An edge is a small step on a big slope. Everything in quantification is about subtracting the slope without touching the step.
Load a core-loss spectrum (and the low-loss spectrum that goes with it) or start from the synthetic pair, fit the power-law background before each edge, integrate the edge over its window, compute the hydrogenic K-shell partial cross-section for your collection angle and window, take the plural scattering out by Fourier-ratio deconvolution or fold it into the cross-section instead, and read the areal density of each element and their ratio.
Text files with two columns (energy loss in eV, counts) or an EMSA/MSA file; one column is read with the dispersion and offset below. Lines starting with # are skipped.
I0 is the integral of the low-loss spectrum. Without a low-loss spectrum only ratios between edges are available, or enter I0 directly: (counts × eV, the same units as the spectrum integral).
The hydrogenic model covers K edges (Li to Zn). For an L23 or M45 edge enter the partial cross-section for the same β and Δ from Egerton's SIGMAL, a Hartree-Slater table or a standard; the background fit, integration and deconvolution still apply.
The areal density of an element from its core-loss edge is N = Ik(β,Δ) / [I0(β,Δ) σk(β,Δ)]: the edge counts above background in a window Δ beyond the threshold, divided by the low-loss counts collected with the same aperture and by the partial cross-section for that aperture and window. Each of the three factors has its own procedure, and the page performs them in order. The background before the edge is fitted as A E−r by least squares in log-log coordinates over the window you choose and extrapolated under the edge; the edge is integrated by the trapezoidal rule over Δ after subtraction; the cross-section is computed from the hydrogenic generalised oscillator strength of the K shell with the screening constant 0.3125 that Egerton's SIGMAK uses, integrated over scattering angle up to β and over energy loss across Δ, with the relativistic kinematics of the beam. The hydrogenic model was checked against the exact hydrogen threshold, the continuum oscillator-strength sum rule and the Bethe total cross-section before it was used here.
A specimen more than a few tens of nanometres thick redistributes the edge intensity by plasmon scattering after the core loss, so the counts inside Δ fall below the single-scattering value and the fine structure smears. Two remedies are offered. Fourier-ratio deconvolution divides the Fourier transform of the core-loss spectrum by that of the low-loss spectrum and reconvolves with a Gaussian of the zero-loss width, which returns the single-scattering distribution and its window integral; the alternative keeps the measured spectrum and instead convolves the cross-section with the low-loss spectrum to give an effective σ* that already contains the plural scattering, as Egerton describes. On the synthetic pair both routes recover the areal density that was put in. With two edges the ratio NA/NB needs neither I0 nor an absolute scale, only the two cross-sections.
Choose the pre-edge fit window in a region free of other edges, as wide as the background allows (Egerton's guidance is a window of roughly 30 percent of the edge energy ending just before the threshold) and check that the extrapolated background follows the spectrum before the edge and does not cross it after; the exponent r is reported and should lie between about 2 and 5. Keep Δ the same for the edge and the cross-section, avoid windows that reach into the next edge, and use a low-loss spectrum recorded under the same conditions, with the same dispersion, in which the zero-loss peak is not saturated. For the ratio of two edges the same Δ for both reduces the sensitivity to the cross-section model.
The cross-sections are hydrogenic, valid for K edges and, with the published corrections, within about 10 to 20 percent of Hartree-Slater values; the fine structure at the threshold and the white lines of transition-metal L edges are not in the model, which is why the L and M cross-sections must be supplied. The background model is the power law; where the pre-edge region contains the tail of another edge or the plasmon multiples of a thick specimen, a power law fails and a two-window or polynomial fit outside this page is needed. The convergence angle is not included: for a probe with a convergence comparable to β the effective collection angle differs and Egerton's correction applies. Deconvolution amplifies noise at high frequencies; the reconvolution width sets that trade-off, and the page uses the zero-loss width unless another is entered.
@misc{tripathy2026eelscorelossquantification,
author = {Tripathy, Manisha},
title = {EELS Core-Loss Quantification},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/eels-core-loss-quantification}},
note = {Interactive web tool}
}