Spatial characterization of light beams analyzed by cylindrical-grating slit-less spectrometers

In this work, we theoretically analyze the spatial information provided by cylindrical-grating slit-less spectrometers. We raise attention on the often not considered property that the spatial features acquired using these spectrometers are different from what can be obtained using a spectrometer with an entrance slit. In relation to this, we also highlight that they do not provide information directly on the real spatial beam profile. It is important to consider this fact in spatio-spectral analysis of extreme ultraviolet radiation, often carried out using cylindrical-grating slit-less spectrometers. Since the models used are based on the Fresnel diffraction integral and ideal optical systems, the results are valid also for other spectral regions.