Deconvolution in EELS
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In order to improve the energy resolution of EEL spectrum, before spectrum deconvolution, scripts (e.g. applied in Gatan Digital Micrograph) can be used to automatically acquire and store each spectrum separately, and then to evaluate and correct the energy drift in each acquisition. [1, 2] After the drift correction, the EEL spectrum can be deconvoluted using software. For instance, some deconvolution techniques are Fourier ratio method, maximum-entropy (ME) [3,4] and Richardson–Lucy (RL) algorithms [5]. In the Fourier ratio method, the "ideal" core-loss spectrum is obtained by inverse Fourier transform. Since the Fourier ratio deconvolution is a high-frequency enhancement technique, high-frequency noise in the core-loss spectrum is substantially amplified. The ME and RL algorithms estimate a predicted spectrum by convoluting it with an observed low-loss spectrum, and thus they are not so significantly affected by high-frequency noise as compared with the Fourier ratio deconvolution technique.

For thick TEM specimens, an incident electron that has undergone inner-shell scattering can also cause outer-shell excitation with very high probability. This mixed inelastic scatterings is the sum of both inner-shell and outer-shell scatterings, resulting in a mixed energy loss and a peak broadening (plasmon behavior) above the ionization threshold. If necessary, this outer-shell scattering intensity can be removed from the spectrum by deconvolution.

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. The deconvolution procedures then are:
        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.

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. 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.

The low loss region in Figure 3936 shows the overlap between Fe-M edge and Li-K edge in an EEL spectrum taken from discharged FeOF materials in a Li-ion battery. The extracted Li-K edge was obtained by deconvolution technique.

EEL spectrum taken from discharged FeOF materials in a Li-ion battery

Figure 3936. EEL spectrum taken from discharged FeOF materials in a Li-ion battery. Adapted from [6]





[1] Kimoto K and Matsui Y (2002) Software techniques for EELS to realize about 0.3 eV energy resolution using 300 kV FEG-TEM. J. Microsc. 208: 224–228. 
[2] Koji Kimoto, Kazuo Ishizuka, Teruyasu Mizoguchi, Isao Tanaka and Yoshio Matsui, The study of Al-L23 ELNES with resolution-enhancement software and first-principles calculation, Journal of Electron Microscopy 52(3): 299–303 (2003).
[3] Kuzuo R and Tanaka M (1993) Resolution enhancement of electron energy-loss spectra using the maximum entropy method. J. Electron Microsc. 42: 240–243.
[4] Overwijk M H F and Reefman D (2000) Maximum-entropy deconvolution applied to electron energy-loss spectroscopy. Micron 31: 325–331. 
[5] Gloter A, Douiri A, Tencé M, Imhoff D, and Colliex C (2002) Improving energy resolution of EELS spectra: an alternative to the monochromator solution. In: Proc. of 15th ICEM, Durban, South Africa, pp. 141–142. 
[6] F. Cosandey, Analysis of Li-Ion Battery Materials by Electron Energy Loss Spectroscopy, Microscopy: Science, Technology, Applications and Education, A. Méndez-Vilas and J. Díaz (Eds.), 1662, (2010).