## 1 Introduction  
X-ray absorption spectroscopy (XAS) is a common method for characterizing materials in a variety of fields due to its fundamental simplicity, flexibility and element-specificity. Tuning to absorption edges allows probing the unoccupied electronic states localized around specific elements. Although experimentally more challenging, this information content is especially high at the absorption edges in the soft X-ray regime [1], since core hole lifetimes are longer and spectral features sharper than at higher photon energies. In a pump-probe experiment with sufficiently short pulses, e.g., in free electron lasers (FELs), transient XAS can be used to track changes of the electronic structure during chemical reactions and phase transitions on the femtosecond (fs) to picosecond (ps) scale [2; 3; 4]. XAS measures the spectral absorption coefficient, i.e., the imaginary part of the index of refraction. Measurements in specular reflectivity additionally measure the real part of the refractive index, which is rigorously connected with the imaginary part, through the Kramers-Kronig transform [5]. Thus, the same spectroscopic information is transported [6]. The most straightforward method of measuring XAS is in transmission by monitoring the intensity of an incident and the transmitted monochromatic beam as a function of photon energy. However, short absorption lengths in the soft X-ray regime necessitate sub-\(\upmu\)m thin samples, which can be a prohibitive limitation in terms of properties and manufacturability of the sample. Therefore, XAS is often performed indirectly, by observing either electron yield or drain current resulting from the photoelectric effect or the fluorescence yield. Each of these methods has advantages and disadvantages. Broadly speaking, electron-based methods constitute a powerful approach but limit the obtained information to the surface region and suffer from space-charge and capacitance effects when implemented with intense pulsed sources. Fluorescence based methods are free of such charge effects but struggle from low signal levels in the soft X-ray regime, as the Auger process is dominant and suppresses radiative decay. Furthermore, additional selection rules constraining fluorescent decay as well as competing fluorescence channels can lead to deviations in the spectra that can only be fully interpreted and disentangled [7; 8; 9] after spectral analysis of the isotropically emitted fluorescence from the sample, using a spectrometer. As in the soft X-ray regime, spectrometers operate with gratings at grazing incidence angles, such spectrometers exhibit small solid acceptance angles, strongly reducing the overall detected signal. Therefore, although a multitude of these methods are applied with great success at synchrotron sources, performing XAS studies at FEL facilities [2; 10; 11] remains challenging. Another challenge particular to FELs, is the stochastic nature of radiation from the self-amplified spontaneous emission (SASE) process on which most FELs rely (except those that implement seeding). The X-ray pulses produced by the SASE process exhibit a number of Fourier-limited modes of random intensity, which are randomly distributed within overall pulse durations typically on the order of 50 fs and a spectral bandwidth of typically 0.5-1% [12]. Using a monochromator to gain higher spectral resolution enhances the strong intensity fluctuations of the resulting beam and discards a significant part of the incoming flux. For XAS measurements, this means that the incident flux cannot be approximated as constant, but must be measured with the same fidelity, sensitivity and dynamic range as the signal. Furthermore, monochromators can significantly elongate the FEL pulse duration due to grating induced pulse-front tilting, which scales with the number of illuminated grating lines and is thus especially severe (up to a picosecond) at very high spectral resolutions.