An applied noise model for low-loss EELS maps

Electron energy-loss spectroscopy (EELS) performed in a scanning transmission electron microscope (STEM) is susceptible to noise, just like every other measurement. EELS measurements are also affected by signal blurring, related to the energy distribution of the electron beam and the detector point spread function (PSF). Moreover, the signal blurring caused by the detector introduces correlation effects, which smooth the noise. A general understanding of the noise is essential for evaluating the quality of measurements or for designing more effective post-processing techniques such as deconvolution, which especially in the context of EELS is a common practice to enhance signals. Therefore, we offer theoretical insight into the noise smoothing by convolution and characterize the resulting noise correlations by Pearson coefficients. Additional effects play a role in EELS mapping, where multiple spectra are acquired sequentially at various specimen positions. These three-dimensional datasets are affected by energy drifts of the electron beam, causing spectra to shift relative to each other, and by beam current deviations, which alter their relative proportion. We investigate several energy alignment techniques to correct energy drifts on a sub-channel level and describe the intensity normalization necessary to correct for beam current deviations. Both procedures affect noises and uncertainties of the measurement to various degrees. In this paper, we mathematically derive an applied noise model for EELS measurements, which is straightforward to use. Therefore, we provide the necessary methods to determine the most important noise parameters of the EELS detector enabling users to adapt the model. In summary, we aim to provide a comprehensive understanding of the noises faced in EELS and offer the necessary tools to apply this knowledge in practice.