Practical Electron Microscopy and Database

As discussed on page4360, the energy-loss process of incident electrons can be treated by the dielectric response of the electrons. Therefore, the EELS contains information about the dielectric constant ε. The single-scattering spectrum intensity I is given by,
          I = I₀(t/k)Im(-1/ε)ln[1 + (β/θ_E)²] --------------------------------- [4290]
where,
          I₀ -- The intensity in the zero-loss peak.
          t -- The specimen thickness.
          k – A constant incorporating the electron momentum and Bohr radius.

Kramers-Kronig analysis is normally used to obtain the real part of the dielectric constant from the imaginary part (Im) in Equation 4290. In such evaluation, deconvolution has to be performed because a single-scattering spectrum is needed. The low-energy plasmon part of the energy-loss spectrum to ~25 eV corresponds to an optical analysis of the dielectric response from the visible to the ultraviolet.