# An Easy Technique for Focus Characterization and Optimization of XUV and Soft X-ray Pulses
## 3 Results and Discussion  
To minimize the effect of aberrations from the focusing mirror and achieve a small well-defined focus in the Zr window, the XUV beam diameter was reduced to \(\approx\)0.8 mm in the first test. The measured focus of this beam is shown in Figure 3. This illustrates that the CMOS camera is capable of measuring signals with \(\approx\)1 pixel in size and it does not show any unwanted effects such as blooming under these conditions. Although the iris clipped a significant part of the XUV beam, the signal-to-background ratio (ratio of maximum of signal to average of background) of a single-shot image was still 100, as is shown in Figure 3a-d. In this article, we used the signal-to-background ratio instead of the signal-to-noise ratio because the root mean square (RMS) noise was well below one count. The gain of the camera was set to 1.5\(\times\) amplification--full amplification scale of the CMOS camera: 1\(\times\)-16\(\times\). We estimated that 44 electrons give one count at an amplification of 1\(\times\), and one photon with the central energy in the Zr window (100 eV) makes 27 electrons. The FWHM beam sizes of the x and y projections were 1.9 \(\times\) 5.6 \(\upmu\)m, while the equivalent circle FWHM diameter was 3.6 \(\upmu\)m, which are resolution limited. We thereby defined the equivalent circle diameter as the diameter of a circle with the same area as the sum of the area of all pixels with more or equal 50% of the maximal intensity. Furthermore, we defined the energy content above half maximum as the energy in this region divided by the total energy. The energy content above the half maximum with closed iris was 25%. With a fully open iris and the full energy of the Zr window, the gain of the CMOS camera had to be reduced to 1.1\(\times\) amplification to avoid saturation with the XUV signal from a single laser pulse. Furthermore, the signal-to-background ratio increased to 150. Figure 4b shows the measured image of this XUV focus. The focus was slightly elongated in the downwards direction. We infer that this was caused by imperfections of the ellipsoidal focusing mirror, which produce aberrations in the XUV beam. Although the intensity of the signal from these aberrations was on average 10 times weaker than the main signal, it was still easily detectable. The FWHM beam sizes of the x and y projections were 7 \(\times\) 26 \(\upmu\)m, while the equivalent circle FWHM diameter was 3.6 \(\upmu\)m. This result also shows  
Figure 3: Focus of the XUV beam in the Zr window with closed iris (\(\approx\)0.8 mm). The resolution of the camera is only limited by its pixel size. (**a–d**) Four single-shot images. (**e**) Average of 300 single-shot images. The black lines indicate the horizontal and vertical projections of the 2D focal image with FWHM spot sizes of 1.9 \(\times\) 5.6 \(\upmu\)m. The equivalent circle FWHM diameter is 3.6 \(\upmu\)m.  
that the measurement of the projections is sometimes misleading, even if both projections are observed. The energy content above the half maximum was 11%. The high sensitivity of the CMOS camera allowed for the measurement of the XUV beam profile outside of the focus. Figure 4a,c shows two such beam profiles measured 1 mm in front of and 1 mm behind the focus. Due to the high signal-to-background ratio and the resolution of 1.85 \(\upmu\)m, very fine and weak structures can be identified in those images. The aberrations introduced by the ellipsoidal mirror generated up to two side peaks in the profiles close to the focus, which were relevant to the open iris. It should be mentioned that typical XUV sources based on HHG have \(\approx\)100 times less pulse energy than the attosecond beamline we were using for this experiment. This decreases the signal-to-background ratio for a single-shot acquisition, especially for measurements outside of the focal plane. However, the repetition rate of those sources is typically at least 100 times higher. Hence, an image with a good signal-to-background ratio can still be acquired within less than a second.