# Flat Field Soft X-ray Spectrometry with Reflection Zone Plates on a Curved Substrate
## 6 Discussion  
A classical VLS grating on a plane substrate can also cover such an energy range with good resolution and theoretical diffraction efficiency in the order of 10% [10]. However, the conventional VLS design needs many motion degrees of freedom for the grating, as well as the detector, to maintain a competitive performance. Alternatively, the pattern of a reflection zone plate (RZP) can be inscribed into a curved grating blank, enabling elegant access to the wide range of 150-750 eV, with only two RZPs for adjacent energy bands; to cover the central interval from 200 eV to 550 eV, only one translation in the sagittal direction of the RZP is needed to switch between the channels. The energy range between 200 eV and 370 eV can be covered by RZP 1 without moving. Similarly, RZP 2 covers the interval of 350-550 eV, also without moving. Hence, all optical components are fixed.  
As it was already mentioned, the RZP on a plane substrate suffers from an extremely limited high-resolution energy range around the designed energy. To cover a larger range while a highly resolved spectrum is maintained, it is necessary to vary the input angle in proper steps. In this way, the spectrum is recorded sequentially part by part, at a high resolution. As an example, we considered the optical layout as shown in Figure 1a,b. The energy range, defined as the FWHM of the resolving power E/\(\Delta\)E around E\({}_{0}\) = 277 eV, amounted to 3.1 eV or 1.1%. This means that parts of the spectral band of 200-350 eV must have been recorded in the sequential mode with approximately 50 steps.  
Figure 10: Total quantum efficiency of the spectrometer, using RZP 1 and RZP 2 (Figure 6a).  
Figure 9: Boron metal spectra measured on RZP 1. The sample was naturally contaminated with a CO layer.  
The same spectrum, recorded with an RZP on a curved substrate, could be measured in one step. Hence, with the same photon counting statistics, the recording time for the same spectral range is 50 times shorter for the curved RZP compared to the planar RZP.  
Moreover, our instrument was a real flat field spectrometer, where the CCD sensor was placed in normal orientation to the beam. In other words, a full spectrum from 200 eV to 550 eV could be recorded \"in parallel\" with two exposures. Depending on the required spectral resolution, the energy range could be varied and extended to, e.g., 150-750 eV by an additional re-adjustment of the detector, optimizing the application of the spectrometer. The CCD, which was used in our laboratory, featured \(2048\times 512\) pixels of 13.5 \(\upmu\)m in size, so a meridional angular movement of the detector of \(0.46^{\circ}\) was needed to access the spectral region outside from 200 to 550 eV. Using more than 2 RZP channels, even 50-1000 eV may be reached. The energy range of parallel spectra registration with one fixed RZP depends mainly on the size of the CCD camera. For detectors with a pixel number \(>\)4000 (or better, \(>\)6000) in the dispersion direction, the energy range can be as large as 50-400 eV for RZP 1 and 350-1000 eV for RZP 2. Such an expensive detector is available from greateyes GmbH or ANDOR Technology Ltd. To avoid a high cost in our proof-of-principle experiment, we therefore managed with a \"synthesized detector aperture\" to simulate the large detector, as described in Section 5.  
In the present design, we chose an input distance of 838 mm. RZP 1 had an aperture of 6 mm (sagittal, S) \(\times\) 80 mm (meridional, M). RZP 2 had an aperture of 4 mm (S) \(\times\) 80 mm (M). With the input grazing angle of 2.59\({}^{\circ}\), the angular acceptance for RZP 1 amounted to 7.2 mrad (S) \(\times\) 4.3 mrad (M), and for RZP 2 to 4.8 mrad (S) \(\times\) 4.3 mrad (M). For further enhancement of the efficiency, each RZP had an optimal depth of profile etched into the same substrate. Based on these features, the overall quantum efficiency of the spectrometer in the range of 150-700 eV was well above 10%, and exceeded 20% at the designed energies of the RZPs, as it is shown in Figure 10.