Retrieval of the single loss spectrum with Johnson-Spence method
A method using fourier transform and logarithm for the retrieval of the single scattering electron energy loss spectrum from the experimental multiple data has been described and used previously. However, the uniqueness of this method is proved only under an additional assumption that no energy gain processes occur as the incident electron pass through the specimen. This proof is adopted in the later review papers. In this paper we prove the uniqueness without such an assumption, although in comparison with the energy loss processes, the energy gain processes usually have negligible differential cross sections, provided the relaxation times for the excitation inside the specimen are short enough with respect to the amount of energy loss. Also we shall compare deconvolution methods for the low loss region.