Limits of spatial and compositional resolution of electron energy loss spectroscopy of soft materials

We investigate the spatial resolution limit of low electron energy loss spectroscopy (EELS) for imaging of electron beam sensitive materials, particularly for the case of composite materials that undergo phase separation. In order to make optimum use of the information contained in noisy spectra we modify the multiple least squares (MLS) fitting algorithm, which is widely used for fitting experimental spectra with a linear combination of reference spectra. Our approach, which uses the iteratively reweighted least squares (IRLS) routine, allows one to accommodate the non-constant variance in the noise. Assuming that the noise has a Poisson distribution we examine the performance of IRLS fitting. We introduce a parameter that reflects the difference between the spectra of the material components and computationally examine the relation between this parameter and the accuracy of the fitting algorithm. Use of this parameter allows us to derive an equation that relates the spatial resolution of imaging and the achievable level of composition uncertainty, for an ideal detector, based on the experimental parameters. These parameters include not only irradiation exposure, the difference between the spectra and the thickness of the sample but also the composition of the sample. The results presented will guide the proper choice of experimental conditions to obtain the best quality data from radiation sensitive materials.