The electron energy loss (EEL) spectrum (EELS spectrum is redundant) can be roughly split into two different regions: the low-loss spectrum (up until about 50 eV in energy loss) and the high-loss spectrum. The low-loss spectrum contains the zero-loss peak (signal from all the electrons which did not lose measurable energy) as well as the
phonon and
plasmon peaks, and contains information about the band structure and dielectric properties of the sample. It is also possible to resolve the energy spectrum in momentum to directly measure the band structure. The high-loss spectrum contains the ionisation edges that arise due to inner
shell ionisations in the sample. These are characteristic to the species present in the sample, and as such can be used to obtain accurate information about the chemistry of a sample. Typically, EEL spectra are susceptible to noise, especially for measurements of beam sensitive materials, such as polymers or biological specimen, requiring limited acquisition times. The two major noise contributions are
Poisson noise arising from the quantized nature of the beam electrons and
Gaussian distributed detector noise. As EEL spectra are usually measured on
CCD or direct electron detectors, where multiple pixels of a pixel-column are summed to create a spectrum out of a 2D pixel array, the noise statistics of such spectra is altered compared to regular 2D images. Due to the image formation process, especially on scintillation-based CCD detectors, the Poisson noise is also heavily correlated by the detector. Due to the energy distribution of the
electron gun, typically a Schottky-type or cold
field emission gun, and the
point spread function of the
detector, all measurements conducted in EELS appear
convolved with both of the above-mentioned distributions. Without a specimen in the beam path, these blur contributions can be measured in EELS as the vacuum zero-loss peak. Since all features in an EEL spectrum of a specimen are measured with this vacuum zero-loss peak, its distribution is also observable in all features of the spectrum, limiting the energy resolution. Therefore,
deconvolution has become a standard post-processing procedure in order to reduce the effect and sharpen the spectrum. Typical techniqes employed in EELS are the Fourier-ratio method and the
Richardson-Lucy deconvolution algorithm (RLA), It is hence essential to include a suitable noise statistic into the deconvolution algorithm to recover as many higher frequencies as possible. Since the RLA is derived from the pure Poisson statistics, which only covers part of the real noise statistics faced in EELS, it is apparent that more recent deconvolution methods accounting for this have an edge over the older procedures in terms of accuracy of the reconstruction. ==Thickness measurements==