Areal Density, N, is the number of atoms per unit area of the TEM sample through the electron beam. It has been proposed to extract the Areal Density in different ways:
i) Based on Partial CrossSection theory.
In this way, by assuming that the probability of combined plasmon–coreloss multiple excitations included within the coreloss energy window Δ is the same as the fraction that falls within the lowloss integration window of equal width Δ, then the Areal Density, N, can be obtained by, [1,2]
 [950a]
 [950b]
where,
 the corresponding SSD (singlescatter distribution) intensity. However, in practice, the quantity of the SSD is often unavailable.
I_{0}  the zeroloss intensity,
n  the number of atoms per unit volume of the sample, or socalled the concentration of the element,
t  the sample thickness,
σ_{K}(β,Δ)  the partial crosssection of Kshell, E_{K} after background removal. This can be determined by theoretical calculation (e.g. with hydrogenic or Hartree–Slater models) or experimental measurement.
I_{K}(β,Δ)  the electron signal recorded, by an EELS spectrometer system with entrance semiangle β, from Kshell losses between E_{K} and E_{K} + Δ (from the energy window Δ),
I_{1}(β,Δ)  the corresponding lowloss intensity, namely the plamon signal recorded under the same conditions (from the same energy window with an energy loss range of 0 and Δ, which includes the entire zeroloss peak), which corrects the effects of plural scattering.
Note that, to evaluate the concentration using Equation 950b, the absolute thickness t has to be determined.
ii) Based on zeroloss peak. [2]
In this method, the coreloss
signal can be used to quantify elemental concentrations, after removal of the background contribution and
possible deconvolution of plural scattering,
 [950c]
where,
I_{0}(β,Δ)  the zeroloss integral intensity.
This method is based on the approximation that the probability of electrons, entering the anglelimiting aperture is the same for both elastic and inelastic scattering processes. However, this assumption is inaccurate in most cases since their scattering probabilities dependence on many factors such as TEM sample thickness and atomic numbers of the materials.
[1] R. F. Egerton, Kshell ionization crosssections for use in microanalysis, 4(2), (1979) 169179.
[2] P.J. Thomas and P.A. Midgley, An introduction to energyfiltered transmission electron microscopy, Topics in Catalysis, 21 (4), (2002), 109.
