as nonlinear interactions between XUV/soft-X-ray pulses and matter [3], which are a necessary prerequisite for, e.g., XUV pump-XUV probe experiments, a small and well characterized focus is of crucial importance [4]. Furthermore, a high-energy throughput of the focusing system is essential in order to transfer the energy of the XUV source onto the experimental target. For a bandwidth of a few electron volts, a small focus can be achieved via the use of multilayer-coated spherical mirrors in normal incidence geometry. However, for a broad bandwidth, those multilayer mirrors have low overall reflectivity [5, 6, 7]. Therefore, a high energy throughput is typically achieved via the use of grazing incidence focusing optics [8, 9]. The ideal mirror shape to image a source onto a focus spot is given by an ellipsoidal mirror, but those mirrors are very difficult to produce with high surface quality [10, 11]. Therefore, combinations of multiple mirrors that are easier to produce, such as toroidal mirrors, are often used in a geometry that reduces the aberrations [4, 9, 12]. Grazing incidence optics are very difficult to align, due to their high asymmetry and the fact that small misalignments cause large aberrations [13]. However, if aligned well, those mirrors can deliver focus sizes on the single micrometer scale with a high-energy throughput throughout the entire XUV and deep into the soft-X-ray spectral region. To enable an efficient optimization of the mirror alignment, a fast and well-resolved measurement of the XUV/soft X-ray focus is crucial. Therefore, many different methods are nowadays used to accomplish this goal. One way to characterize an XUV/soft X-ray focus is sending it into a gas medium and measuring the distribution of the generated ions. Ion-based characterization methodsprovide a very high resolution down below 1 \(\upmu\)m [14]. However, they typically measure the projection of the XUV focus along a direction normal to the propagation direction [15; 16]. Due to the fact that aberrations of XUV beams often do not fulfill circular symmetry, the information that is lost due to the projection makes the optimization of the focus difficult. Aberrations within the projection direction cannot be seen, which can easily lead to a false characterization and optimization of the focus. Furthermore, typical ion detectors need high or ultrahigh vacuum as well as high voltages, which make them expensive and cumbersome to use. In addition, the number of ions that are generated per laser pulse is limited by space charge effects. This means that the ion signal has to be averaged over many XUV pulses to achieve a good signal-to-noise ratio. This fundamentally hampers single-shot focus measurements. Another common technique for the measurement of the size of a focus is the knife-edge technique. Here, the energy after the focus is determined, while a well-defined straight beam block (referred to as knife-edge) is moved through the focus with very high precision. This method provides very high resolution, well below the micrometer scale [17; 18], and it only needs a precise linear stage and an XUV detector, e.g., an XUV photodiode or an XUV charge-coupled device (CCD) camera. However, a measurement with the knife-edge technique only provides information about the projection of the focus. Furthermore, a scan of the position of the knife-edge is needed to obtain these data, and therefore, single-shot measurements are not possible. It cannot be used to measure the shot-to-shot fluctuations of the focus, and a large pointing fluctuation falsifies the spot size measurement. The measurement of the focus of an XUV/X-ray beam can also be realized with the use of a scintillator [19; 20; 21; 22]. This scintillator generates florescence wherever it is hit by the XUV photons.