Single Scattering EELS Spectrum and its Signal Extraction
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For the single scattering spectrum, the overall intensity of the spectrum can be given by,
Equation 956a can be re-written to represent the spectrum as a power-law background and core-loss profile for each edge:
In EELS measurements, the single scattering spectrum can be approximately given by, 
The step-function in Equations 956d and 956e is introduced to simplify the (weak) angular dependence of the oscillator strength on scattering angle.
Then, the single scattering
into an aperture of semi-angle β can be given by,
The EELS signal from single scattering can be modeled using Poisson Distribution.
 C. Colliex, V. E. Cosslett, R.D.Leapman, P.Trebbia, Contribution of electron energy loss spectroscopy to the development of analytical electron microscopy, 1 (3–4), (1976), 301-315.