Comparison of time-of-flight with MIEZE spectroscopy of H$_2$O: Necessity to go beyond the spin-echo approximation

Here, we discuss the comparability of data acquisitioned with the Modulation of IntEnsity with Zero Effort data, a neutron spin-echo (NSE) technique to neutron Time-of-Flight (ToF) spectroscopy data. As a NSE technique MIEZE records the intermediate scattering function $\mathcal{I}(Q, \tau)$ making it necessary to perform a Fourier transform to directly compare it to $S(Q, E)$, measured by ToF spectroscopy. Transforming either data set into the complementary parameter space requires detailed knowledge of detector efficiency, instrumental resolution, and background. We discuss these aspects by comparing measurements on pure water performed on the spectrometers RESEDA and TOFTOF under the same experimental conditions. Additionally, we discuss the data evaluation of spin-echo data beyond the SE approximation, which limits these techniques to small energy transfers. Furthermore, computational methods like molecular dynamics simulations are essential for understanding these processes and will become increasingly important as we study more complex systems.