## 1 Introduction  
The recent upgrade of high-harmonic (HH) generation in gases towards repetition rates of 50-100 kHz (10-200 \(\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro \  
Spherical-grating monochromators (SGM) made up of a single optical element are widely adopted for third-generation synchrotron sources, achieving resolving powers greater than \(10^{4}\)[12; 13]. In the SGM configuration, the grating-to-exit-slit distance can be varied to achieve focus and the grating subtended angle is fixed, constantly maintaining the efficiency behavior of the system. Microscopy applications need to achieve focus at fixed entrance and exit arms, therefore SGM are made up of a preliminary plane mirror before the spherical grating between the entrance and exit slit in order to change the subtended angle and avoid defocusing [14]. The configuration presents some limitations given by the fact that optimum efficiency is reached at one wavelength for each grating, and as for the standard SGM it has the problems of a limited tuning range per grating. Plane grating monochromators (PGM) require a more complex optical design, i.e., the use of one or more additional mirrors [15; 16]. The resolving power decreases in a slower way with the increasing energy with respect to the SGM, that is proportional to E\({}^{1/2}\). Moreover, the subtended angle falls rapidly as the photon energy decreases, which is a required condition for maximizing the efficiency and obtaining a wide tuning of the subtended angles. Different solutions have been adopted from the original SX700 system proposed by [PERSON] which performs subtended-angle control and exit-slit focusing by means of, respectively, a plane mirror placed before and a focusing mirror (ideally elliptical) placed after a constant line-space (CLS) plane grating [17]. Some of them are--a CLS grating plus a rotating concave (spherical) mirror [18], a variable line-space (VLS) grating plus a fixed concave mirror [19], and a VLS grating plus a rotating-translating plane mirror [20]. The requirement of VLS gratings or elliptical mirrors, for which parameters have to be specifically conceived for the application, make these layouts unfeasible with standard optics. In this paper, we demonstrate the use of an optical configuration which originates from the variable-line-spaced (VLS) grating monochromator, that uses a plane VLS grating illuminated by the light converging from a concave focusing mirror and diffracts the radiation toward the exit slit. Even if only two optical elements are required, it uses a VLS grating--for which parameters have to be specifically designed to keep the spatial and spectral focus fixed on the slit plane and to perform high-order aberrations correction at a specific wavelength--therefore, it is a very expensive component. In order to obtain a cost-effective design, the configuration has been modified for use with standard plane gratings, i.e., a plane grating is illuminated by the light converging from a focusing mirror.