# Flat Field Soft X-ray Spectrometry with Reflection Zone Plates on a Curved Substrate
## 3 Test of the Experimental Arrangement  
In a transmission fs spectrometer, X-rays were emitted by a femtosecond source (HHG, XFEL, etc.) and focused by a toroidal or elliptical mirror onto a sample foil, which was additionally irradiated with a short infrared pulse in the so-called design of a \"pump-probe\" experiment. The X-ray transmission spectrum was subsequently analyzed by the spectrometer. For reasons of simplicity and high efficiency, the spectrometer had only one optical element: a focusing RZP array on a spherical substrate. Finally, the spectra were recorded on a charge-coupled device (CCD) detector. The analytical part of the spectrometer was tested in the IAP laboratory using a fluorescence calibration source. Below, the results of that spectrometer part test are reported. The optical layout of the absorption transmission spectrometer is shown in Figure 2. Only one optical element, a reflection zone plate on a spherical substrate, was used to obtain the emission spectrum of a sample target irradiated by a focused electron beam with an energy of 4.4 keV. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **RZP 1** & **RZP 2** \\ \hline Energy range & 150–370 eV & 350–750 eV \\ \hline Designed energy & 277 eV (C K\(\alpha\)) & 458.6 eV (Ti L\(\beta\), NIST) \\ \hline Designed distances & R\({}_{1}\) = 838 mm, R\({}_{2}\) = 2500 mm \\ \hline Grazing angles & \(\alpha\) = 2.59\({}^{\circ}\), \(\beta\) = 4.11\({}^{\circ}\) \\ \hline Grazing deviation angle & \(\theta\) = 6.7\({}^{\circ}\) \\ \hline Radius of spherical substrate & r = 28.617 m \\ \hline Coating & Ni \\ \hline Groove profile & laminar, 18.5 nm & laminar, 10 nm \\ \hline Meridional line density & 341.7–346.3–349.7 l/mm & 565.7–573.4–578.9 l/mm \\ \hline Optical aperture (mer,/sag.) & 80 mm/6 mm & 80 mm/4 mm \\ \hline Angular acceptance (mer,/sag.) & 4.3 mrad/7.2 mrad & 4.3 mrad/4.8 mrad \\ \hline \end{tabular}
\end{table} 
Table 1: Technical data of the two reflection zone plates (RZPs). See Figure 2 for the meaning of the geometrical parameters. Figure 1: (a) Schematic illustration of the first order diffraction from an RZP on a spherical substrate. (b) Energy resolving power E/\(\Delta\)E for RZPs on a planar (red) and curved (black) substrate. In this arrangement, we used an EBMA instrument from the company JEOL (model no. 6400) with an electron beam current of \(\sim\)10 \(\upmu\)A at an acceleration voltage of 4.4 kV, focused to a beam size of \(\sim\)10 \(\upmu\)m in diameter. The RZP substrate was mounted on a parallel robot (\"SmarPod\", SmarAct GmbH) with 6 degrees of freedom (Figure 3). The camera, a CCD detector with an aperture of 27.6 \(\times\) 6.9 mm\({}^{2}\) (2048 \(\times\) 512 pixels), was located 2500 mm away from the RZP substrate. The photon transport line was a KF40 vacuum tube, connected with the vacuum chamber that contained the SmarPod (Figure 4). The RZP aperture served as the input aperture for the spectrometer. No slit was placed in between the source and RZP position. The total optical aperture and angular acceptance are shown in Table 1.  
The parameters of the RZPs were chosen to cover the energy range between 200 eV and 550 eV at a high resolving power of E/\(\Delta\)E \(>\) 500 (RZP 1) and E/\(\Delta\)E \(>\) 1000 (RZP 2), without RZP rotation and detector translation (see Figure 5). With the central energies of 277 eV (RZP 1) and 459 eV (RZP 2), where the spectra were recorded with maximum resolution, the detector aperture with 2048 pixels covered overlapping energy ranges of 200-370 eV and 350-550 eV. To get an entire spectrum within  
Figure 3: Substrate (100 mm \(\times\) 30 mm) with two RZPs in its holder, mounted on the SmarPod in the vacuum chamber. Figure 2: Optical layout of the spectrometer. The spherical substrate (red rectangle) carried two RZPs in a parallel layout, and one of them was used to select the desired energy range. See Table 1 for a definition and specification of the design parameters.