Electron microscopy
Fourier-Ratio Method for EELS Deconvolution
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In general, if the TEM specimen is too thick (t/λ > 0.4), a deconvolution process must be employed to remove the effect of plural scattering, since the increase of plural scattering intensity in the higher energy region of an ionization edge can cause some artifacts:
        i) Mask the fine structure;
        ii) Make the background signal on subsequent edges deviate significantly from the power law model.

In this case, in order to deconvolute the core-loss spectrum, the Fourier-ratio method is applied. In this method, simply speaking, a spectrum is first background-subtracted by fitting the pre-edge backgrounds with the power-law function and then deconvoluted by the Fourier-ratio method. The deconvolution procedure is then:
        i) Collect both the low- and core-loss spectra from the same region of the specimen under the same conditions (including eV/change, convergence and collection semiangles).
        ii) Isolate the edge of interest and remove the background intensity.
        iii) Fourier-transfer the low-loss spectrum and background-subtracted edge.
        iv) Divide the core-loss spectrum Fourier transform by the low-loss Fourier transform.
        v) Inverse the Fourier transform to yield the desired deconvolved spectrum.

In the Fourier-ratio method, the core-loss intensity that has been redistributed to higher energy-loss by plural inelastic scattering has been brought back into the signal integration window Δ by deconvolution, Ic(β, Δ), is equivalent to ItI1c(β, Δ)/I0. [2] Here, I1c is its single scattering component. Such had been done with a program in FORTRAN. [1]

Different from Fourier-log method, Fourier-ratio method is normally used when only limited spectral data is available. However, in most cases, recording low-loss and core-loss spectra under the same conditions is extremely challenging, since the acquisiton time required for a good SNR (signal to noise ratio) in the core-loss spectrum is usually not short enough to avoid saturation of the signal from the ZLP (zero-loss peak). Therefore, in practice, it is necessary to sacrifice the SNR in the core-loss signal, or utilize a spectrometer system that has an ultrafast electrostatic shutter installed.










[1] Kaikee Wong and R.F. Egerton, Correction for the effects of elastic scattering in core-loss quantification, Journal of Microscopy, Vol. 178, Pt 3, June 1995, pp. 198-207.
[2] R.F. Egerton and Kaikee Wong, Some practical consequences of the Lorentzian angular distribution of inelastic scattering, Ultramicroscopy 59 (1995) 169-180.